text
stringlengths 9
2.4k
|
|---|
That same year, Fulton was appointed coroner in Rapides Parish by territorial Governor William C.C. Claiborne. Alexandria was incorporated as a town in 1818 and received a city charter in 1832.
In 1942, Alexandria was the site of the Lee Street Riot, an incident of racial violence that occurred between mostly civilians and military police. Witnesses state that as many as 20 people may have been killed, however the official report indicates that 3 soldiers were critically injured, and does not mention any deaths.
Geography and climate.
According to the United States Census Bureau, the city has a total area of , of which 26.4 square miles (68.4 km2) is land and 0.6 square mile (1.5 km2) (2.15%) is water.
Alexandria is on a level plain in the center of the Louisiana Longleaf Pine forests, in which pine is interspersed with various hardwoods. A number of small bayous, such as Bayou Rapides, Bayou Robert, and Hynson Bayou, meander throughout the city. In the immediate vicinity of the city, cotton, sugar, alfalfa, and garden vegetables are cultivated.
|
The climate is humid subtropical with some continental influence in the winter. Summers are consistently hot and humid, whereas winters are mild, with occasional cold snaps. On average, the first freeze occurs in early to mid November and the last freeze occurs in early to mid March. The area receives plentiful rainfall year-round, with thunderstorms possible throughout the year. Some storms can be severe, especially during the spring months. According to 'Cities Ranked and Rated' (Bert Sperling and Peter Sander), Alexandria reports an average of 69 days per year with thunder reported, which is nearly double the national average. Snowfall is rare, with measurable snow having occurred 27 times since 1895. The heaviest snowfall event took place February 12–13, 1960, when 9.1" of snow fell.
Tropical storms and hurricanes affect Alexandria from time to time, but rarely cause severe damage, unlike areas closer to the coast. In September 2005, Hurricane Rita moved inland and affected Alexandria and surrounding areas, causing widespread power outages and damaging the roofs of some structures. The most recent hurricane, Gustav in 2008, caused widespread flooding, knocked over trees and power lines leading to power outages, and damaged structures. Some low-lying Alexandria neighborhoods had substantial flooding from Gustav, leaving several feet of water in houses.
|
Demographics.
2020 census.
As of the 2020 United States census, there were 45,275 people, 17,920 households, and 10,933 families residing in the city.
2010 census.
As of the census of 2010, there were 47,723 people, 17,816 households, and 11,722 families residing in the city. The population density was 1,754.6/sq mi (677.5/km2). There were 19,806 housing units at an average density of . The racial makeup of the city was 38.32% White, 57.25% Black, 1.25% Native American, 1.85% Asian, 0.14% Pacific Islander, 1.03% from other races, and 1.09% from two or more races. 6.98% of the population were Hispanic or Latino of any race.
There were 17,816 households, out of which 31.9% had children under the age of 18 living with them, 38.5% were married couples living together, 23.2% had a female householder with no husband present, and 34.2% were non-families. 30.4% of all households were made up of individuals, and 12.1% had someone living alone who was 65 years of age or older. The average household size was 2.50 and the average family size was 3.13.
|
In the city, the population was spread out, with 28.1% under the age of 18, 9.2% from 18 to 24, 26.2% from 25 to 44, 21.4% from 45 to 64, and 15.1% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 83.5 males. For every 100 females age 18 and over, there were 77.7 males.
The median income for a household in the city was $26,097, and the median income for a family was $31,978. Males had a median income of $29,456 versus $20,154 for females. The per capita income for the city was $16,242. About 23.2% of families and 27.4% of the population were below the poverty line, including 37.7% of those under age 18 and 18.5% of those age 65 or over.
Religion.
Like many other southern cities, the largest single church denomination in the Alexandria area is Southern Baptist. Large congregations include the Emmanuel Baptist Church and Calvary Baptist Church. Alexandria is the headquarters of the Louisiana Baptist Convention. Alexandria also has a significant number of Methodists, Presbyterians, Episcopalians, and Pentecostals.
|
A significant Catholic population is also present, a result of the large Catholic Acadian French population which resides in and around Alexandria, many from neighboring Avoyelles Parish. Alexandria is the headquarters for the Diocese of Alexandria.
Alexandria has a small, though active Jewish community which dates back to the mid-19th century. Jews have held positions in local government, civic organizations, education, and medicine. At one time, many large businesses in the downtown were Jewish-owned. The Jewish community in Alexandria maintains two synagogues, which are approximately two blocks apart: Congregation Gemiluth Chassodim (Reform) and B'nai Israel Traditional Synagogue (Conservative).
Annual cultural events and festivals.
Mardi Gras.
Though Alexandria is north of the Cajun cultural area, the city recognizes Mardi Gras as an official holiday. The annual Mardi Gras Krewes Parade – occurring on the Sunday before Mardi Gras – on Texas Avenue is a major cultural festivity in the area. It is featured as a family-oriented event, and parade goers can enjoy over 20 New Orleans style floats, high school and college marching bands, as well as appearances by local celebrities. In addition to the main Sunday parade, the College Cheerleaders & Classic Cars Parade, which was established in 2008, takes place downtown on the Friday before Mardi Gras, the Children's Parade takes place downtown on the Saturday before Mardi Gras, and the Krewe of Provine Parade is held on Fat Tuesday, processing along Coliseum Boulevard. All the events are organized by the Alexandria Mardi Gras Association (AMGA). The Krewe Parade can attract from 120,000 to 150,000; the Children's parade, up to 40,000 to 50,000, and the College Cheerleaders & Classic Cars, about 5,000 to 15,000 people.
|
Alex River Fête.
An annual three-day festival is held in downtown Alexandria around late April and early May. The festival, established in 2013, was created around a former successful stand-alone event, the Louisiana Dragon Boat Races. It features the race and other former stand-alone events such as Dinner on the Bricks and the ArtWalk (now Art Fête) along with various booth venues, food, and live music, as well as the Kids Fête and Classic Car Fête.
Alex Winter Fête.
An annual three day festival held in downtown Alexandria around early December. Launched in 2015, the festival first year drew about double the anticipated crowd of 15,000. The festival, like the Alex River Fête, feature booth venues, food, and live music but also features an ice rink. In January 2017, the Alex Winter Fête was voted Festival of the Year by the Louisiana Travel Promotion Association.
Former events.
Cenlabration.
Begun in the late 1980s, Cenlabration was one of the largest festivals in Central Louisiana (Cenla). The name comes from Central Louisiana ("LA") Celebration, and reflects local culture and heritage, as well as serving as a means of celebrating Labor Day as the end of summer.
|
As many as three stages support a particular type of music, including Cajun and zydeco, blues and jazz, and Country music. In addition there are arts and crafts booths for local artists to sell their wares. In the Children's Village, children can participate in arts and crafts, listen to storytellers, play games with clowns, or watch a play. The festival has plenty of carnival rides available as well. Cenlabration ends with a large fireworks display.
The festival ran for 20 years until cancellation due to finances. The city ended its annual support of $40,000 because of budget constraints.
RiverFest.
In 2002, representatives of local government, businesses, organizations, and community formed the nonprofit organization River Cities Cultural Alliance, Inc. to promote tourism and the arts through a celebration of Central Louisiana's diverse cultural heritage. The nonprofit served to organize and put on RiverFest: Heritage and Arts on the Red. More than ten thousand festival-goers attending the event.
RiverFest was held in downtown Alexandria and on the Alexandria and Pineville levees. The festival features the work of visual artists from across the South, food booths exemplifying southern cuisine, a variety of children's activities, three outdoor stages with a wide range of music, dance, and theatrical performances, and a literary component with readings and panel discussions by Louisiana authors and scholars.
|
RiverFest was canceled in 2007.
Que'in on the Red.
An annual barbecue festival launched in 2006, the festival was held on the levee near downtown Alexandria and was well known for its big-name entertainment. The event was cancelled in 2012 due to its high cost and the city deciding against continued support of $100,000 annually.
Museums.
The Alexandria Museum of Art was founded in 1977 and occupies an historic Rapides Bank Building on the banks of the Red River. The building was built c. 1898 and is listed on the National Register of Historic Places. The museum opened to the public in March 1998. In 1998, the Alexandria Museum of Art expanded and constructed its grand foyer and offices as an annex to the Rapides Bank Building. In 1999, the Alexandria Museum of Art was honored as an Outstanding Arts Organization in the Louisiana Governor's Arts Awards. In 2007, the Alexandria Museum of Art entered into a collaborative endeavor agreement with Louisiana State University of Alexandria (LSUA). The Alexandria Museum of Art now also serves as a downtown campus for LSUA classes, and is host to multidisciplinary community events, including concerts and recitals, lectures, yoga classes, Second Saturday Markets, and Museum Afterhours.
|
The Louisiana History Museum is located downtown on the bottom floor of the former library. A small facility, it showcases the history of all Louisiana, with emphasis on the central portion of the state, Rapides Parish, and Alexandria. Major exhibit areas concern Native Americans, Louisiana geography, politics, health care, farming, and the impact of war.
The T.R.E.E. House Children's Museum and Arna Bontemps African American Museum are located within the Cultural Arts District.
The Kent Plantation House in Alexandria, completed by 1800, was located on a Spanish land grant. It is the oldest standing structure in Central Louisiana, one of only two buildings in the city to survive the burning of 1864 by Union troops fleeing after having been defeated at the Battle of Mansfield in DeSoto Parish. The house has been moved from its original location but is still located on part of the first land grant. It is open for tours daily except Sundays at 9, 10, and 11 a.m. and 1, 2, and 3 p.m. The tour is led by costumed docents and includes the house furnished in period pieces, some belonging to the original family, and all nine outbuildings, including an 1840-50s sugar mill, blacksmith shop, barn, two slave cabins, open-hearth kitchen, and milk house.
|
Performing arts.
The performing arts are centered in the Alexandria Cultural Arts District in the downtown. Located within a few blocks of each other are three performance venues: Coughlin-Saunders Performing Arts Center, the Hearn Stage, and the Riverfront Amphitheater.
The Coughlin-Saunders Performing Arts Center is the home of the Rapides Symphony Orchestra, which has performed in Alexandria since 1968. The center hosts the Performing Arts Series of the Arts Council of Central Louisiana, the Red River Chorale (an auditioned community chorus), and presentations of numerous local theater groups. The land for the center was donated by "The Alexandria Town Talk" newspaper, owned by the Gannett Company of McLean, Virginia.
Businesswoman Jacqueline Seagall Caplan (1935–2016) was the president of the Arts Council of Central Louisiana and the chairman of the group's executive committee when the Coughlin-Saunders Performing Arts Center opened in 2004. She predicted that Coughlin-Saunders would in time "provide a place people can point to and say it's theirs. ... [Until now], we've never had a performing arts center where every type of performing art can come."
|
The Hearn Stage is a black box theater for smaller productions. The Arts Council provides day-to-day management of both the Coughlin-Saunders Center and the Hearn Stage.
The Riverfront Amphitheater hosts each April a "Jazz on the River" music festival, sponsored by the Arna Bontemps African American Museum. The Rapides Symphony holds an annual fall Pops concert in the amphitheater. In recent years, the amphitheater has welcomed musical guests in conjunction with the springtime Dragonboat Races sponsored by the Alexandria Museum of Art.
The spring and fall seasons also feature Downtown Rocks, a free outdoor concert series in nearby Fulton Park.
Sports.
Alexandria was home to the Alexandria Aces, a summer college league baseball team. The Aces were champions in various leagues in 1997, 1998, 2006, and 2007. They played their home games at Bringhurst Field. Due to lack of repairs on the stadium, combined with the aging of it caused interest in the team to drop, with much of the wooden stands being barricaded. The remaining games of the 2013 season were canceled in mid-July because of low attendance, which averaged fewer than two hundred per game. The stadium's office and clubhouse were destroyed by a fire in 2014 and were subsequently torn down. In 2017, it was decided that the stadium would become a green space, open to the public and welcome news to those concerned about the building's future. The scoreboard and outfield walls have been removed, but most of the stadium is still intact. In 1974, a Little League team from Alexandria won the Louisiana state championship.
|
Alexandria had a minor league ice hockey team, the Alexandria Warthogs. They played their home games at the Rapides Parish Coliseum.
A professional indoor football team, the Louisiana Rangers, played their home games at the Rapides Parish Coliseum. They played in the Central District of the Southern American Football League, and the Southern Conference of the National Indoor Football League (NIFL). The team was owned by a Lafayette business group before moving in 2003 to Beaumont, Texas.
Soccer has also become a growing interest in the area. The Crossroads Soccer Association has had multiple youth teams achieve success in various travel soccer leagues. One of the earliest teams to do so was the then- U-14 Crossroads Pride soccer team, winning the 2012 Louisiana Soccer Association State Cup.
