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August 2 | Events | Events |
August 2 | Pre-1600 | Pre-1600
338 BC β A Macedonian army led by Philip II defeated the combined forces of Athens and Thebes in the Battle of Chaeronea, securing Macedonian hegemony in Greece and the Aegean.
216 BC β The Carthaginian army led by Hannibal defeats a numerically superior Roman army at the Battle of Cannae.
49 BC β Caesar, who ... |
August 2 | 1601β1900 | 1601β1900
1610 β During Henry Hudson's search for the Northwest Passage, he sails into what is now known as Hudson Bay.
1776 β The signing of the United States Declaration of Independence took place.
1784 β The first British mail coach service ran from Bristol to London.
1790 β The first United States Census is conduc... |
August 2 | 1901βpresent | 1901βpresent
1903 β The IlindenβPreobrazhenie Uprising against the Ottoman Empire begins.
1914 β The German occupation of Luxembourg during World War I begins.
1916 β World War I: Austrian sabotage causes the sinking of the Italian battleship Leonardo da Vinci in Taranto.
1918 β The first general strike in Canadian his... |
August 2 | Births | Births |
August 2 | Pre-1600 | Pre-1600
1260 β Kyawswa of Pagan, last ruler of the Pagan Kingdom (d. 1299)
1455 β John Cicero, Elector of Brandenburg (d. 1499)
1533 β Theodor Zwinger, Swiss physician and scholar (d. 1588)
1549 β MikoΕaj Krzysztof "the Orphan" RadziwiΕΕ, Polish nobleman (d. 1616) |
August 2 | 1601β1900 | 1601β1900
1612 β Saskia van Uylenburgh, Dutch model and wife of Rembrandt van Rijn (d. 1642)
1627 β Samuel Dirksz van Hoogstraten, Dutch painter (d. 1678)
1630 β Estephan El Douaihy, Maronite patriarch (d. 1704)
1646 β Jean-Baptiste du Casse, French admiral and buccaneer (d. 1715)
1672 β Johann Jakob Scheuchzer, Swiss ... |
August 2 | 1901βpresent | 1901βpresent
1902 β Pope Cyril VI of Alexandria (d. 1971)
1902 β Mina Rees, American mathematician (d. 1997)
1905 β Karl Amadeus Hartmann, German composer (d. 1963)
1905 β Myrna Loy, American actress (d. 1993)
1905 β Ruth Nelson, American actress (d. 1992)"Ruth Nelson". IBDb. Retrieved November 1, 2022.Haun... |
August 2 | Deaths | Deaths |
August 2 | Pre-1600 | Pre-1600
216 BC β Gnaeus Servilius Geminus, Roman consul
216 BC β Lucius Aemilius Paullus, Roman consul and general
216 BC β Marcus Minucius Rufus, Roman consul
257 β Pope Stephen I
575 β Ahudemmeh, Syriac Orthodox Grand Metropolitan of the East.
640 β Pope Severinus
686 β Pope John V
855 β Ahmad ibn Hanbal, A... |
August 2 | 1601β1900 | 1601β1900
1605 β Richard Leveson, English admiral (b. c. 1570)
1611 β KatΕ Kiyomasa, Japanese daimyΕ (b. 1562)
1667 β Francesco Borromini, Swiss architect, designed San Carlo alle Quattro Fontane and Sant'Agnese in Agone (b. 1599)
1696 β Robert Campbell of Glenlyon (b. 1630)
1769 β Daniel Finch, 8th Earl of Winchilsea,... |
August 2 | 1901βpresent | 1901βpresent
1903 β Eduard Magnus Jakobson, Estonian missionary and engraver (b. 1847)
1903 β Edmond Nocard, French veterinarian and microbiologist (b. 1850)
1911 β Ioryi Mucitano, Aromanian revolutionary
1913 β Ferenc Pfaff, Hungarian architect and academic, designed Zagreb Central Station (b. 1851)
1915 β John Do... |
August 2 | Holidays and observances | Holidays and observances
Christian feast day:
Ahudemmeh (Syriac Orthodox Church).
