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Computer | https://en.wikipedia.org/wiki?curid=7878457 | 61,532 | A computer will solve problems in exactly the way it is programmed to, without regard to efficiency, alternative solutions, possible shortcuts, or possible errors in the code. Computer programs that learn and adapt are part of the emerging field of artificial intelligence and machine learning. Artificial intelligence b... |
J. Robert Oppenheimer | https://en.wikipedia.org/wiki?curid=39034 | 66,432 | In the late 1930s, Oppenheimer became interested in astrophysics, most likely through his friendship with Richard Tolman, resulting in a series of papers. In the first of these, a 1938 paper co-written with Robert Serber entitled "On the Stability of Stellar Neutron Cores", Oppenheimer explored the properties of white ... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,587 | Asperger syndrome (AS), also known as Asperger's, is a former neurodevelopmental disorder characterized by significant difficulties in social interaction and nonverbal communication, along with restricted and repetitive patterns of behaviour and interests. The syndrome is no longer recognised as a diagnosis in itself, ... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,591 | The extent of the overlap between Asperger syndrome and high-functioning autism (HFA – autism unaccompanied by intellectual disability) is unclear. The ASD classification is to some extent an artifact of how autism was discovered, and may not reflect the true nature of the spectrum; methodological problems have beset A... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,595 | People with Asperger syndrome may not be as withdrawn around others, compared with those with other forms of autism; they approach others, even if awkwardly. For example, a person with Asperger syndrome may engage in a one-sided, long-winded speech about a favorite topic, while misunderstanding or not recognizing the l... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,600 | Evidence suggests that in the "double empathy problem model, autistic people have a unique interaction style which is significantly more readable by other autistic people, compared to non-autistic people." People with Asperger syndrome can display behavior, interests, and activities that are restricted and repetitive a... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,606 | Three aspects of communication patterns are of clinical interest: poor prosody, tangential and circumstantial speech, and marked verbosity. Although inflection and intonation may be less rigid or monotonic than in classic autism, people with AS often have a limited range of intonation: speech may be unusually fast, jer... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,610 | Hans Asperger's initial accounts and other diagnostic schemes include descriptions of physical clumsiness. Children with AS may be delayed in acquiring skills requiring dexterity, such as riding a bicycle or opening a jar, and may seem to move awkwardly or feel "uncomfortable in their own skin". They may be poorly coor... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,616 | Neuroanatomical studies and the associations with teratogens strongly suggest that the mechanism includes alteration of brain development soon after conception. Abnormal fetal development may affect the final structure and connectivity of the brain, resulting in altered neural circuits controlling thought and behavior.... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,621 | Underdiagnosis and overdiagnosis may be problems. The cost and difficulty of screening and assessment can delay diagnosis. Conversely, the increasing popularity of drug treatment options and the expansion of benefits has motivated providers to overdiagnose ASD. There are indications AS has been diagnosed more frequentl... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,628 | Managing AS ideally involves multiple therapies that address core symptoms of the disorder. While most professionals agree that the earlier the intervention, the better, there is no treatment combination that is recommended above others. AS treatment resembles that of other high-functioning ASDs, except that it takes i... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,632 | There is some evidence that children with AS may see a lessening of symptoms; up to 20% of children may no longer meet the diagnostic criteria as adults, although social and communication difficulties may persist. , no studies addressing the long-term outcome of individuals with Asperger syndrome are available and ther... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,636 | Anxiety disorders and major depressive disorder are the most common conditions seen at the same time; comorbidity of these in persons with AS is estimated at 65%. Reports have associated AS with medical conditions such as aminoaciduria and ligamentous laxity, but these have been case reports or small studies and no fac... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,639 | Asperger's paper was published during World War II and in German, so it was not widely read elsewhere. Lorna Wing used the term "Asperger syndrome" in 1976, and popularized it to the English-speaking medical community in her February 1981 publication of case studies of children showing the symptoms described by Asperge... |
Asperger syndrome | https://en.wikipedia.org/wiki?curid=37556 | 67,643 | By contrast, Pier Jaarsma and Welin wrote in 2011 that the "broad version of the neurodiversity claim, covering low-functioning as well as high-functioning autism, is problematic. Only a narrow conception of neurodiversity, referring exclusively to high-functioning autists, is reasonable." They say that "higher functio... |
Sukhoi Su-57 | https://en.wikipedia.org/wiki?curid=2971192 | 68,326 | The Su-57 is a fifth-generation multirole fighter aircraft and the first operational stealth aircraft for the Russian armed forces. In addition to stealth, the fighter emphasizes supermaneuverability in all aircraft axes, capacious internal payload bays for multirole versatility, and advanced sensor systems such as act... |
International Phonetic Alphabet | https://en.wikipedia.org/wiki?curid=14761 | 70,847 | Diphthongs are typically specified with a non-syllabic diacritic, as in or , or with a superscript for the on- or off-glide, as in or . Sometimes a tie bar is used: , especially if it is difficult to tell if the diphthong is characterized by an on-glide, an off-glide or is variable. |