Also run by Crossroads is Alexandria's first amateur soccer team, Central Louisiana FC (formerly called Pool Boys FC and Alexandria Pool Boys FC). They are a founding member of the Gulf Coast Premier League, playing their games at Johnny Downs Sports Complex and Louisiana Christian University's Wildcat Stadium in neighboring Pineville. Central Louisiana FC runs both men's and women's amateur teams, as well as a developmental team that competes in the GCL2, the Gulf Coast Premier League's second division.
|
Nearby is Bringhurst Golf Course, popularly known as "the nation's oldest par-three course." A full-scale renovation was completed in mid-2010. In addition to Bringhurst, named for the late industrialist R.W. Bringhurst, Alexandria is home to four other golf courses: Oak Wing, The Links on the Bayou, at LSUA, and Alexandria Golf and Country Club.
Alexandria was also home to the Cenla Derby Dames, a roller derby team that operates under the Women's Flat Track Derby Association. The Dames played their home games at the Rapides Parish Coliseum.
Media.
Newspapers.
Established March 17, 1883, "The Alexandria Town Talk" is a daily newspaper for Alexandria-Pineville and the thirteen parishes which comprise central Louisiana. The newspaper was owned by the family of the late Jane Wilson Smith and Joe D. Smith, Jr., until March 1996, when it was sold to Central Newspapers. In August 2000, the Gannett Company acquired the Central Newspapers properties, including "The Town Talk". The name of the paper on its inaugural issue was the "Alexandria Daily Town Talk". Although it has since been shorted to the current "The Town Talk", it is still frequently referred to by long-time residents as the "Daily Town Talk".
|
Television.
Alexandria is served by local television stations KALB-TV (NBC / CBS/ The CW), WNTZ (Fox), KLAX-TV (ABC), KLPA (PBS/LPB), and KBCA (Heroes & Icons). KALB is the oldest television station in central Louisiana.
Parks and outdoor attractions.
Alexandria Zoological Park.
The Alexandria Zoological Park is a zoo first opened to the public in 1926. Owned by the City of Alexandria and operated by the Division of Public Works, it is home to about 500 animals and includes an award-winning Louisiana Habitat exhibit. The zoo is accredited by the Association of Zoos and Aquariums (AZA) and takes part in about 20 Species Survival Plans (SSP) as part of its conservation efforts.
Cotile Lake Recreation Area.
Cotile Lake is a man-made impoundment located in the uplands approximately west-northwest of Alexandria, Louisiana. The lake is approximately in size and was completed in October 1965. The Louisiana Wild Life and Fisheries Commission stocked this impoundment with the proper species and number of game fish in 1965–66 shortly after its completion date. The recreational facilities include a large area cleared and zoned for swimming with complete bath house facilities nearby. There is a water skiing area that is cleared and snagged for safety of the skiers. The picnic and camping areas are modern and complete. There is also space available for campers.
|
Indian Creek Lake and Recreation Area.
Encompasses a lake, of developed recreation facilities and a primitive camping area all within the Alexander State Forest. The lake, located in central Louisiana, was constructed as a joint venture of the Louisiana Forestry Commission, the Rapides Parish Police Jury, and the Lower West Red River Soil and Water Conservation District as a reservoir for agricultural irrigation in times of need and for recreation purposes.
The recreation area camping area contains 109 campsites with conventional full utility hookups, 3 beaches for swimming, bath houses, a boat launch, and 75 picnic sites. A covered pavilion within the developed area provides for groups up to 100 people. The recreation area is open year-round and operates on user fees.
Kisatchie National Forest.
Alexandria sits in the middle of the Kisatchie National Forest. Ranger districts are north, northwest, west and southwest of the city. An abundance of large timberlands and forest nurseries, as well as lake and recreation areas, are within a short driving distance.
|
Military.
Louisiana National Guard.
Alexandria is home to both Headquarters and Company B of the 199th Brigade Support Battalion (BSB). The 199th BSB is the logistical component of the 256th Infantry Brigade that served in Operation Iraqi Freedom from October 2004 until September 2005. The 199th BSB provides supply and transportation (Company A), medical (Company C) and maintenance (Company B) support and services that keep the 256th Brigade operational. The battalion also has units located in Jonesboro, Winnfield, Colfax, and St. Martinville, Louisiana.
England Air Force Base.
Alexandria served as the home of England Air Force Base from its origins as an emergency airstrip for Esler Regional Airport until its closure. England AFB was officially closed on December 15, 1992, pursuant to the Defense Base Closure and Realignment Act (Public Law 101–510) and recommendations of the Defense Secretary's Commission on Base Realignment and Closure. The base now serves as Alexandria International Airport (see below).
Economy.
|
According to Census ACS 1-year survey for 2016, the per capita income of Alexandria was $23,962. This is $1,702 lower than the Louisiana average for per capita income in the same period. That figure is at $31,128 nationally. The Alexandria workforce consists of about 55,000 residents. Union Tank Car Company has recently located a plant northwest of Alexandria near the airport creating hundreds of jobs. Expansions at the Procter & Gamble plant and the construction of a PlastiPak plant in nearby Pineville have also created a number of new jobs for the area. Sundrop Fuels Inc., a Colorado-based biofuels start-up, plans to construct an over 1,200 acre plant just southwest of Alexandria in Rapides Station area. The facility will serve as the headquarters for the company because aside from the plant itself, Sundrop has also bought Cowboy Town, an abandon entertainment venue that sits inside the surrounding land that was purchased, to house their offices and their maintenance and fabrication operations.
In 2007, Inc. Magazine rated Alexandria as the 77th best place in which to conduct business out of the 393 U.S. cities ranked, a significant increase from its ranking as No. 276 in 2006. Among other Louisiana cities, Alexandria ranked second, following only Baton Rouge, which ranked 59th nationally.
|
Healthcare.
Alexandria is home to two major hospitals: Rapides Regional Medical Center, a former Baptist hospital is located downtown. Christus St. Frances Cabrini Hospital was opened in 1950 and is located at the corner of Masonic Drive and Texas Avenue. Both hospitals have undergone expansion.
Additionally, located just across the Red River in Pineville, the Veteran's Affairs Medical Center at Alexandria serves central Louisiana and surrounding areas.
Meanwhile, in 2013, the state allocated $15 million to move the medical services long provided at no or minimal charge at the Huey P. Long Medical Center in Pineville to the former hospital at England Park at the site of the closed England Air Force Base.
Port of Alexandria.
In the early 19th century, the Port of Alexandria brought goods to the area and shipped cotton and other local products to the rest of the country. A ferry connected the cities of Alexandria and Pineville until a bridge was built across the Red in 1900.
Today, Port facilities include: a 40-ton crane for off-loading, a warehouse, 13,600-ton bulk fertilizer warehouse, a 3,400-ton bulk fertilizer dome structure and a 5,000-ton dome which was added in January 2005.
|
The petroleum off-loading facility includes two tanks, one tank capable of handling two barges and five truck off-loading simultaneously. There is also a general cargo dock with access to rail and a hopper barge unloading dock with conveyor system.
Today's modern facilities and the Port's central location with its connection to the Mississippi River provide excellent opportunities for importers and exporters.
Alexandria International Airport.
Alexandria International Airport (AEX) is a regional airport, providing flights to Atlanta, Dallas/Ft. Worth, and Houston. In 2006 a new-state-of-the-art passenger terminal was dedicated. Alexandria is served by American and Delta.
Current military use.
Formerly known as England AFB until 1992, Alexandria International Airport additionally has numerous international charter airlines using the airport in the transport of military personnel attached to the United States Army base at Fort Johnson. A new military personnel terminal opened in 2007.
Government and politics.
Local government.
|
History.
Following the Civil War, all public records in Alexandria had been destroyed. On September 29, 1868, the city was granted a new charter with a government consisting of a Mayor, Treasurer, and Justice of the Peace. Nine aldermen represented the four wards of the city – two from each ward and one elected at-large.
In 1912, the Lawrason Act established Alexandria municipal government in a strong mayor format, where the mayor was also the Commissioner of Public Health and Safety (Police, Fire, Sanitation). There were separate Commissioners of Streets and Parks and Finance and Utilities, elected citywide. Those positions were discontinued in 1977.
Today.
Alexandria has a mayoral-council system of government. The Mayor serves as the executive branch of the local government.
The City Council serves as the legislative branch. The five districts of the city are represented on the council; in addition there are two council members elected to serve as at-large representatives of the city.
The Alexandria Court has a limited jurisdiction, consisting of the citizens of Wards 1, 2 and 8 in Rapides Parish. Within those boundaries the court has the power to hear and decide both criminal and civil cases, rule in civil cases and hand down judgment for punishment in criminal cases.
|
United States Congressional district.
From 1913 to 1993, Alexandria served as the seat of Louisiana's Eighth Congressional district. A Democratic seat, it was held by the Long family for nearly half of its existence, from 1953 to 1987, broken only by the two terms of Harold B. McSween and three terms of Republican Clyde Holloway of Forest Hill. The seat was removed after the 1990 census indicated Louisiana no longer had the population to support it. The district was split among the Fourth, Fifth and Sixth Congressional districts. Alexandria is now in the Fifth district and was represented from 2003 to 2013 by Rodney Alexander, a Democrat-turned-Republican. From November 2013 to January 2015 the representative is Vance McAllister of Ouachita Parish. Since March 2021, the Fifth has been represented by Julia Letlow of Start in Richland Parish.
Education.
Colleges and universities.
Situated south of the city, Louisiana State University at Alexandria (or LSUA) is a regional campus of the state's flagship university system, Louisiana State University. From its establishment in 1959, the campus offered only two-year degrees; students seeking baccalaureate degrees had to commute or move to the main campus in Baton Rouge in order to gain a four-year degree. After 1976, students could either commute or telecommute in order to attend upper-level courses, including graduate classes. In 2002, following approval by the Louisiana State University Board of Supervisors and the Louisiana Board of Regents the Louisiana Legislature passed legislation allowing LSUA to offer baccalaureate degrees.
|
A four-year degree is also attainable through Southern Baptist-affiliated Louisiana Christian University in Pineville, founded in 1906.
Two of Central Louisiana Technical Community College's campuses, including its main campus and administration, are located in Alexandria.
Primary and secondary schools.
Rapides Parish School Board operates public schools.
Alexandria has three public high schools: Bolton High School, Alexandria Senior High School, and Peabody Magnet High School. In addition, there are two private high schools: the Roman Catholic Holy Savior Menard Central High School, and Grace Christian.
Transportation.
Roads.
Alexandria serves as the crossroads of Louisiana. To reach either Shreveport or Monroe from the southern portion of the state, the easiest method of travel takes the driver through Alexandria. Likewise, if a visitor is to head from the northern portion of the state to the Cajun portions of the state (Lake Charles and Lafayette), or the greater metropolitan areas of either Baton Rouge or New Orleans, the easiest method of travel involves driving down Interstate 49 through Alexandria.
|
In addition to I-49, travelers can follow Louisiana 1 up to Alexandria from Baton Rouge and points south. Also, Highway 167 could be taken from Opelousas north to Ruston, crossing through Alexandria at one of the few bridges over the Red River in central Louisiana. Highways 165 and 71 also link Alexandria and points south with the northern and southern portions of the state via the Curtis-Coleman bridge.
There are talks about a 50-80 mile, 4 lane beltway to encircle Alexandria and Pineville, and an East-West Interstate (I14) connecting Natchez, MS and Jasper, TX called the Gulf Coast Strategic Highway. As of now, they are in the planning stages of development.
Bridges.
Three road bridges cross the Red River in the Alexandria area. They are:
Former bridges include:
There are two railroad bridges over the Red River in Alexandria. One is located near the Buhlow area north of the OK Allen bridge. The other is south of the Purple Heart Memorial Bridge.
Mass transit.
Regional mass transit is handled by ATRANS (Alexandria Transportation Authority).
|
For those leaving or arriving at the city by bus, Greyhound Lines has a terminal downtown.
Airports.
Alexandria is served by the Alexandria International Airport and the Esler Regional Airport in Pineville.
Rail.
Alexandria does not have Amtrak service, nor a commuter rail system. The Kansas City Southern ("Southern Belle") and the Missouri Pacific (since absorbed by Union Pacific) ("Louisiana Eagle" and "Louisiana Daylight") operated train stations in the area in the early part of the 20th century but passenger services ended in the 1960s and the stations have closed.
Surrounding cities and towns.
Rapides Parish
Grant Parish
|
Alexandria Troas
Alexandria Troas ("Alexandria of the Troad"; ; , "Old Istanbul") is the site of an ancient Greek city situated on the Aegean Sea near the northern tip of Turkey's western coast, the area known historically as Troad, a little south of Tenedos (modern Bozcaada). It is located southeast of modern Dalyan, a village in the Ezine district of Çanakkale Province. The site sprawls over an estimated ; among the few structures remaining today are a ruined bath, an odeon, a theatre, gymnasium complex and a recently uncovered stadion. The circuit of the old walls can still be traced.
History.
Hellenistic.