Basil Fool for Christ (Russian Orthodox Church)
Justin Russolillo
Eusebius of Vercelli
Peter Faber
Peter Julian Eymard
Plegmund
Pope Stephen I
Portiuncola Indulgence ("Pardon of Assisi"), the plenary indulgence related to St. Francis of ... |
August 2 | References | References |
August 2 | External links | External links
Category:Days of August |
August 2 | Table of Content | About, Events, Pre-1600, 1601β1900, 1901βpresent, Births, Pre-1600, 1601β1900, 1901βpresent, Deaths, Pre-1600, 1601β1900, 1901βpresent, Holidays and observances, References, External links |
Atlantic (disambiguation) | Wiktionary | The Atlantic Ocean is the second largest of the world's oceans, that separates the old world from the new world.
Atlantic may also refer to: |
Atlantic (disambiguation) | Places | Places |
Atlantic (disambiguation) | In Canada | In Canada
Atlantic, Nova Scotia
Atlantic Canada |
Atlantic (disambiguation) | In the United States | In the United States
Atlantic, Iowa
Atlantic, Massachusetts
Atlantic, North Carolina, an unincorporated community in eastern Carteret County
Atlantic, Pennsylvania
Atlantic, Seattle, a neighborhood in Washington state
Atlantic, Virginia
Atlantic City, New Jersey
Atlantic County, New Jersey
Atlantic Peak (Color... |
Atlantic (disambiguation) | Art, entertainment, and media | Art, entertainment, and media |
Atlantic (disambiguation) | Companies and labels | Companies and labels
Atlantic Books, an independent British publishing house
Atlantic Monthly Press, an American publishing house
Atlantic Entertainment Group, a defunct movie studio company
Atlantic FM, a former radio station serving Cornwall, United Kingdom
Atlantic Records, a record company |
Atlantic (disambiguation) | Music | Music
The Atlantics, an Australian surf rock band formed in the early 1960s |
Atlantic (disambiguation) | Albums | Albums
Atlantic (Dufresne album) |
Atlantic (disambiguation) | Songs | Songs
"Atlantic" (song), by Keane
"Atlantic", a song by BjΓΆrk from Vessel (DVD)
"Atlantic", a song by Thrice from Vheissu
"Atlantic", a song by Sleep Token from This Place Will Become Your Tomb |
Atlantic (disambiguation) | Other art, entertainment, and media | Other art, entertainment, and media
Atlantic (film), a 1929 black and white British film
The Atlantic, an American magazine founded as The Atlantic Monthly in 1857
Atlantic., a 2014 Dutch film
Atlantic (2015 film), an Irish documentary film, awarded Best Irish Documentary at the 2016 Dublin International Film Festiv... |
Atlantic (disambiguation) | Enterprises and organizations | Enterprises and organizations
Atlantic (cinema), a movie theater in Warsaw, Poland
Atlantic (toy company), a defunct Italian toy manufacturer
Atlantic (supermarkets), a defunct supermarket chain in Greece
Atlantic Broadband, a cable company in Massachusetts
Atlantic City Electric, a division of Elexon supplying ele... |
Atlantic (disambiguation) | Sports | Sports
Atlantic Championship Series, developmental open-wheel racing series in North America
Atlantic League of Professional Baseball, an American professional baseball league |
Atlantic (disambiguation) | Structures | Structures
Atlantic Building or Edificio Atlantic, a condominium building in Havana, Cuba
The Atlantic (Atlanta), a skyscraper in Atlanta, Georgia, United States |
Atlantic (disambiguation) | Transportation | Transportation |
Atlantic (disambiguation) | Airlines | Airlines
Air Atlantic, a Canadian airline
Atlantic Airways, a Faroese airline company |
Atlantic (disambiguation) | Aircraft | Aircraft
Breguet Atlantic, a French long-range maritime patrol aircraft (1961) |
Atlantic (disambiguation) | Motor vehicles | Motor vehicles
Atlantic (1921 automobile), a defunct automobile company
Austin Atlantic, a British car produced by the Austin Motor Company from 1949 to 1952
Fisker Atlantic, a 2012 plug-in electric concept car |
Atlantic (disambiguation) | Railroads and trains | Railroads and trains
Atlantic (locomotive), name of an early steam-powered locomotive of the Baltimore and Ohio Railroad
Atlantic station (Los Angeles Metro)
Atlantic station (Staten Island Railway)
Atlantic (train), a named passenger train operated by Canadian Pacific Railway and later Via Rail
Atlantic, a type o... |
Atlantic (disambiguation) | Ships | Ships
, any one of several vessels by that name
Atlantic (yacht), a three-masted gaff-rigged schooner
Atlantic 85-class lifeboats, lifeboats that serve the shores of the United Kingdom and Ireland as a part of the RNLI inshore fleet |
Atlantic (disambiguation) | Other uses | Other uses
Atlantic (period) of palaeoclimatology
Atlantic languages (formerly West Atlantic), a language family in West Africa
Atlantic (horse), British-bred Thoroughbred racehorse of the 1870s |
Atlantic (disambiguation) | See also | See also
Atlantik (disambiguation)
Atlantique (disambiguation)
Atlantic Beach (disambiguation)
Atlantic Bridge (disambiguation)
Atlantic City (disambiguation) |
Atlantic (disambiguation) | Table of Content | Wiktionary, Places, In Canada, In the United States, Art, entertainment, and media, Companies and labels, Music, Albums, Songs, Other art, entertainment, and media, Enterprises and organizations, Sports, Structures, Transportation, Airlines, Aircraft, Motor vehicles, Railroads and trains, Ships, Other uses, See also |
Algebraic number | Short description | thumb|200px|The square root of 2 is an algebraic number equal to the length of the hypotenuse of a right triangle with legs of length 1.
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is a... |
Algebraic number | Examples | Examples
All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, because is the root of a non-zero polynomial, namely .Some of the following examples come from
Quadratic irrational numbers, irrational solutio... |
Algebraic number | <span class="anchor" id="Degree of an algebraic number"></span> Properties | Properties
thumb|Algebraic numbers on the complex plane colored by degree (bright orange/red = 1, green = 2, blue = 3, yellow = 4). The larger points come from polynomials with smaller integer coefficients.
If a polynomial with rational coefficients is multiplied through by the least common denominator, the resulting... |
Algebraic number | Degree of simple extensions of the rationals as a criterion to algebraicity | Degree of simple extensions of the rationals as a criterion to algebraicity
For any , the simple extension of the rationals by , denoted by , is of finite degree if and only if is an algebraic number.
The condition of finite degree means that there is a finite set in such that ; that is, every member in can be wri... |
Algebraic number | Field | Field
thumb|Algebraic numbers colored by degree (blue = 4, cyan = 3, red = 2, green = 1). The unit circle is black.
The sum, difference, product, and quotient (if the denominator is nonzero) of two algebraic numbers is again algebraic:
For any two algebraic numbers , , this follows directly from the fact that the simp... |
Algebraic number | Algebraic closure | Algebraic closure
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic. That can be rephrased by saying that the field of algebraic numbers is algebraically closed. In fact, it is the smallest algebraically closed field containing the rationals and so it is called the algebrai... |
Algebraic number | Related fields | Related fields |
Algebraic number | Numbers defined by radicals | Numbers defined by radicals
Any number that can be obtained from the integers using a finite number of additions, subtractions, multiplications, divisions, and taking (possibly complex) th roots where is a positive integer are algebraic. The converse, however, is not true: there are algebraic numbers that cannot be ob... |
Algebraic number | Closed-form number | Closed-form number
Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers. One may generalize this to "closed-form numbers", which may be defined in various ways. Most broadly, all numbers that can be defined explicitly or implicitly i... |
Algebraic number | Algebraic integers | Algebraic integers
thumb|Visualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate the leading integer coefficient of the polynomial the number is a root of (red = 1 i.e. the algebraic integers, green = 2, blue = 3, yellow = 4...). Points becomes smaller as the other coefficient... |
Algebraic number | Special classes | Special classes
Algebraic solution
Gaussian integer
Eisenstein integer
Quadratic irrational number
Fundamental unit
Root of unity
Gaussian period
PisotβVijayaraghavan number
Salem number |
Algebraic number | Notes | Notes |
Algebraic number | References | References
|
Algebraic number | Table of Content | Short description, Examples, <span class="anchor" id="Degree of an algebraic number"></span> Properties, Degree of simple extensions of the rationals as a criterion to algebraicity, Field, Algebraic closure, Related fields, Numbers defined by radicals, Closed-form number, Algebraic integers, Special classes, Notes, Ref... |
Automorphism | Short description | thumb|right|400px|An automorphism of the Klein four-group shown as a mapping between two Cayley graphs, a permutation in cycle notation, and a mapping between two Cayley tables.