According to Strabo, this site was first called Sigia (Σιγία); around 306 BC Antigonus refounded the city as the much-expanded Antigonia Troas by settling the people of five other towns in Sigia, including the once influential city of Neandreia. It did not receive its name until its name was changed by Lysimachus to Alexandria Troas, in 301 BC, in memory of Alexander the Great of Macedon (Pliny merely states that the name changed from Antigonia to Alexandria). The city continued being called Alexandria Troas, as is stated in the 4th-5th c. AD Tabula Peutingeriana. As the chief port of north-west Asia Minor, the place prospered greatly in Roman times, becoming a "free and autonomous city" as early as 188 BC, and the existing remains sufficiently attest its former importance. In its heyday the city may have had a population of about 100,000. Strabo mentions that a Roman colony was created at the location in the reign of Augustus, named Colonia Alexandria Augusta Troas (called simply Troas during this period). Augustus, Hadrian and the rich grammarian Herodes Atticus contributed greatly to its embellishment; the aqueduct still preserved is due to the latter. Julius Caesar and Constantine considered making Troas the capital of the Roman Empire.
|
Roman.
In Roman times, it was a significant port for travelling between Anatolia and Europe. According to the account in the Acts of the Apostles, Paul of Tarsus sailed for Europe for the first time from Alexandria Troas and returned there from Europe (it was there that the episode of the raising of Eutychus occurred). Ignatius of Antioch also paused at this city before continuing to his martyrdom at Rome.
Byzantine.
Several of its later bishops are known: Marinus in 325; Niconius in 344; Sylvanus at the beginning of the 5th century; Pionius in 451; Leo in 787; Peter, friend of the Patriarch Ignatius, and adversary to Michael, in the ninth century. In the 10th century Troas is given as a suffragan of Cyzicus and distinct from the famous Troy (Heinrich Gelzer, "Ungedruckte ... Texte der Notitiae episcopatuum", 552; "Georgii Cyprii descriptio orbis romani", 64); it is not known when the city was destroyed and the diocese disappeared. The bishopric remains a titular see of the Catholic Church under the name Troas, vacant since 1971.
|
Troas is also a titular see of the Eastern Orthodox Church under the Ecumenical Patriarchate. Bishop Savas (Zembillas) of Troas served as hierarch from 2002 to 2011, and then became Metropolitan Savas (Zembillas) of Pittsburgh in the Greek Orthodox Archdiocese of America.
Ottoman.
Karasid Turkomans settled in the area of the Troad in the 14th century. Their "beylik" was conquered by the Ottomans in 1336. The ruins of Alexandria Troas came to be known among the Turks as "Eski Stambul", the "Old City". The site's stones were much plundered for building material (for example Mehmed IV took columns to adorn his Yeni Valide Mosque in Istanbul). As of the mid-18th century the site served as "a lurking place for bandetti".
Modern.
By 1911, the site had been overgrown with Vallonea oaks and much plundered, but the circuit of the old walls could still be traced, and in several places they were fairly well preserved.
They had a circumference of about ten kilometres, and were fortified with towers at regular intervals.
|
Remains of an ancient bath and gymnasium complex can be found within this area; this building is locally known as "Bal Saray" (Honey Palace) and was originally endowed by Herodes Atticus in the year 135. Trajan built an aqueduct which can still be traced.
The harbour had two large basins, now almost choked with sand.
It is the subject of an early twenty-first century study by German archaeologists digging and surveying at the site.
Their excavation uncovered the remains of a large stadium dating to about 100 BC.
|
Alexandria, West Dunbartonshire
Alexandria (, ) is a town in West Dunbartonshire, Scotland. The town is on the River Leven, north of Dumbarton and north-west of Glasgow.
Demographics.
In 2016, the estimated population of the town was 6,860. It is one of five towns in the Vale of Leven, the others being Balloch, Bonhill, Jamestown and Renton; their combined population is over 20,000.
Economy.
The town's traditional industries, most importantly cotton manufacturing, bleaching and printing, have been phased out. In the 1970s Alexandria was redeveloped, with a new town centre layout and traffic system. Local landmarks include Christie Park and the Category B listed Smollett Fountain in the town centre. Lomond Galleries on North Main Street is a former car factory with an impressive dome and an even more impressive marble entrance hall and staircase. It was originally built in 1906 as the Argyll Motor Works, for Argyll Motors Ltd. A carving above the entrance shows one of the company's cars. After the car production ceased in 1914, it was used by the Admiralty for the manufacture of torpedoes, which were test-fired in Loch Long, and in the early 1970s was the scene of the Plessey sit-in. The building now hosts a shopping mall but has retained many of its striking architectural features.
|
Major employers in the area were Westclox and Polaroid, both based in the Leven Industrial Estate; Aggreko based a major purpose-built factory in the estate from 2000 to 2010. The Ballantine's whisky distillery continues to operate in the estate.
Transport.
Alexandria sits on the former A82 main road between Glasgow and Loch Lomond. There are regular bus services on the route, and the town has a railway station on the rail line between Balloch and Glasgow Queen Street.
Alexandria is reputed to be the only town in the UK with a railway station, carnival (periodically Codona's travelling fair sets up in the car park) and a pub in the middle of a roundabout. A. J. Cronin's uncle owned a pub in Bridge Street. Alexandria Library is located on Gilmour Street.
Sport.
The town is home to Vale of Leven football club, who play at Millburn Park. The club was a dominant force in early Scottish football history, winning the Scottish Cup in 1877, 1878 and 1879, and were founder members of the Scottish Football League.
Gordon Reid, born in Alexandria, has won the Wimbledon Tennis Men's Wheelchair Doubles, with his partner Alfie Hewett, three times.
ROC Bunker.
Between 1961 and 1991, the village was the location of a Royal Observer Corps Master bunker, to be used in the event of a nuclear attack. It remains mostly intact.
|
Alexandria, Romania
Alexandria () is the capital city of the Teleorman County, Muntenia, Romania. It is located south-west of Bucharest, towards the Bulgarian border, and has over 40,000 inhabitants. The 44th parallel north passes just north of the city.
Geography.
Alexandria is situated in the middle of the Wallachian Plain, on the banks of the Vedea River. It is located in the central part of Teleorman County, at a distance of from Giurgiu and from Bucharest.
The city is traversed by the national road DN6, which links Bucharest to the Banat region in western Romania; the road is part of European route E70. The Alexandria train station serves the CFR Line 909, with service towards Roșiorii de Vede (to the northwest) and Zimnicea (to the south, on the Danube).
History.
Alexandria was named after its founder, Alexandru D. Ghica, Prince of Wallachia from April 1834 to 7 October 1842. Its population in 1900 was 1,675. Grain, which was Alexandria's main trade at the time, was dispatched both by rail to the Danubian port of Zimnicea and by river to Giurgiu.
|
In 1989, the city had over 63,000 inhabitants and more than six large factories. The 2021 census puts the population at 40,390.
Education.
There are four high schools in Alexandria: the Alexandru D. Ghica National College, the Alexandru Ioan Cuza Theoretical High School, the Mircea Scarlat National Pedagogical College and the Constantin Noica Theoretical High School.
In 1897, the Ștefan cel Mare School moved from its former location to 310 Libertății Street; a local entrepreneur, M. Frangulea, obtained the plot and hired renowned architect Alexandru Săvulescu to build the new boys' primary school for the city.
Religion.
The Diocese of Alexandria and Teleorman is a diocese of the Romanian Orthodox Church. Its see is in Alexandria and its ecclesiastical territory covers Teleorman County.
Sports.
CSM Alexandria is a football club founded in 1948; it plays in the Romanian Liga III. CS Universitatea Alexandria is a women's football club founded in 2012. Stadionul Municipal, which holds 5,000 people, is the home ground for both clubs; the stadium is currently undergoing reconstruction. The Alexandria women's basketball team plays in the Liga Națională.
|
Angela Vincent
Angela Vincent (born 1942) is a British neuroscientist who is emeritus professor at the University of Oxford and a Fellow of Somerville College, Oxford.
Career and research.
Angela Vincent was born in 1942, the third child of Carmen and Joseph Molony (later KCVO). After St Mary's Convent, Ascot, she studied medicine at King's College London and Westminster Hospital School of Medicine (now merged with Imperial College School of Medicine). After one year as a junior doctor at St Steven's and St Charles' hospitals in London (1966–1967), she obtained an MSc in biochemistry from University College London. In 1967 she married Philip Morse Vincent and they have four children.
After the MSc, she spent three frustrating years trying to fractionate rat brain synaptosomes, until she was taken on by Ricardo Miledi FRS in the biophysics department to work on acetylcholine receptors.
|
After the MSc, she spent three frustrating years trying to fractionate rat brain synaptosomes, until she was taken on by Ricardo Miledi FRS in the biophysics department to work on acetylcholine receptors. After his retirement in 1998, Vincent led the group until 2016. During this time she was head of the department of clinical neurology (2005–2008) at the University of Oxford, president of the International Society of Neuroimmunology (2001–2004), and an associate editor of "Brain" (2004–2013). Her research group was initially located in the Weatherall Institute of Molecular Medicine at the John Radcliffe Hospital, working on a wide range of biological disciplines encompassing molecular biology, biochemistry, cellular immunology and intracellular neurophysiology. The group's research focused on autoimmune and genetic disorders of the neuromuscular junction, peripheral nerves and more recently the exciting field of central nervous system diseases. The principal autoimmune diseases studied were myasthenia gravis, the Lambert–Eaton myasthenic syndrome, limbic encephalitis, other types of autoimmune encephalitis and acquired neuromyotonia.
|
Her contributions have been on the roles of antibodies directed against acetylcholine receptors and muscle specific kinase (MuSK) in myasthenia gravis, and glycine receptors or potassium channel-associated proteins LGI1, CASPR2 and Contactin-2 in CNS diseases.
She demonstrated that transfer of antibodies across the placenta from the pregnant woman to the fetus in utero can cause both acute and longer-term neuromuscular and neurodevelopmental abnormalities.
Since 2016 she has been emeritus Professor at Oxford University, emeritus Fellow of Somerville College, and holds an honorary appointment at UCL; she continues to work on neuromuscular disorders and advise young researchers. Her work in Oxford on brain disorders continues under Associate Professor Sarosh Irani and Dr Patrick Waters.
She is a strong supporter of Freedom from Torture (formerly The Medical Foundation for Treatment of Torture Victims) and a Patron of British Pugwash (that brings together scientists and others concerned with international affairs and disarmament).
|
Awards and honours.
In 2009, she presented the Leslie Oliver Oration at Queen's Hospital. In 2009, she received the medal of the Association of British Neurologists and in 2017, the World Federation of Neurology Scientific Contributions to Neurology award. In 2015, she was awarded the British Neuroscience Association Award for Outstanding Contribution to Neuroscience. In Cologne 2018, she was awarded with J Posner and J Dalmau, the International Prize for Translational Neuroscience of the Gertrud Reemtsma Foundation (formerly the Klaus Joachim Zülch Prize), and in Washington in 2019, the America Epilepsy Society Clinical Science Research Award (with J Dalmau). She received the Inaugural Distinguished Alumni Award, Imperial College, London, 2020 and the Life-time Award of the German Neurological Society (DGN) in 2021.
In 2002, she was elected a Fellow of the Academy of Medical Sciences (FMedSci) and in 2011, a Fellow of the Royal Society (FRS).
|
Arithmetic–geometric mean
In mathematics, the arithmetic–geometric mean (AGM or agM) of two positive real numbers and is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The arithmetic–geometric mean is used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some mathematical constants, in particular, computing.
The AGM is defined as the limit of the interdependent sequences formula_1 and formula_2. Assuming formula_3, we write:formula_4These two sequences converge to the same number, the arithmetic–geometric mean of and ; it is denoted by , or sometimes by or .
The arithmetic–geometric mean can be extended to complex numbers and, when the branches of the square root are allowed to be taken inconsistently, it is a multivalued function.
Example.
To find the arithmetic–geometric mean of and , iterate as follows:formula_5The first five iterations give the following values:
The number of digits in which and agree (underlined) approximately doubles with each iteration. The arithmetic–geometric mean of 24 and 6 is the common limit of these two sequences, which is approximately .
|
History.
The first algorithm based on this sequence pair appeared in the works of Lagrange. Its properties were further analyzed by Gauss.
Properties.
Both the geometric mean and arithmetic mean of two positive numbers and are between the two numbers. (They are "strictly" between when .) The geometric mean of two positive numbers is never greater than the arithmetic mean. So the geometric means are an increasing sequence ; the arithmetic means are a decreasing sequence ; and for any . These are strict inequalities if .
is thus a number between and ; it is also between the geometric and arithmetic mean of and .
If then .
There is an integral-form expression for :formula_6where is the complete elliptic integral of the first kind:formula_7Since the arithmetic–geometric process converges so quickly, it provides an efficient way to compute elliptic integrals, which are used, for example, in elliptic filter design.
The arithmetic–geometric mean is connected to the Jacobi theta function formula_8 byformula_9which upon setting formula_10 givesformula_11
|
Related concepts.
The reciprocal of the arithmetic–geometric mean of 1 and the square root of 2 is Gauss's constant.formula_12In 1799, Gauss proved thatformula_13where formula_14 is the lemniscate constant.