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a... |
Automorphism | Definition | Definition
In an algebraic structure such as a group, a ring, or vector space, an automorphism is simply a bijective homomorphism of an object into itself. (The definition of a homomorphism depends on the type of algebraic structure; see, for example, group homomorphism, ring homomorphism, and linear operator.)
More ... |
Automorphism | Automorphism group | Automorphism group
The automorphisms of an object form a group under composition of morphisms, which is called the automorphism group of . This results straightforwardly from the definition of a category.
The automorphism group of an object in a category is often denoted , or simply Aut(X) if the category is clear... |
Automorphism | Examples | Examples
In set theory, an arbitrary permutation of the elements of a set X is an automorphism. The automorphism group of X is also called the symmetric group on X.
In elementary arithmetic, the set of integers, , considered as a group under addition, has a unique nontrivial automorphism: negation. Considered as a ri... |
Automorphism | History | History
One of the earliest group automorphisms (automorphism of a group, not simply a group of automorphisms of points) was given by the Irish mathematician William Rowan Hamilton in 1856, in his icosian calculus, where he discovered an order two automorphism, writing:
so that is a new fifth root of unity, connected ... |
Automorphism | Inner and outer automorphisms | Inner and outer automorphisms
In some categoriesβnotably groups, rings, and Lie algebrasβit is possible to separate automorphisms into two types, called "inner" and "outer" automorphisms.
In the case of groups, the inner automorphisms are the conjugations by the elements of the group itself. For each element a of a g... |
Automorphism | See also | See also
Antiautomorphism
Automorphism (in Sudoku puzzles)
Characteristic subgroup
Endomorphism ring
Frobenius automorphism
Morphism
Order automorphism (in order theory).
Relation-preserving automorphism
Fractional Fourier transform |
Automorphism | References | References |
Automorphism | External links | External links
Automorphism at Encyclopaedia of Mathematics
Category:Morphisms
Category:Abstract algebra
Category:Symmetry |
Automorphism | Table of Content | Short description, Definition, Automorphism group, Examples, History, Inner and outer automorphisms, See also, References, External links |
Accordion | short description | thumb|upright=1.2|An accordionist
Accordions (from 19th-century German , from β"musical chord, concord of sounds")accordion, entry in Online Etymology Dictionary are a family of box-shaped musical instruments of the bellows-driven free reed aerophone type (producing sound as air flows past a reed in a frame). The essen... |
Accordion | History | History
thumb|left|Eight-key bisonoric diatonic accordion (c. 1830)
The accordion's basic form is believed to have been invented in Berlin, in 1822, by Christian Friedrich Ludwig Buschmann,There is not a single document to back up this belief. Christian Friedrich Ludwig Buschmann was 16 years old at that time; handwri... |
Accordion | Other audio samples | Other audio samples |
Accordion | See also | See also
List of accordionists
Steirische Harmonika
ConfΓ©dΓ©ration internationale des accordΓ©onistes |
Accordion | Notes | Notes |
Accordion | References | References |
Accordion | External links | External links
Category:Folk music instruments
Category:Articles containing video clips
Category:German inventions
Category:19th-century inventions
Category:Symbols of Rio Grande do Sul |
Accordion | Table of Content | short description, History, Other audio samples, See also, Notes, References, External links |
Artificial intelligence | Short description | Artificial intelligence (AI) refers to the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that e... |
Artificial intelligence | Goals | Goals
The general problem of simulating (or creating) intelligence has been broken into subproblems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below have received the most attention and cover the scope of AI research. |
Artificial intelligence | Reasoning and problem-solving | Reasoning and problem-solving
Early researchers developed algorithms that imitated step-by-step reasoning that humans use when they solve puzzles or make logical deductions.Problem-solving, puzzle solving, game playing, and deduction: , (constraint satisfaction), , , By the late 1980s and 1990s, methods were develo... |
Artificial intelligence | Knowledge representation | Knowledge representation
thumb|upright=1.2|An ontology represents knowledge as a set of concepts within a domain and the relationships between those concepts.
Knowledge representation and knowledge engineeringKnowledge representation and knowledge engineering: , , , allow AI programs to answer questions intelligent... |
Artificial intelligence | Planning and decision-making | Planning and decision-making
An "agent" is anything that perceives and takes actions in the world. A rational agent has goals or preferences and takes actions to make them happen. In automated planning, the agent has a specific goal.Automated planning: . In automated decision-making, the agent has preferencesβthere a... |
Artificial intelligence | Learning | Learning
Machine learning is the study of programs that can improve their performance on a given task automatically.Learning: , , , It has been a part of AI from the beginning.
right|upright=1.4|frameless
There are several kinds of machine learning. Unsupervised learning analyzes a stream of data and finds patterns ... |
Artificial intelligence | Natural language processing | Natural language processing
Natural language processing (NLP)Natural language processing (NLP): , , allows programs to read, write and communicate in human languages such as English. Specific problems include speech recognition, speech synthesis, machine translation, information extraction, information retrieval an... |
Artificial intelligence | Perception | Perception
Machine perception is the ability to use input from sensors (such as cameras, microphones, wireless signals, active lidar, sonar, radar, and tactile sensors) to deduce aspects of the world. Computer vision is the ability to analyze visual input.Computer vision: ,
The field includes speech recognition, i... |
Artificial intelligence | Social intelligence | Social intelligence
thumb|Kismet, a robot head which was made in the 1990s; it is a machine that can recognize and simulate emotions.
Affective computing is a field that comprises systems that recognize, interpret, process, or simulate human feeling, emotion, and mood.Affective computing: , , , For example, some vi... |
Artificial intelligence | General intelligence | General intelligence
A machine with artificial general intelligence should be able to solve a wide variety of problems with breadth and versatility similar to human intelligence.Artificial general intelligence: Proposal for the modern version: Warnings of overspecialization in AI from leading researchers: , , |
Artificial intelligence | Techniques | Techniques
AI research uses a wide variety of techniques to accomplish the goals above. |
Artificial intelligence | Search and optimization | Search and optimization
AI can solve many problems by intelligently searching through many possible solutions.Search algorithms: , , , There are two very different kinds of search used in AI: state space search and local search. |
Artificial intelligence | State space search | State space search
State space search searches through a tree of possible states to try to find a goal state.State space search: For example, planning algorithms search through trees of goals and subgoals, attempting to find a path to a target goal, a process called means-ends analysis.
Simple exhaustive searchesUn... |
Artificial intelligence | Local search | Local search
class=skin-invert-image|thumb|Illustration of gradient descent for 3 different starting points; two parameters (represented by the plan coordinates) are adjusted in order to minimize the loss function (the height) Local search uses mathematical optimization to find a solution to a problem. It begins with... |
Artificial intelligence | Logic | Logic
Formal logic is used for reasoning and knowledge representation.Logic: , ,
Formal logic comes in two main forms: propositional logic (which operates on statements that are true or false and uses logical connectives such as "and", "or", "not" and "implies")Propositional logic: , , and predicate logic (which al... |
Artificial intelligence | Probabilistic methods for uncertain reasoning | Probabilistic methods for uncertain reasoning
class=skin-invert-image|thumb|upright=1.7|A simple Bayesian network, with the associated conditional probability tables
Many problems in AI (including in reasoning, planning, learning, perception, and robotics) require the agent to operate with incomplete or uncertain inf... |
Artificial intelligence | Classifiers and statistical learning methods | Classifiers and statistical learning methods
The simplest AI applications can be divided into two types: classifiers (e.g., "if shiny then diamond"), on one hand, and controllers (e.g., "if diamond then pick up"), on the other hand. ClassifiersStatistical learning methods and classifiers: , are functions that use pat... |
Artificial intelligence | Artificial neural networks | Artificial neural networks
right|thumb|A neural network is an interconnected group of nodes, akin to the vast network of neurons in the human brain.