In 1941, formula_15 (and hence formula_16) was proved transcendental by Theodor Schneider. The set formula_17 is algebraically independent over formula_18, but the set formula_19 (where the prime denotes the derivative with respect to the second variable) is not algebraically independent over formula_18. In fact,formula_21The geometric–harmonic mean GH can be calculated using analogous sequences of geometric and harmonic means, and in fact .
The arithmetic–harmonic mean is equivalent to the geometric mean.
The arithmetic–geometric mean can be used to compute – among others – logarithms, complete and incomplete elliptic integrals of the first and second kind, and Jacobi elliptic functions.
Proof of existence.
The inequality of arithmetic and geometric means implies thatformula_22and thusformula_23that is, the sequence is nondecreasing and bounded above by the larger of and . By the monotone convergence theorem, the sequence is convergent, so there exists a such that:formula_24However, we can also see that:formula_25
|
and so:
formula_26
Q.E.D.
Proof of the integral-form expression.
This proof is given by Gauss.
Let
formula_27
Changing the variable of integration to formula_28, where
formula_29
formula_30
formula_31
formula_32
formula_33
This yields
formula_34
gives
formula_35
Thus, we have
formula_36
The last equality comes from observing that formula_37.
Finally, we obtain the desired result
formula_38
Applications.
The number "π".
According to the Gauss–Legendre algorithm,
formula_39
where
formula_40
with formula_41 and formula_42, which can be computed without loss of precision using
formula_43
Complete elliptic integral "K"(sin"α").
Taking formula_44 and formula_45 yields the AGM
formula_46
where is a complete elliptic integral of the first kind:
formula_47
That is to say that this quarter period may be efficiently computed through the AGM,
formula_48
Other applications.
Using this property of the AGM along with the ascending transformations of John Landen, Richard P. Brent suggested the first AGM algorithms for the fast evaluation of elementary transcendental functions (, , ). Subsequently, many authors went on to study the use of the AGM algorithms.
|
Akira Toriyama
was a Japanese manga artist and character designer. He came to be regarded as one of the most influential and important authors in the history of manga, authoring highly influential and popular series, particularly "Dragon Ball".
Toriyama first achieved mainstream recognition for creating the manga series "Dr. Slump", for which he earned the 1981 Shogakukan Manga Award for best "shōnen"/"shōjo". Dr. Slump went on to sell over 35 million copies in Japan. It was adapted into an anime, with a second series created in 1997, 13 years after the manga ended.
From 1984 to 1995 he wrote and illustrated the "Dragon Ball" manga, serialized in "Weekly Shōnen Jump". It became one of the best-selling manga series of all time, with 260 million copies sold worldwide, and is considered a key work in increasing manga circulation to its peak in the mid-1980s and mid-1990s. Overseas, "Dragon Ball"s anime adaptations have been more successful than the manga and similarly boosted anime's general popularity.
Beside his manga works, Toriyama acted as a character designer for several video games such as the "Dragon Quest" series, "Chrono Trigger", and "Blue Dragon".
|
In 2019, Toriyama was decorated a "Chevalier" of the French Ordre des Arts et des Lettres for his contributions to the arts. In October 2024, Toriyama was posthumously inducted into the Harvey Awards Hall of Fame.
Early life.
Akira Toriyama was born in the town of Kiyosu, Aichi Prefecture, Japan. He had a younger sister. Toriyama drew pictures since a young age, mainly of the animals and vehicles that he was fond of. He related being blown away after seeing "One Hundred and One Dalmatians" (1961), and said he was drawn deeper into the world of illustration by hoping to draw pictures that good. He was shocked again in elementary school when he saw the manga collection of a classmate's older brother, and again when he saw a television set for the first time at a neighbor's house. He cited Osamu Tezuka's "Astro Boy" (1952–1968) as the original source for his interest in manga. Toriyama recalled that when he was in elementary school all of his classmates drew imitating anime and manga, as a result of not having many forms of entertainment. He believed that he began to advance above everyone else when he started drawing pictures of his friends. Despite being engrossed with manga in elementary school, Toriyama said he took a break from it in middle school, probably because he became more interested in films and TV shows. When asked if he had any formative experiences with "tokusatsu" entertainment, Toriyama said he enjoyed the "Ultraman" TV show and "Gamera" series of "kaiju" films.
|
Toriyama said it was a "no-brainer" that he would attend a high school focused on creative design, but admitted he was more interested in having fun with friends. Although he still did not read much manga, he would draw one himself every once in a while. Despite his parents' strong opposition, Toriyama was confident about going into the work force upon graduation instead of continuing his education. He worked at an advertising agency in Nagoya designing posters for three years. Although Toriyama said he adapted to the job quickly, he admitted that he was often late because he was not a "morning person" and got reprimanded for dressing casually. Resenting the routine, he became sick of the environment and quit.
Career.
Early work and "Dr. Slump" (1978–1983).
|
"Dr. Slump", which was serialized in "Weekly Shōnen Jump" from 1980 to 1984, was a huge success and made Toriyama a household name. It follows the adventures of a perverted professor and his small but super-strong robot Arale. In 1981, "Dr. Slump" earned Toriyama the Shogakukan Manga Award for best "shōnen" or "shōjo" manga series of the year. An anime adaptation began airing that same year, during the prime time Wednesday 19:00 slot on Fuji TV. Adaptations of Toriyama's work would occupy this time slot continuously for 18 years—through "Dr. Slump"s original run, "Dragon Ball" and its two sequels, and finally a rebooted "Dr. Slump" concluding in 1999. By 2008, the "Dr. Slump" manga had sold over 35 million copies in Japan.
Although "Dr. Slump" was popular, Toriyama wanted to end the series within roughly six months of creating it, but publisher Shueisha would only allow him to do so if he agreed to start another serial for them shortly after. So he worked with Torishima on several one-shots for "Weekly Shōnen Jump" and the monthly "Fresh Jump". In 1981, Toriyama was one of ten artists selected to create a 45-page work for "Weekly Shōnen Jump"s Reader's Choice contest. His manga "Pola & Roid" took first place. Toriyama was selected to participate in the contest again in 1982 and submitted "Mad Matic". His one-shot "Pink" was published in the December issue of "Fresh Jump". Selected to participate in "Weekly Shōnen Jump"s Reader's Choice contest for a third time, Toriyama had the bad luck of drawing the first slot and had to work over New Year's on 1983's "Chobit". Angry that it was unpopular, he decided to try again and created "Chobit 2" (1983).
|
An official Toriyama fan club, , was established in 1982. Its newsletters were called "Bird Land Press" and were sent to members until the club closed in 1987. Toriyama founded Bird Studio in the early 1980s, which is a play on his name; meaning "bird". He began employing an assistant, mostly to work on backgrounds.
"Dragon Ball" and international success (1983–1997).
Torishima suggested that, as Toriyama enjoyed kung fu films, he should create a kung fu "shōnen" manga. This led to the two-part "Dragon Boy", published in the August and October 1983 issues of "Fresh Jump". It follows a boy, adept at martial arts, who escorts a princess on a journey back to her home country. "Dragon Boy" was well-received and evolved to become the serial "Dragon Ball" in 1984. But before that, "The Adventure of Tongpoo" was published in "Weekly Shōnen Jump"s 52nd issue of 1983 and also contained elements that would be included in "Dragon Ball".
Serialized in "Weekly Shōnen Jump" from 1984 to 1995 and having sold 159.5million "tankōbon" copies in Japan alone, "Dragon Ball" is one of the best-selling manga series of all time. It began as an adventure/gag manga but later turned into a martial arts fighting series, considered by many to be the "most influential "shōnen" manga". "Dragon Ball" was one of the main reasons for the magazine's circulation hitting a record high of 6.53 million copies (1995). At the series' end, Toriyama said that he asked everyone involved to let him end the manga, so he could "take some new steps in life". During that near-11-year period, he produced 519 chapters that were collected into 42 volumes. Moreover, the success of the manga led to five anime adaptations, several animated films, numerous video games, and mega-merchandise. Aside from its popularity in Japan, "Dragon Ball" was successful internationally as well, including Asia, Europe, and the Americas, with 300–350million copies of the manga sold worldwide.
|
While Toriyama was serializing "Dragon Ball" weekly, he continued to create the occasional one-shot manga. In 1986, "Mr. Ho" was published in the 49th issue of "Weekly Shōnen Jump". The following year saw publication of "Young Master Ken'nosuke", which had a Japanese "jidaigeki" setting. Toriyama published two "Weekly Shōnen Jump" one-shots in 1988; "The Elder" and "Little Mamejiro". "Karamaru and the Perfect Day" followed in issue #13 of 1989.
Also during "Dragon Ball"s serialization, Torishima recruited him to work as character designer for the 1986 role-playing video game "Dragon Quest". The artist admitted he was pulled into it without even knowing what an RPG was and that it made his already busy schedule even more hectic, but he was happy to have been a part after enjoying the finished game. Toriyama continued to work on every installment in the "Dragon Quest" series until his death. He also served as the character designer for the Super Famicom RPG "Chrono Trigger" (1995) and for the fighting games "Tobal No. 1" (1996) and "Tobal 2" (1997) for the PlayStation.
|
The September 23, 1988, festival film "Kosuke & Rikimaru: The Dragon of Konpei Island" marked the first time Toriyama made substantial contributions to an animation. He came up with the original story idea, co-wrote the screenplay with its director Toyoo Ashida, and designed the characters. It was screened at the Jump Anime Carnival, which was held to commemorate the 20th anniversary of "Weekly Shōnen Jump".
Short stories and other projects (1996–2011).
A third anime adaptation based on "Dragon Ball", entitled "Dragon Ball GT", began airing in 1996, though this was not based on Toriyama's manga directly. He was involved in some overarching elements, including the name of the series and designs for the main cast. Toriyama continued drawing manga in this period, predominantly one-shots and short (100–200-page) pieces, including "Cowa!" (1997–1998), "Kajika" (1998), and "Sand Land" (2000). On December 6, 2002, Toriyama made his only promotional appearance in the United States at the launch of "Weekly Shōnen Jump"s North American counterpart, "Shonen Jump", in New York City. Toriyama's "Dragon Ball" and "Sand Land" were published in the magazine in the first issue, which also included an in-depth interview with him. Toriyama also wrote a short self-parody of "Dragon Ball" entitled "Neko Majin", in the form of eight one-shots released sporadically from 1999 to 2005. The eight chapters were collected into a single volume and published in April 2005.
|
On March 27, 2005, CQ Motors began selling an electric car designed by Toriyama. The one-person QVOLT is part of the company's Choro-Q series of small electric cars, with only 9 being produced. It cost 1,990,000 yen (about $19,000 US), has a top speed of and was available in five colors. Toriyama stated that the car took over a year to design, "but due to my genius mini-model construction skills, I finally arrived at the end of what was a very emotional journey."
He worked on a 2006 one-shot called "Cross Epoch", in cooperation with "One Piece" creator Eiichiro Oda. The story is a short crossover that presents characters from both "Dragon Ball" and "One Piece". Toriyama was the character designer and artist for the 2006 Mistwalker Xbox 360 exclusive RPG "Blue Dragon", working with Hironobu Sakaguchi and Nobuo Uematsu, both of whom he had previously worked with on "Chrono Trigger". At the time, Toriyama felt the 2007 "Blue Dragon" anime might potentially be his final work in animation.
In 2008, he collaborated with Masakazu Katsura, his good friend and creator of "I"s" and "Zetman", for the "Jump SQ" one-shot "Sachie-chan Good!!". It was later published in North America in the free SJ Alpha Yearbook 2013, which was mailed out to annual subscribers of the digital manga magazine "Shonen Jump Alpha" in December 2012. The two worked together again in 2009, for the three-chapter one-shot "Jiya" in "Weekly Young Jump".
|
Toriyama was engaged by 20th Century Fox as a creative consultant on "Dragonball Evolution", an American live-action film adaptation of "Dragon Ball". The film was released in 2009 and failed both critically and financially. Toriyama later stated in 2013 that he had felt the script did not "capture the world or the characteristics" of his series and was "bland" and not interesting, so he cautioned them and gave suggestions for changes. But the Hollywood producers did not heed his advice, "And just as I thought, the result was a movie I cannot call "Dragon Ball"." Avex Trax commissioned Toriyama to draw a portrait of pop singer Ayumi Hamasaki, and it was printed on the CD of her 2009 single "Rule", which was used as the theme song to the film.
Toriyama drew a 2009 manga titled "Delicious Island's Mr. U" for Anjō's Rural Society Project, a nonprofit environmental organization that teaches the importance of agriculture and nature to young children. They originally asked him to do the illustrations for a pamphlet, but Toriyama liked the project and decided to expand it into a story. It is included in a booklet about environmental awareness that is distributed by the Anjō city government. As part of "Weekly Shōnen Jump"s "Top of the Super Legend" project, a series of six one-shots by famed "Jump" artists, Toriyama created "Kintoki" for its November 15, 2010, issue. He collaborated with "Weekly Shōnen Jump" to create a video to raise awareness and support for those affected by the 2011 Tōhoku earthquake and tsunami on March 11, 2011.
|
Return to "Dragon Ball" (2012–2024).
In 2012, ' was announced to be in development, with Toriyama involved in its creation. The film marked the series' first theatrical film in 17 years, and the first time Toriyama had been involved in one as early as the screenwriting stages. The film opened on March 30, 2013. A special "dual ticket" that could be used to see both "Battle of Gods" and ' was created with new art by both Toriyama and Eiichiro Oda.
On March 27, 2013, the "Akira Toriyama: The World of "Dragon Ball"" exhibit opened at the Takashimaya department store in Nihonbashi, garnering 72,000 visitors in its first nineteen days. The exhibit was separated into seven areas. The first provided a look at the series' history, the second showed the 400-plus characters from the series, the third displayed Toriyama's manga manuscripts from memorable scenes, the fourth showed special color illustrations, the fifth displayed rare "Dragon Ball"-related materials, the sixth included design sketches and animation cels from the anime, and the seventh screened "Dragon Ball"-related videos. It was there until April 15, when it moved to Osaka from April 17 to 23, and ended in Toriyama's native Nagoya from July 27 to September 1.
|
To celebrate the 45th anniversary of "Weekly Shōnen Jump", Toriyama launched a new manga series in its July 13, 2013, issue titled "Jaco the Galactic Patrolman". Viz Media began serializing it in English in their digital "Weekly Shonen Jump" magazine, beginning just two days later. The final chapter reveals that the story is set before the events of "Dragon Ball" and features some of its characters. It would become the final manga that Toriyama wrote and illustrated himself.
The follow-up film to "Battle of Gods", ', released on April 18, 2015, features even more contributions from Toriyama, who personally wrote its original script. Toriyama provided the basic story outline and some character designs for "Dragon Ball Super", which began serialization in "V Jump" in June 2015 with an anime counterpart following in July. Although the anime ended in 2018, he continued to provide story ideas for the manga while Toyotarou illustrated it. ', released in theaters on December 14, 2018, and "", released on June 11, 2022, continued Toriyama's deep involvement with the films, the latter being his final complete work on the Dragon Ball franchise.
|
In January 2024, a logo Toriyama designed to celebrate the 20th anniversary of his hometown of Kiyosu was unveiled. Toriyama created a new story arc for the 2024 original net animation adaptation of his manga "Sand Land". He also created the story and character designs for the upcoming "Dragon Ball Daima" anime series. Toriyama's final contribution to "Dragon Ball" was directing Toyotarou to redraw the end of chapter 103 of "Dragon Ball Super", so that a departing Piccolo appears to wave back at the reader. A short tribute was included at the bottom of the page when it was published on March 28, 2024.
On October 11, 2024, the Harvey Awards announced that Toriyama was one of five comics creators to be inducted into the Harvey Awards Hall of Fame at the 36th annual Harvey Awards ceremony on October 18 at the New York Comic Con. Acknowledging the accolade for Toriyama, Bird Studio Co., Ltd. and Capsule Corporation Tokyo issued a statement saying, "We are very honored to receive the news that Akira Toriyama has been selected for the prestigious Harvey Award Hall of Fame. As a creator, he had always said that his work says it all. We are especially grateful to the American fans for their long-standing enthusiasm and dedicated support. We hope you will continue to support his work for many years to come as we continue to develop and expand upon his masterpieces."
|
Personal life.
Toriyama married Yoshimi Katō on May 2, 1982. She is a former manga artist from Nagoya under the pen name Nachi Mikami, and occasionally helped Toriyama and his assistant on "Dr. Slump" when they were short on time. They had two children: a son named Sasuke (born 1987) and a daughter named Kikka (born 1990). Toriyama lived in his home studio in Kiyosu. He was a well-known recluse, who avoided appearing in public or media. In an extension to his shyness, Toriyama had used an avatar called "Tori-Bot" since 1980 to represent himself in manga and interviews.
Toriyama had a love of cars and motorcycles, something he inherited from his father who used to race motorbikes and operated an auto repair business for a brief time, although he did not understand the mechanics himself. He was an animal lover, and had kept birds, dogs, cats, fish, lizards, and bugs as pets since childhood. Some were used as models for characters he created such as Karin and Beerus. Toriyama had a lifelong passion for plastic models, and designed several for the Fine Molds brand. He also collected autographs of famous manga artists, having over 30 including Yudetamago and Hisashi Eguchi, a hobby he gave to the character Peasuke Soramame.
|
Death.
On March 1, 2024, Toriyama died of an acute subdural hematoma, at the age of 68. A funeral was held privately with only his family in attendance. His death was announced by his production company Bird Studio one week later on March 8. According to sources close to Toriyama, he had planned to undergo surgery for a brain tumor in February 2024. The news of his death caused an outpouring of grief among admirers of his works, who took to social media to express their condolences and celebrate his legacy. On Twitter, the trending topics of Akira Toriyama and "Dragon Ball" surpassed United States President Joe Biden's State of the Union address, which was held at the same time the news of Toriyama's death was announced. Tributes to the artist were given by "One Piece" creator Eiichiro Oda, "Naruto" creator Masashi Kishimoto, "Bleach" creator Tite Kubo, "My Hero Academia" creator Kōhei Horikoshi, "Yu Yu Hakusho "and "Hunter × Hunter" creator Yoshihiro Togashi, "Video Girl Ai" creator Masakazu Katsura, and video game designer Yuji Horii, who worked with Toriyama on "Dragon Quest" and "Chrono Trigger". In Tokyo, fans publicly mourned while visiting a life-sized statue of "Dragon Ball" protagonist Goku located outside the headquarters of toy manufacturer Bandai. Japan's Chief Cabinet Secretary Yoshimasa Hayashi credited Toriyama and his work with playing an "extremely important role in demonstrating Japan's soft power" around the world.
|
French President Emmanuel Macron shared a photo of an autographed illustration Toriyama gave him as a gift and paid tribute to him and his fans on social media. French Prime Minister Gabriel Attal also paid tribute and lamented that not even "the [Dragon Balls] and Shenron" could revive him. The foreign ministries of China and El Salvador issued statements of condolences over Toriyama's death. Justin Chatwin, who portrayed Goku in the live-action film "Dragonball Evolution", apologized for the quality of the film by posting on his Instagram story, "sorry we messed up that adaptation so badly". Several Mexican voice actors who dubbed "Dragon Ball" characters in Spanish for Latin America also lamented Toriyama's death via social media. A large gathering was held at the Plaza de la Constitución in Mexico City, where hundreds of fans did the Genki-dama hand motion (arms up, palm facing the zenith, pooling energy together) to honor the artist. During the 18th Seiyu Awards on March 9, a moment of silence was held for Toriyama and voice actress Tarako, who died on March 4, in recognition of their contributions to the anime industry. On March 10, in Argentina, thousands of fans gathered at the Obelisco monument to remember Toriyama. In Lima, Peru, over 40 artists led by "Peko" painted a mural tribute to Toriyama, which showcases characters from "Dragon Ball" as well as Toriyama himself, spanning six meters high and over 110 meters long.
|
Style.
Toriyama admired Osamu Tezuka's "Astro Boy" and was impressed by Walt Disney's "One Hundred and One Dalmatians", which he remembered for its high-quality animation. He was a fan of Hong Kong martial arts films, especially Bruce Lee films such as "Enter the Dragon" (1973) and Jackie Chan films such as "Drunken Master" (1978), which went on to have a large influence on his later work. He also cited the science fiction films "Alien" (1979) and "Galaxy Quest" (1999) as influences. Toriyama stated he was influenced by animator Toyoo Ashida and the anime television series adaptation of his own "Dragon Ball", from which he learned that separating colors instead of blending them makes the art cleaner and coloring illustrations easier.
|
"Dr. Slump" is mainly a comedy series, filled with puns, toilet humor, and sexual innuendos. But it also contained many science fiction elements: aliens, anthropomorphic characters, time travel, and parodies of works such as Godzilla, "Star Wars," and "Star Trek". Toriyama also included many real-life people in the series, such as his assistants, wife, and colleagues (such as Masakazu Katsura), but most notably his editor Kazuhiko Torishima as the series' main antagonist, Dr. Mashirito. A running gag in "Dr. Slump" that utilizes feces has been reported as an inspiration for the Pile of Poo emoji.
When "Dragon Ball" began, it was loosely based on the classic Chinese novel "Journey to the West", with Goku being Sun Wukong and Bulma as Tang Sanzang. It was also inspired by Hong Kong martial arts films, particularly those of Jackie Chan, and was set in a fictional world based on Asia, taking inspiration from several Asian cultures including Japanese, Chinese, Indian, Central Asian, Arabic, and Indonesian cultures. Toriyama continued to use his characteristic comedic style in the beginning, but over the course of serialization this slowly changed, with him turning the series into a "nearly-pure fighting manga" later on. He did not plan out in advance what would happen in the series, instead choosing to draw as he went. This, coupled with him simply forgetting things he had already drawn, caused him to find himself in situations that he had to write himself out of.
|
Toriyama was commissioned to illustrate the characters and monsters for the first "Dragon Quest" video game (1986) in order to separate it from other role-playing games of the time. He worked on every installment in the series until he died. For each game Yuji Horii first sends rough sketches of the characters with their background information to Toriyama, who then re-draws them. Lastly, Horii approves the finished work. Toriyama explained in 1995 that for video games, because the sprites are so small, as long as they have a distinguishing feature so people can tell which character it is, he can make complex designs without concern of having to reproduce it like he usually would in manga. Besides the character and monster designs, Toriyama also does the games' packaging art and, for "Dragon Quest VIII", the boats and ships. In 2016, Toriyama revealed that because of the series' established time period and setting, his artistic options are limited, which makes every iteration harder to design for than the last. The series' Slime character, which has become a mascot for the franchise, is considered to be one of the most recognizable figures in gaming.
|
Manga critic Jason Thompson declared Toriyama's art influential, saying that his "extremely personal and recognizable style" was a reason for "Dragon Ball"'s popularity. He points out that the popular "shōnen" manga of the late 1980s and early 1990s had "manly" heroes, such as "City Hunter" and "Fist of the North Star", whereas "Dragon Ball" starred the cartoonish and small Goku, thus starting a trend that Thompson says continues to this day. Toriyama himself said he went against the normal convention that the strongest characters should be the largest in terms of physical size, designing many of the series' most powerful characters with small statures. Thompson concluded his analysis by saying that only Akira Toriyama drew like this at the time and that "Dragon Ball" is "an action manga drawn by a gag manga artist." James S. Yadao, author of "The Rough Guide to Manga", points out that an art shift does occur in the series, as the characters gradually "lose the rounded, innocent look that [Toriyama] established in "Dr. Slump" and gain sharper angles that leap off the page with their energy and intensity."
|
Legacy and accolades.
Patrick St. Michel of "The Japan Times" compared Toriyama to animator Walt Disney and Marvel Comics creator Stan Lee, "All three of these individuals, Toriyama included, had a personal artistic style that has become the shorthand for their respective media." Speaking of "Dragon Ball", David Brothers of ComicsAlliance wrote that: "Like Osamu Tezuka and Jack Kirby before him, Toriyama created a story with his own two hands that seeped deep into the hearts of his readers, creating a love for both the cast and the medium at the same time." Thompson stated in 2011 that ""Dragon Ball" is by far the most influential shonen manga of the last 30 years, and today, almost every "Shōnen Jump" artist lists it as one of their favorites and lifts from it in various ways." Patrick W. Galbraith, an associate professor at the School of International Communication at Senshu University, similarly said, "One can sense the DNA of Toriyama's work in all subsequent shōnen releases."
|
In 2008, Oricon conducted a poll of people's favorite manga artists, with Toriyama coming in second, behind only "Nana" author Ai Yazawa. He was number one among male respondents and among those over 30 years of age. They held a poll on the Mangaka that Changed the History of Manga in 2010, "mangaka" being the Japanese word for a manga artist. Toriyama came in second, after only Osamu Tezuka, due to his works being highly influential and popular worldwide. Toriyama won the Special 40th Anniversary Festival Award at the 2013 Angoulême International Comics Festival, honoring his years in cartooning. He actually received the most votes for the festival's Grand Prix de la ville d'Angoulême award that year, though the selection committee chose Willem as the recipient. In a 2014 NTT Docomo poll for the manga artist that best represents Japan, Toriyama came in third place. That same year, entomologist Enio B. Cano named a new species of beetle, "Ogyges toriyamai", after Toriyama, and another, "Ogyges mutenroshii", after the "Dragon Ball" character Muten Roshi. Toriyama was decorated a "Chevalier" or "Knight" of the Ordre des Arts et des Lettres by the French government on May 30, 2019, for his contributions to the arts. He was also a 2019 nominee for entry into the Will Eisner Hall of Fame. Toriyama was honored with a Lifetime Achievement Award at the 2024 Tokyo Anime Awards Festival. Due to his video game design work, "IGN" named Toriyama number 74 on their list of the Top 100 Game Creators of All Time.
|
Works.