An artificial neural network is based on a collection of nodes also known as artificial neurons, which loosely model the neurons in a biological brain. It is trained to... |
Artificial intelligence | Deep learning | Deep learning
thumb|upright
Deep learningDeep learning: , , , uses several layers of neurons between the network's inputs and outputs. The multiple layers can progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may ide... |
Artificial intelligence | GPT | GPT
Generative pre-trained transformers (GPT) are large language models (LLMs) that generate text based on the semantic relationships between words in sentences. Text-based GPT models are pretrained on a large corpus of text that can be from the Internet. The pretraining consists of predicting the next token (a token b... |
Artificial intelligence | Hardware and software | Hardware and software
In the late 2010s, graphics processing units (GPUs) that were increasingly designed with AI-specific enhancements and used with specialized TensorFlow software had replaced previously used central processing unit (CPUs) as the dominant means for large-scale (commercial and academic) machine learn... |
Artificial intelligence | Applications | Applications
AI and machine learning technology is used in most of the essential applications of the 2020s, including: search engines (such as Google Search), targeting online advertisements, recommendation systems (offered by Netflix, YouTube or Amazon), driving internet traffic, targeted advertising (AdSense, Faceb... |
Artificial intelligence | Health and medicine | Health and medicine
The application of AI in medicine and medical research has the potential to increase patient care and quality of life. Through the lens of the Hippocratic Oath, medical professionals are ethically compelled to use AI, if applications can more accurately diagnose and treat patients.
For medical res... |
Artificial intelligence | Games | Games
Game playing programs have been used since the 1950s to demonstrate and test AI's most advanced techniques. Deep Blue became the first computer chess-playing system to beat a reigning world chess champion, Garry Kasparov, on 11 May 1997. In 2011, in a Jeopardy! quiz show exhibition match, IBM's question answer... |
Artificial intelligence | Mathematics | Mathematics
Large language models, such as GPT-4, Gemini, Claude, LLaMa or Mistral, are increasingly used in mathematics. These probabilistic models are versatile, but can also produce wrong answers in the form of hallucinations. They sometimes need a large database of mathematical problems to learn from, but also me... |
Artificial intelligence | Finance | Finance
Finance is one of the fastest growing sectors where applied AI tools are being deployed: from retail online banking to investment advice and insurance, where automated "robot advisers" have been in use for some years.Matthew Finio & Amanda Downie: IBM Think 2024 Primer, "What is Artificial Intelligence (AI) i... |
Artificial intelligence | Military | Military
Various countries are deploying AI military applications.PD-notice The main applications enhance command and control, communications, sensors, integration and interoperability. Research is targeting intelligence collection and analysis, logistics, cyber operations, information operations, and semiautonomous... |
Artificial intelligence | Generative AI | Generative AI
thumb|Vincent van Gogh in watercolour created by generative AI software |
Artificial intelligence | Agents | Agents
Artificial intelligent (AI) agents are software entities designed to perceive their environment, make decisions, and take actions autonomously to achieve specific goals. These agents can interact with users, their environment, or other agents. AI agents are used in various applications, including virtual assista... |
Artificial intelligence | Sexuality | Sexuality
Applications of AI in this domain include AI-enabled menstruation and fertility trackers that analyze user data to offer prediction, AI-integrated sex toys (e.g., teledildonics), AI-generated sexual education content, and AI agents that simulate sexual and romantic partners (e.g., Replika). AI is also use... |
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