Besides "Dr. Slump" (1980–1984) and "Dragon Ball" (1984–1995), Toriyama predominantly drew one-shot manga and short (100–200-page) pieces, including "Pink" (1982), "Go! Go! Ackman" (1993–1994), "Cowa!" (1997–1998), "Kajika" (1998), "Sand Land" (2000) and "Jaco the Galactic Patrolman" (2013). Many of his one-shots were collected in his three-volume anthology series, "Akira Toriyama's Manga Theater" (1983–1997). He also collaborated with other manga artists, such as Katsura and Oda, to produce one-shots and crossover shorts.
Toriyama also created many character designs for various video games such as the "Dragon Quest" series (1986–2023), "Chrono Trigger" (1995), "Blue Dragon" (2006), and some "Dragon Ball" video games. He also designed several characters and mascots for various manga magazines property of Shueisha, his career-long employer and Japan's largest publishing company.
Besides manga-related works, Toriyama also created various illustrations, album and book covers, model kits, mascots and logos. For example, he sketched several versions of the "Dragon Ball Z" logo, which Toei Animation then refined into a definitive design.
|
Alioth
Alioth , also called Epsilon Ursae Majoris, is a star in the northern constellation of Ursa Major. The designation is Latinised from ε Ursae Majoris and abbreviated Epsilon UMa or ε UMa. Despite being designated "ε" (epsilon), it is the brightest star in the constellation and at magnitude 1.77 is the thirty-third brightest star in the sky.
It is the star in the tail of the bear closest to its body, and thus the star in the handle of the Big Dipper (or Plough) closest to the bowl. It is also a member of the large and diffuse Ursa Major moving group. Historically, the star was frequently used in celestial navigation in the maritime trade, because it is listed as one of the 57 navigational stars.
Physical characteristics.
According to "Hipparcos", Epsilon Ursae Majoris is from the Sun. Its spectral type is A1p; the "p" stands for "peculiar", as its spectrum is characteristic of an α2 Canum Venaticorum variable. Epsilon Ursae Majoris, as a representative of this type, may harbor two interacting processes: first, the star's strong magnetic field separating different elements in its hydrogen 'fuel'; second, a rotation axis at an angle to the magnetic axis may be spinning different bands of magnetically sorted elements into the line of sight between Epsilon Ursae Majoris and the Earth. The intervening elements react differently at different frequencies of light as they whip in and out of view, causing Epsilon Ursae Majoris to have very strange spectral lines that fluctuate over a period of 5.1 days. The "kB9" suffix to the spectral type indicates that the calcium K line is present and representative of a B9 spectral type even though the rest of the spectrum indicates A1.
|
Epsilon Ursae Majoris's rotational and magnetic poles are at almost 90 degrees to one another. Darker (denser) regions of chromium form a band at right angles to the equator.
It has long been suspected that Epsilon Ursae Majoris is a spectroscopic binary, possibly with more than one companion. A more recent study suggests Epsilon Ursae Majoris's 5.1-day variation may be due to a substellar object of about 14.7 Jupiter masses in an eccentric orbit (e=0.5) with an average separation of 0.055 astronomical units. It is now thought that the 5.1-day period is the rotation period of the star, and no companions have been detected using the most modern equipment. Observations of Alioth with the Navy Precision Optical Interferometer also did not detect a companion.
Epsilon Ursae Majoris has a relatively weak magnetic field for a variable of this type, 15 times weaker than α Canum Venaticorum, but it is still 100 times stronger than that of the Earth.
Name and etymology.
"ε Ursae Majoris" (Latinised to "Epsilon Ursae Majoris") is the star's Bayer designation.
|
The traditional name "Alioth" comes from the Arabic "alyat al-hamal" ("the sheep's fat tail"). In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN's first bulletin of July 2016 included a table of the first two batches of names approved by the WGSN; which included "Alioth" for this star.
This star was known to the Hindus as "Añgiras", one of the Seven Rishis.
In Chinese, (), meaning "Northern Dipper", refers to an asterism equivalent to the Big Dipper. Consequently, the Chinese name for Epsilon Ursae Majoris itself is (, ) and (, ).
Namesakes.
The United States Navy's Crater class cargo ship was named after the star.
|
Amiga 500
The Amiga 500, also known as the A500, was the first popular version of the Amiga home computer, "redefining the home computer market and making so-called luxury features such as multitasking and colour a standard long before Microsoft or Apple sold these to the masses." It contains the same Motorola 68000 as the Amiga 1000, as well as the same graphics and sound coprocessors, but is in a smaller case similar to that of the Commodore 128.
Commodore announced the Amiga 500 at the January 1987 winter Consumer Electronics Showat the same time as the high-end Amiga 2000. It was initially available in the Netherlands in April 1987, then the rest of Europe in May. In North America and the UK it was released in October 1987 with a list price. It competed directly against models in the Atari ST line.
The Amiga 500 was sold in the same retail outlets as the Commodore 64, as opposed to the computer store-only Amiga 1000. It proved to be Commodore's best-selling model, particularly in Europe. Although popular with hobbyists, arguably its most widespread use was as a gaming machine, where its graphics and sound were of significant benefit. It was followed by a revised version of the computer, the Amiga 500 Plus, and the 500 series was discontinued in 1992.
|
Releases.
In mid-1988, the Amiga 500 dropped its price from £499 to £399 (https://amr.abime.net/issue_535_pages page 7), and it was later bundled with the "Batman Pack" in the United Kingdom (from October 1989 to September 1990) which included the games "Batman", "F/A-18 Interceptor", "The New Zealand Story" and the bitmap graphics editor Deluxe Paint 2. Also included was the Amiga video connector which allows the A500 to be used with a conventional CRT television.
In November 1991, the enhanced Amiga 500 Plus replaced the 500 in some markets. It was bundled with the "Cartoon Classics" pack in the United Kingdom at £399, although many stores still advertised it as an 'A500'. The Amiga 500 Plus was virtually identical except for its new operating system, integrated 1MB of Chip memory, different 'trap-door' expansion slot and slightly different keyboard, and in mid-1992, the two were discontinued and effectively replaced by the Amiga 600. In late 1992, Commodore released the Amiga 1200, a machine closer in concept to the original Amiga 500, but with significant technical improvements. Despite this, neither the A1200 nor the A600 replicated the commercial success of its predecessor. By this time, the home market was strongly shifting to IBM PC compatibles with VGA graphics and the low-cost Macintosh Classic, LC, and IIsi models.
|
Description.
Outwardly resembling the Commodore 128 and codenamed "Rock Lobster" during development, the Amiga 500's base houses a keyboard and a CPU in one shell, unlike the Amiga 1000. The keyboard for Amiga 500s sold in the United States contains 94 keys, including ten function keys, four cursor keys, and a number pad. All European versions the keyboard have an additional two keys, except for the British variety, which still uses 94 keys. It uses a Motorola 68000 microprocessor running at in NTSC regions and in PAL regions. The CPU implements a 32-bit model and has 32-bit registers, but it has a 16-bit main ALU and uses a 16-bit external data bus and a 24-bit address bus, providing a maximum of 16 MB of address space. Also built in to the base of the computer is a -inch floppy disk drive. The user can also install up to three external floppy drives, either - or -inch, via the disk drive port. The second and third additional drives are installed by daisy-chaining them. Supported by these drives are double-sided disks with a capacity of 901,120 bytes, as well as 360- and 720-KB disks formatted for IBM PC compatibles.
|
The earliest Amiga 500 models use nearly the same Original Amiga chipset as the Amiga 1000. So graphics can be displayed in multiple resolutions and color depths, even on the same screen. Resolutions vary from 320×200 (up to 32 colors) to 640×400 (up to 16 colors) for NTSC (704×484 overscan) and 320×256 to 640×512 for PAL (704×576 overscan.) The system uses planar graphics, with up to five bitplanes (four in high resolution) allowing 2-, 4-, 8-, 16-, and 32-color screens, from a palette of 4096 colors. Two special graphics modes are also available: Extra HalfBrite, which uses a sixth bitplane as a mask to cut the brightness of any pixel in half (resulting in 32 arbitrary colors plus 32 more colors set at half the value of the first 32), and Hold-And-Modify (HAM) which allows all 4096 colors to be used on screen simultaneously. Later revisions of the chipset are PAL/NTSC switchable in software.
The sound chip produces four hardware-mixed channels, two to the left and two to the right, of 8-bit PCM at a sampling frequency up to . Each hardware channel has its own independent volume level and sampling rate, and can be designated to another channel where it can modulate both volume and frequency using its own output. With DMA disabled it's possible to output with a sampling frequency up to . There is a common trick to output sound with 14-bit precision that can be combined to output 14-bit sound.
|
The stock system comes with AmigaOS version 1.2 or 1.3 and of chip RAM (150 ns access time), one built-in double-density standard floppy disk drive that is completely programmable and can read IBM PC disks, standard Amiga disks, and up to using custom-formatting drivers.
Despite the lack of Amiga 2000-compatible internal expansion slots, there are many ports and expansion options. There are two DE9M Atari joystick ports for joysticks or mice, and stereo audio RCA connectors (1 V p-p). There is a floppy drive port for daisy-chaining up to three extra floppy disk drives via a DB23F connector. The then-standard RS-232 serial port (DB25M) and Centronics parallel port (DB25F) are also included. The power supply is (, ).
The system displays video in analog RGB PAL or NTSC through a proprietary DB23M connector and in NTSC mode the line frequency is HSync for standard video modes, which is compatible with NTSC television and CVBS/RGB video, but out of range for most VGA-compatible monitors, while a multisync monitor is required for some of the higher resolutions. This connection can also be genlocked to an external video signal. The system was bundled with an RF adapter to provide output on televisions with a coaxial RF input, while monochrome video is available via an RCA connector (also coaxial). On the left side, behind a plastic cover, there is a Zorro (Zorro I) bus expansion external edge connector with 86 pins. Peripherals such as a hard disk drive can be added via the expansion slot and are configured automatically by the Amiga's AutoConfig standard, so that multiple devices do not conflict with each other. Up to of so-called "fast RAM" (memory that can be accessed by the CPU only) can be added using the side expansion slot. This connector is electronically identical with the Amiga 1000's, but swapped on the other side.
|
The Amiga 500 has a "trap-door" slot on the underside for a RAM upgrade (typically ). This extra RAM is classified as "fast" RAM, but is sometimes referred to as "slow" RAM: due to the design of the expansion bus, it is actually on the chipset bus. Such upgrades usually include a battery-backed real-time clock. All versions of the A500 can have the additional RAM configured as chip RAM by a simple hardware modification, which involves fitting a later model (8372A) Agnus chip. Likewise, all versions of the A500 can be upgraded to chip RAM by fitting the chip and adding additional memory.
The Amiga 500 also sports an unusual feature for a budget machine, socketed chips, which allow easy replacement of defective chips. The CPU can be directly upgraded on the motherboard to a 68010; or to a 68020, 68030, or 68040 via the side expansion slot; or by removing the CPU and plugging a CPU expansion card into the CPU socket (this requires opening the computer and thus voided any remaining warranty). In fact, all the custom chips can be upgraded to the Amiga Enhanced Chip Set (ECS) versions.
|
The plastic case is made of acrylonitrile butadiene styrene, or ABS. ABS degrades with time due to exposure to oxygen, causing a yellowing of the case. Other factors contributing to the degradation and yellowing include heat, shear, and ultraviolet light. The yellowing can be reversed by using an optical brightener, though without stabilizing agents or antioxidants to block oxygen, the yellowing will return.
Technical specifications.
Memory.
Using various expansion techniques, the A500's total RAM can reach up to 138 MB – 2 MB Chip RAM, 8 MB 16-bit Fast RAM, and 128 MB 32-bit Fast RAM.
Chip RAM.
The stock 512 KB Chip RAM can be complemented by 512 KB using a "trapdoor" expansion (Commodore A501 or compatible). While that expansion memory is connected to the chip bus, hardware limitations of early stock Agnus chip revisions prevent its use as Chip RAM, only the CPU can access it. Suffering from the same contention limitations as Chip RAM, that memory is known as "Slow RAM" or "Pseudo-fast RAM". Agnus revisions shipped with late A500 are ECS and allow use of trapdoor RAM as real Chip RAM for a total 1 MB.
|
Additionally, several third-party expansions exist with up to 2 MB on the trapdoor board. Using a Gary adapter, that memory will be mapped as either split on Chip RAM and Slow RAM or fully as Slow RAM, depending on configuration.
Furthermore, using an A3000 Agnus on an adapter board, it is possible to expand the Chip RAM to 2 MB, matching the A500+.
Fast RAM.
"Fast" RAM is located on the CPU-side bus. Its access is exclusive to the CPU and not slowed by any chipset access. The side expansion port allows for up to 8 MB of Zorro-style expansion RAM. Alternatively, a CPU adapter allows for internal expansion.
Accelerator RAM.
Internal or external CPU accelerators often include their own expansion memory. 16-bit CPUs are limited by the 24-bit address space but they can repurpose otherwise unused memory space for their included RAM. 32-bit CPU accelerators aren't limited by 24-bit addressing and can include up to 128 MB of Fast RAM (and potentially more).
Diagnostics.
When the computer is powered on a self-diagnostic test is run that will indicates failure with a specific colour:
|
The keyboard LED uses blink codes:
Measurements
Overall (base): 6.2 cm x 47.4 cm x 33 cm; 2 7/16 in x 18 11/16 in x 13 in.
Trap-door expansion 501.
A popular expansion for the Amiga 500 was the Amiga 501 circuit board that can be installed underneath the computer behind a plastic cover. The expansion contains RAM configured by default as "Slow RAM" or "trap-door RAM" and a battery-backed real-time clock (RTC).
The 512 KB trap-door RAM and 512 KB of original chip RAM will result in 1 MB of total memory. The added memory is known as "Slow RAM", as its access is impacted by chip-bus bandwidth contention, while the chipset is not actually able to address it.
Later revisions of the motherboard provide solder-jumpers to relocate the trap-door RAM to the chip memory pool, given the Agnus chip is the newer ECS version, shipped in later A500 motherboards. Newest (rev 8) A500s would share motherboard with A500+, and configure the expansion memory as CHIP by default.
Software.
Each time the Amiga 500 is booted, it executes code from the Kickstart ROM. The Amiga 500 initially came shipped with AmigaOS 1.2, but units since October 1988 had version 1.3 installed.
|
Reception and sales.
The Amiga 500 was the best-selling model in the Amiga family of computers. The German computer magazine "Chip" awarded the model the annual "Home Computer of the Year" title three consecutive times. At the European Computer Trade Show 1991, it also won the Leisure Award for the similar "Home Computer of the Year" title.
Owing to the inexpensive cost of the Amiga 500 in then price-sensitive Europe, sales of the Amiga family of computers were strongest there, constituting 85 percent of Commodore's total sales in the fourth quarter of 1990. The Amiga 500 was widely perceived as a gaming machine and the Amiga 2000 a computer for artists and hobbyists.
It has been claimed that Commodore sold as many as six million units worldwide. However, Commodore UK refuted that figure and said that the entire Amiga line sold between four and five million computers. Indeed, "Ars Technica" provides a year-by-year graph of the sales of all Amiga computers.
The machine is reported to have sold 1,160,500 units in Germany (including Amiga 500 Plus sales).
|
Amiga 500 Plus.
The Amiga 500 Plus (often A500 Plus or simply A500+) is a revised version of the original Amiga 500 computer. The A500+ featured minor changes to the motherboard to make it cheaper to produce than the original A500. It was notable for introducing new versions of Kickstart and Workbench, and for some minor improvements in the custom chips, known as the Enhanced Chip Set (or ECS).
Although officially introduced in 1992, some Amiga 500 units sold in late 1991 actually featured the revised motherboard used in the A500+. Although the Amiga 500+ was an improvement to the Amiga 500, it was minor. It was discontinued and replaced by the Amiga 600 in summer 1992, making it the shortest-lived Amiga model.
Compatibility problems.
|
Aga
Aga or AGA may refer to:
|
Amiga 1000
The Amiga 1000, also known as the A1000, is the first personal computer released by Commodore International in the Amiga line. It combines the 16/32-bit Motorola 68000 CPU which was powerful by 1985 standards with one of the most advanced graphics and sound systems in its class. It runs a preemptive multitasking operating system that fits into of read-only memory and was shipped with 256 KB of RAM. The primary memory can be expanded internally with a manufacturer-supplied 256 KB module for a total of 512 KB of RAM. Using the external slot the primary memory can be expanded up to
Design.
The A1000 has a number of characteristics that distinguish it from later Amiga models: It is the only model to feature the short-lived Amiga check-mark logo on its case, the majority of the case is elevated slightly to give a storage area for the keyboard when not in use (a "keyboard garage"), and the inside of the case is engraved with the signatures of the Amiga designers (similar to the Macintosh); including Jay Miner and the paw print of his dog Mitchy. The A1000's case was designed by Howard Stolz. As Senior Industrial Designer at Commodore, Stolz was the mechanical lead and primary interface with Sanyo in Japan, the contract manufacturer for the A1000 casing.
|
The Amiga 1000 was manufactured in two variations: One uses the NTSC television standard and the other uses the PAL television standard. The NTSC variant was the initial model manufactured and sold in North America. The later PAL model was manufactured in Germany and sold in countries using the PAL television standard. The first NTSC systems lack the EHB video mode which is present in all later Amiga models.
Because AmigaOS was rather buggy at the time of the A1000's release, the OS was not placed in ROM then. Instead, the A1000 includes a daughterboard with 256 KB of RAM, dubbed the "writable control store" (WCS), into which the core of the operating system is loaded from floppy disk (this portion of the operating system is known as the "Kickstart"). The WCS is write-protected after loading, and system resets do not require a reload of the WCS. In Europe, the WCS was often referred to as WOM (Write Once Memory), a play on the more conventional term "ROM" (read-only memory).
Technical information.
The preproduction Amiga (which was codenamed "Velvet") released to developers in early 1985 contained of RAM with an option to expand it to Commodore later increased the system memory to due to objections by the Amiga development team. The names of the custom chips were different; Denise and Paula were called Daphne and Portia respectively. The casing of the preproduction Amiga was almost identical to the production version: the main difference being an embossed Commodore logo in the top left corner. It did not have the developer signatures.
|
The Amiga 1000 has a Motorola 68000 CPU running at 7.15909 MHz on NTSC systems or 7.09379 MHz on PAL systems, precisely double the video color carrier frequency for NTSC or 1.6 times the color carrier frequency for PAL. The system clock timings are derived from the video frequency, which simplifies glue logic and allows the Amiga 1000 to make do with a single crystal. In keeping with its video game heritage, the chipset was designed to synchronize CPU memory access and chipset DMA so the hardware runs in real time without wait-state delays.
Though most units were sold with an analog RGB monitor, the A1000 also has a built-in composite video output which allows the computer to be connected directly to some monitors other than their standard RGB monitor. The A1000 also has a "TV MOD" output, into which an RF Modulator can be plugged, allowing connection to older televisions that did not have a composite video input.
The original 68000 CPU can be directly replaced with a Motorola 68010, which can execute instructions slightly faster than the 68000 but also introduces a small degree of software incompatibility. Third-party CPU upgrades, which mostly fit in the CPU socket, use faster 68020 or 68030 microprocessors and integrated memory, as well as provide support for a 68881 or 68882 FPU. Such upgrades often have the option to revert to 68000 mode for full compatibility. Some boards have a socket to seat the original 68000, whereas the 68030 cards typically come with an on-board 68000.
|
The original Amiga 1000 is the only model to have 256 KB of Amiga Chip RAM, which can be expanded to 512 KB with the addition of a daughterboard under a cover in the center front of the machine. RAM may also be upgraded via official and third-party upgrades, with a practical upper limit of about 9 MB of "fast RAM" due to the 68000's 24-bit address bus. This memory is accessible only by the CPU permitting faster code execution as DMA cycles are not shared with the chipset.
The Amiga 1000 features an 86-pin expansion port (electrically identical to the later Amiga 500 expansion port, though the A500's connector is inverted). This port is used by third-party expansions such as memory upgrades and SCSI adapters. These resources are handled by the Amiga Autoconfig standard. Other expansion options are available including a bus expander which provides two Zorro-II slots.
Retail.
Introduced on July 23, 1985, during a star-studded gala featuring Andy Warhol and Debbie Harry held at the Vivian Beaumont Theater at Lincoln Center in New York City, machines began shipping in September with a base configuration of 256 KB of RAM at the retail price of . A analog RGB monitor was available for around , bringing the price of a complete Amiga system to US$1,595 (). Before the release of the Amiga 500 and Amiga 2000 models in 1987, the A1000 was marketed as simply the "Amiga", although the model number was there from the beginning, as the original box indicates.
|
In the US, the A1000 was marketed as "The Amiga from Commodore", with the Commodore logo omitted from the case. The Commodore branding was retained for the international versions.
Additionally, the Amiga 1000 was sold exclusively in computer stores in the US rather than the various non computer-dedicated department and toy stores through which the VIC-20 and Commodore 64 were retailed. These measures were an effort to avoid Commodore's "toy-store" computer image created during the Tramiel era.
Along with the operating system, the machine came bundled with a version of AmigaBASIC developed by Microsoft and a speech synthesis library developed by Softvoice, Inc.
Aftermarket upgrades.
Many A1000 owners remained attached to their machines long after newer models rendered the units technically obsolete, and it attracted numerous aftermarket upgrades. Many CPU upgrades that plugged into the Motorola 68000 socket functioned in the A1000. Additionally, a line of products called the "Rejuvenator" series allowed the use of newer chipsets in the A1000, and an Australian-designed replacement A1000 motherboard called "The Phoenix" utilized the same chipset as the A3000 and added an A2000-compatible video slot and on-board SCSI controller.
|
Reception and impact.
In its product preview, "Byte" magazine was impressed by the computer's multitasking capabilities and the quality of its graphics and sound systems. It also praised its text-to-speech library for voice output, and predicted that the Amiga would be successful enough to influence the personal computer industry.
The Amiga 1000 was released to positive reviews. "Compute!" lauded it as an inexpensive, truly general-purpose computer that might break preconceptions dividing the microcomputer marketplace. In this case, it was capable of outperforming most business, as well as arcade game machines and delivering sampled sound, making it suitable for offices, gamers, and digital artists. "Computer Gaming World" praised the machine's versatility without any obvious hardware shortcomings and stressed that it was ideal for game designers demanding fewer system constraints. "Creative Computing" magazine had only minor criticisms for what they otherwise called a "dream machine." These criticisms were directed toward its case quality, the disk drives slowing during certain operations, and not finding an codice_1 command in AmigaDOS, though the marketing vice president of Commodore, Clive Smith, assured the magazine that later production units would address most of its complaints. Months after the Amiga 1000 was released, "InfoWorld" offered a mixed review. It praised Intuition and the customizability of Workbench, but took issue with the operating system's bugs such as memory overflow and screen flickering of single lines as a result of their being interleaved when displayed in high resolution mode. It also criticized the sparseness of the software library preventing the publication from fully realizing the computer's potential.
|
In 1994, as Commodore filed for bankruptcy, "Byte" magazine called the Amiga 1000 "the first multimedia computer... so far ahead of its time that almost nobody—including Commodore's marketing department—could fully articulate what it was all about". In 2006, "PC World" rated the Amiga 1000 as the 7th greatest PC of all time. In 2007, it was rated by the same magazine as the 37th best tech product of all time. Also that year, IDG Sweden ranked it the 10th best computer of all time.
Joe Pillow.
"Joe Pillow" was the name given on the ticket for the extra airline seat purchased to hold the first Amiga prototype while on the way to the January 1984 Consumer Electronics Show. The airlines required a name for the airline ticket and Joe Pillow was born. The engineers (RJ Mical and Dale Luck) who flew with the Amiga prototype (codenamed "Lorraine") drew a happy face on the front of the pillowcase and even added a tie.
Joe Pillow extended his fifteen minutes of fame when the Amiga went to production. All fifty-three Amiga team members who worked on the project signed the Amiga case. This included Joe Pillow and Jay Miner's dog Michy who each got to "sign" the case in their own unique way.
|
Asymptote
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the "x" or "y" coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.
The word asymptote is derived from the Greek ἀσύμπτωτος ("asumptōtos") which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.
There are three kinds of asymptotes: "horizontal", "vertical" and "oblique". For curves given by the graph of a function , horizontal asymptotes are horizontal lines that the graph of the function approaches as "x" tends to Vertical asymptotes are vertical lines near which the function grows without bound. An oblique asymptote has a slope that is non-zero but finite, such that the graph of the function approaches it as "x" tends to
|
More generally, one curve is a "curvilinear asymptote" of another (as opposed to a "linear asymptote") if the distance between the two curves tends to zero as they tend to infinity, although the term "asymptote" by itself is usually reserved for linear asymptotes.
Asymptotes convey information about the behavior of curves "in the large", and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.
Introduction.
The idea that a curve may come arbitrarily close to a line without actually becoming the same may seem to counter everyday experience. The representations of a line and a curve as marks on a piece of paper or as pixels on a computer screen have a positive width. So if they were to be extended far enough they would seem to merge, at least as far as the eye could discern. But these are physical representations of the corresponding mathematical entities; the line and the curve are idealized concepts whose width is 0 (see Line). Therefore, the understanding of the idea of an asymptote requires an effort of reason rather than experience.
|
Consider the graph of the function formula_1 shown in this section. The coordinates of the points on the curve are of the form formula_2 where x is a number other than 0. For example, the graph contains the points (1, 1), (2, 0.5), (5, 0.2), (10, 0.1), ... As the values of formula_3 become larger and larger, say 100, 1,000, 10,000 ..., putting them far to the right of the illustration, the corresponding values of formula_4, .01, .001, .0001, ..., become infinitesimal relative to the scale shown. But no matter how large formula_3 becomes, its reciprocal formula_6 is never 0, so the curve never actually touches the "x"-axis. Similarly, as the values of formula_3 become smaller and smaller, say .01, .001, .0001, ..., making them infinitesimal relative to the scale shown, the corresponding values of formula_4, 100, 1,000, 10,000 ..., become larger and larger. So the curve extends further and further upward as it comes closer and closer to the "y"-axis. Thus, both the "x" and "y"-axis are asymptotes of the curve. These ideas are part of the basis of concept of a limit in mathematics, and this connection is explained more fully below.
|
Asymptotes of functions.
The asymptotes most commonly encountered in the study of calculus are of curves of the form . These can be computed using limits and classified into "horizontal", "vertical" and "oblique" asymptotes depending on their orientation. Horizontal asymptotes are horizontal lines that the graph of the function approaches as "x" tends to +∞ or −∞. As the name indicates they are parallel to the "x"-axis. Vertical asymptotes are vertical lines (perpendicular to the "x"-axis) near which the function grows without bound. Oblique asymptotes are diagonal lines such that the difference between the curve and the line approaches 0 as "x" tends to +∞ or −∞.
Vertical asymptotes.
The line "x" = "a" is a "vertical asymptote" of the graph of the function if at least one of the following statements is true:
where formula_11 is the limit as "x" approaches the value "a" from the left (from lesser values), and formula_12 is the limit as "x" approaches "a" from the right.
For example, if ƒ("x") = "x"/("x"–1), the numerator approaches 1 and the denominator approaches 0 as "x" approaches 1. So
|
and the curve has a vertical asymptote "x" = 1.
The function "ƒ"("x") may or may not be defined at "a", and its precise value at the point "x" = "a" does not affect the asymptote. For example, for the function
has a limit of +∞ as , "ƒ"("x") has the vertical asymptote , even though "ƒ"(0) = 5. The graph of this function does intersect the vertical asymptote once, at (0, 5). It is impossible for the graph of a function to intersect a vertical asymptote (or a vertical line in general) in more than one point. Moreover, if a function is continuous at each point where it is defined, it is impossible that its graph does intersect any vertical asymptote.
A common example of a vertical asymptote is the case of a rational function at a point x such that the denominator is zero and the numerator is non-zero.
If a function has a vertical asymptote, then it isn't necessarily true that the derivative of the function has a vertical asymptote at the same place. An example is
This function has a vertical asymptote at formula_18 because
|
and
The derivative of formula_21 is the function
For the sequence of points
that approaches formula_25 both from the left and from the right, the values formula_26 are constantly formula_27. Therefore, both one-sided limits of formula_28 at formula_27 can be neither formula_30 nor formula_31. Hence formula_32 doesn't have a vertical asymptote at formula_25.
Horizontal asymptotes.
"Horizontal asymptotes" are horizontal lines that the graph of the function approaches as . The horizontal line "y" = "c" is a horizontal asymptote of the function "y" = "ƒ"("x") if
In the first case, "ƒ"("x") has "y" = "c" as asymptote when "x" tends to , and in the second "ƒ"("x") has "y" = "c" as an asymptote as "x" tends to .
For example, the arctangent function satisfies
So the line is a horizontal asymptote for the arctangent when "x" tends to , and is a horizontal asymptote for the arctangent when "x" tends to .
Functions may lack horizontal asymptotes on either or both sides, or may have one horizontal asymptote that is the same in both directions. For example, the function has a horizontal asymptote at "y" = 0 when "x" tends both to and because, respectively,
|
Other common functions that have one or two horizontal asymptotes include (that has an hyperbola as it graph), the Gaussian function formula_39 the error function, and the logistic function.
Oblique asymptotes.
When a linear asymptote is not parallel to the "x"- or "y"-axis, it is called an "oblique asymptote" or "slant asymptote". A function "ƒ"("x") is asymptotic to the straight line ("m" ≠ 0) if
In the first case the line is an oblique asymptote of "ƒ"("x") when "x" tends to +∞, and in the second case the line is an oblique asymptote of "ƒ"("x") when "x" tends to −∞.
An example is "ƒ"("x") = "x" + 1/"x", which has the oblique asymptote "y" = "x" (that is "m" = 1, "n" = 0) as seen in the limits
Elementary methods for identifying asymptotes.
The asymptotes of many elementary functions can be found without the explicit use of limits (although the derivations of such methods typically use limits).
General computation of oblique asymptotes for functions.
The oblique asymptote, for the function "f"("x"), will be given by the equation "y" = "mx" + "n". The value for "m" is computed first and is given by
|
where "a" is either formula_31 or formula_30 depending on the case being studied. It is good practice to treat the two cases separately. If this limit doesn't exist then there is no oblique asymptote in that direction.
Having "m" then the value for "n" can be computed by
where "a" should be the same value used before. If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining "m" exist. Otherwise is the oblique asymptote of "ƒ"("x") as "x" tends to "a".
For example, the function has
so that is the asymptote of "ƒ"("x") when "x" tends to +∞.
The function has
So does not have an asymptote when "x" tends to +∞.
Asymptotes for rational functions.
A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes.
The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or oblique asymptotes. The cases are tabulated below, where deg(numerator) is the degree of the numerator, and deg(denominator) is the degree of the denominator.
|
The vertical asymptotes occur only when the denominator is zero (If both the numerator and denominator are zero, the multiplicities of the zero are compared). For example, the following function has vertical asymptotes at "x" = 0, and "x" = 1, but not at "x" = 2.
Oblique asymptotes of rational functions.
When the numerator of a rational function has degree exactly one greater than the denominator, the function has an oblique (slant) asymptote. The asymptote is the polynomial term after dividing the numerator and denominator. This phenomenon occurs because when dividing the fraction, there will be a linear term, and a remainder. For example, consider the function
shown to the right. As the value of "x" increases, "f" approaches the asymptote "y" = "x". This is because the other term, 1/("x"+1), approaches 0.
If the degree of the numerator is more than 1 larger than the degree of the denominator, and the denominator does not divide the numerator, there will be a nonzero remainder that goes to zero as "x" increases, but the quotient will not be linear, and the function does not have an oblique asymptote.
|
Transformations of known functions.
If a known function has an asymptote (such as "y"=0 for "f"(x)="e""x"), then the translations of it also have an asymptote.
If a known function has an asymptote, then the scaling of the function also have an asymptote.
For example, "f"("x")="e""x"-1+2 has horizontal asymptote "y"=0+2=2, and no vertical or oblique asymptotes.
General definition.
Let be a parametric plane curve, in coordinates "A"("t") = ("x"("t"),"y"("t")). Suppose that the curve tends to infinity, that is:
A line ℓ is an asymptote of "A" if the distance from the point "A"("t") to ℓ tends to zero as "t" → "b". From the definition, only open curves that have some infinite branch can have an asymptote. No closed curve can have an asymptote.
For example, the upper right branch of the curve "y" = 1/"x" can be defined parametrically as "x" = "t", "y" = 1/"t" (where "t" > 0). First, "x" → ∞ as "t" → ∞ and the distance from the curve to the "x"-axis is 1/"t" which approaches 0 as "t" → ∞. Therefore, the "x"-axis is an asymptote of the curve. Also, "y" → ∞ as "t" → 0 from the right, and the distance between the curve and the "y"-axis is "t" which approaches 0 as "t" → 0. So the "y"-axis is also an asymptote. A similar argument shows that the lower left branch of the curve also has the same two lines as asymptotes.
|
Although the definition here uses a parameterization of the curve, the notion of asymptote does not depend on the parameterization. In fact, if the equation of the line is formula_55 then the distance from the point "A"("t") = ("x"("t"),"y"("t")) to the line is given by
if γ("t") is a change of parameterization then the distance becomes
which tends to zero simultaneously as the previous expression.
An important case is when the curve is the graph of a real function (a function of one real variable and returning real values). The graph of the function "y" = "ƒ"("x") is the set of points of the plane with coordinates ("x","ƒ"("x")). For this, a parameterization is
This parameterization is to be considered over the open intervals ("a","b"), where "a" can be −∞ and "b" can be +∞.
An asymptote can be either vertical or non-vertical (oblique or horizontal). In the first case its equation is "x" = "c", for some real number "c". The non-vertical case has equation , where "m" and formula_59 are real numbers. All three types of asymptotes can be present at the same time in specific examples. Unlike asymptotes for curves that are graphs of functions, a general curve may have more than two non-vertical asymptotes, and may cross its vertical asymptotes more than once.
|
Curvilinear asymptotes.
Let be a parametric plane curve, in coordinates "A"("t") = ("x"("t"),"y"("t")), and "B" be another (unparameterized) curve. Suppose, as before, that the curve "A" tends to infinity. The curve "B" is a curvilinear asymptote of "A" if the shortest distance from the point "A"("t") to a point on "B" tends to zero as "t" → "b". Sometimes "B" is simply referred to as an asymptote of "A", when there is no risk of confusion with linear asymptotes.
For example, the function
has a curvilinear asymptote , which is known as a "parabolic asymptote" because it is a parabola rather than a straight line.
Asymptotes and curve sketching.
Asymptotes are used in procedures of curve sketching. An asymptote serves as a guide line to show the behavior of the curve towards infinity. In order to get better approximations of the curve, curvilinear asymptotes have also been used although the term asymptotic curve seems to be preferred.
Algebraic curves.
The asymptotes of an algebraic curve in the affine plane are the lines that are tangent to the projectivized curve through a point at infinity. For example, one may identify the asymptotes to the unit hyperbola in this manner. Asymptotes are often considered only for real curves, although they also make sense when defined in this way for curves over an arbitrary field.
|
A plane curve of degree "n" intersects its asymptote at most at "n"−2 other points, by Bézout's theorem, as the intersection at infinity is of multiplicity at least two. For a conic, there are a pair of lines that do not intersect the conic at any complex point: these are the two asymptotes of the conic.
A plane algebraic curve is defined by an equation of the form "P"("x","y") = 0 where "P" is a polynomial of degree "n"
where "P""k" is homogeneous of degree "k". Vanishing of the linear factors of the highest degree term "P""n" defines the asymptotes of the curve: setting , if , then the line
is an asymptote if formula_63 and formula_64 are not both zero. If formula_65 and formula_66, there is no asymptote, but the curve has a branch that looks like a branch of parabola. Such a branch is called a , even when it does not have any parabola that is a curvilinear asymptote. If formula_67 the curve has a singular point at infinity which may have several asymptotes or parabolic branches.
Over the complex numbers, "P""n" splits into linear factors, each of which defines an asymptote (or several for multiple factors). Over the reals, "P""n" splits in factors that are linear or quadratic factors. Only the linear factors correspond to infinite (real) branches of the curve, but if a linear factor has multiplicity greater than one, the curve may have several asymptotes or parabolic branches. It may also occur that such a multiple linear factor corresponds to two complex conjugate branches, and does not corresponds to any infinite branch of the real curve. For example, the curve has no real points outside the square formula_68, but its highest order term gives the linear factor "x" with multiplicity 4, leading to the unique asymptote "x"=0.
|
Asymptotic cone.
The hyperbola
has the two asymptotes
The equation for the union of these two lines is
Similarly, the hyperboloid
is said to have the asymptotic cone
The distance between the hyperboloid and cone approaches 0 as the distance from the origin approaches infinity.
More generally, consider a surface that has an implicit equation
formula_74
where the formula_75 are homogeneous polynomials of degree formula_76 and formula_77. Then the equation formula_78 defines a cone which is centered at the origin. It is called an asymptotic cone, because the distance to the cone of a point of the surface tends to zero when the point on the surface tends to infinity.
|
Andrew S. Tanenbaum
Andrew Stuart Tanenbaum (born March 16, 1944), sometimes referred to by the handle AST, is an American-born Dutch computer scientist and retired professor emeritus of computer science at the Vrije Universiteit Amsterdam in the Netherlands.
He is the author of MINIX, a free Unix-like operating system for teaching purposes, and has written multiple computer science textbooks regarded as standard texts in the field. He regards his teaching job as his most important work. Since 2004 he has operated Electoral-vote.com, a website dedicated to analysis of polling data in federal elections in the United States.
Biography.
Tanenbaum was born in New York City and grew up in suburban White Plains, New York, where he attended the White Plains High School. His paternal grandfather was born in Khorostkiv in the Austro-Hungarian empire.
He received his Bachelor of Science degree in physics from MIT in 1965 and his Doctor of Philosophy degree in astrophysics from the University of California, Berkeley in 1971.
|
As an undergraduate, he had obtained experience at computer programming, which helped him get a summer internship at the National Radio Astronomy Observatory in West Virginia. After receiving his doctorate, he decided that he was more interested in programming. He became an assistant professor in Amsterdam based in part on his expertise in programming the university's new computer. He taught courses on Computer Organization and Operating Systems and supervised the work of PhD candidates at the VU University Amsterdam. On July 9, 2014, he announced his retirement. He is married to a Dutch woman, but retains his American citizenship.
Teaching.
Books.
Tanenbaum's textbooks on computer science include:
His book, "Operating Systems: Design and Implementation" and MINIX were Linus Torvalds' inspiration for the Linux kernel. In his autobiography "Just for Fun", Torvalds describes it as "the book that launched me to new heights".
Doctoral students.
Tanenbaum has had a number of PhD students who themselves have gone on to become widely known computer science researchers.
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.