2021 Formula One World Championship | https://en.wikipedia.org/wiki?curid=57373873 | 87,210 | The "dual-axis steering" (DAS) system developed by Mercedes in 2020 was banned, starting from 2021. The DAS system allowed the driver to adjust the toe of the front wheels to optimise mechanical grip by pulling or pushing on the steering wheel. The FIA introduced newly revised wing load tests mid-season at the French G... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,415 | The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radiation, and is the most important source of energy for life on Earth. The Sun's ra... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,420 | The English word "sun" developed from Old English . Cognates appear in other Germanic languages, including West Frisian , Dutch , Low German , Standard German , Bavarian , Old Norse , and Gothic . All these words stem from Proto-Germanic . This is ultimately related to the word for "sun" in other branches of the Indo-E... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,424 | The Sun is by far the brightest object in the Earth's sky, with an apparent magnitude of −26.74. This is about 13 billion times brighter than the next brightest star, Sirius, which has an apparent magnitude of −1.46. The Sun does not have a definite boundary, but its density decreases exponentially with increasing heig... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,428 | Since the Sun formed, the main fusion process has involved fusing hydrogen into helium. Over the past 4.6 billion years, the amount of helium and its location within the Sun has gradually changed. Within the core, the proportion of helium has increased from about 24% to about 60% due to fusion, and some of the helium a... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,432 | The proton–proton chain occurs around times each second in the core, converting about 3.7 protons into alpha particles (helium nuclei) every second (out of a total of ~8.9 free protons in the Sun), or about . However, each proton (on average) takes around 9 billion years to fuse with one another using the PP chain. Fus... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,435 | The radiative zone and the convective zone are separated by a transition layer, the tachocline. This is a region where the sharp regime change between the uniform rotation of the radiative zone and the differential rotation of the convection zone results in a large shear between the two—a condition where successive hor... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,439 | The photosphere is tens to hundreds of kilometers thick, and is slightly less opaque than air on Earth. Because the upper part of the photosphere is cooler than the lower part, an image of the Sun appears brighter in the center than on the edge or "limb" of the solar disk, in a phenomenon known as limb darkening. The s... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,445 | The corona is the next layer of the Sun. The low corona, near the surface of the Sun, has a particle density around 10 m to 10 m. The average temperature of the corona and solar wind is about 1,000,000–2,000,000 K; however, in the hottest regions it is 8,000,000–20,000,000 K. Although no complete theory yet exists to a... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,449 | The Sun emits light across the visible spectrum, so its color is white, with a CIE color-space index near (0.3, 0.3), when viewed from space or when the Sun is high in the sky. The Solar radiance per wavelength peaks in the green portion of the spectrum when viewed from space. When the Sun is very low in the sky, atmos... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,453 | Neutrinos are also released by the fusion reactions in the core, but, unlike photons, they rarely interact with matter, so almost all are able to escape the Sun immediately. For many years measurements of the number of neutrinos produced in the Sun were lower than theories predicted by a factor of 3. This discrepancy w... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,458 | An 11-year sunspot cycle is half of a 22-year Babcock–Leighton dynamo cycle, which corresponds to an oscillatory exchange of energy between toroidal and poloidal solar magnetic fields. At solar-cycle maximum, the external poloidal dipolar magnetic field is near its dynamo-cycle minimum strength, but an internal toroida... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,462 | In December 2019, a new type of solar magnetic explosion was observed, known as forced magnetic reconnection. Previously, in a process called spontaneous magnetic reconnection, it was observed that the solar magnetic field lines diverge explosively and then converge again instantaneously. Forced Magnetic Reconnection w... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,466 | The Sun is gradually becoming hotter in its core, hotter at the surface, larger in radius, and more luminous during its time on the main sequence: since the beginning of its main sequence life, it has expanded in radius by 15% and the surface has increased in temperature from to , resulting in a 48% increase in luminos... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,469 | When the helium is exhausted, the Sun will repeat the expansion it followed when the hydrogen in the core was exhausted. This time, however, it all happens faster, and the Sun becomes larger and more luminous, engulfing Venus if it has not already. This is the asymptotic-giant-branch phase, and the Sun is alternately r... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,473 | The Sun is moved by the gravitational pull of the planets. The center of the Sun is always within 2.2 solar radii of the barycenter. This motion of the Sun is mainly due to Jupiter, Saturn, Uranus, and Neptune. For some periods of several decades, the motion is rather regular, forming a trefoil pattern, whereas between... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,477 | The theory that the Sun is the center around which the planets orbit was first proposed by the ancient Greek Aristarchus of Samos in the third century BC, and later adopted by Seleucus of Seleucia (see Heliocentrism). This view was developed in a more detailed mathematical model of a heliocentric system in the 16th cen... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,483 | Not until 1904 was a documented solution offered. Ernest Rutherford suggested that the Sun's output could be maintained by an internal source of heat, and suggested radioactive decay as the source. However, it would be Albert Einstein who would provide the essential clue to the source of the Sun's energy output with hi... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,487 | Various authors have considered the existence of a gradient in the isotopic compositions of solar and planetary noble gases, e.g. correlations between isotopic compositions of neon and xenon in the Sun and on the planets. Prior to 1983, it was thought that the whole Sun has the same composition as the solar atmosphere.... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,492 | Elemental abundances in the photosphere are well known from spectroscopic studies, but the composition of the interior of the Sun is more poorly understood. A solar wind sample return mission, "Genesis", was designed to allow astronomers to directly measure the composition of solar material. The temperature of the phot... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,498 | The brightness of the Sun can cause pain from looking at it with the naked eye; however, doing so for brief periods is not hazardous for normal non-dilated eyes. Looking directly at the Sun (sungazing) causes phosphene visual artifacts and temporary partial blindness. It also delivers about 4 milliwatts of sunlight to ... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,503 | The ancient Sumerians believed that the Sun was Utu, the god of justice and twin brother of Inanna, the Queen of Heaven, who was identified as the planet Venus. Later, Utu was identified with the East Semitic god Shamash. Utu was regarded as a helper-deity, who aided those in distress, and, in iconography, he is usuall... |
Sun | https://en.wikipedia.org/wiki?curid=26751 | 93,508 | Tonatiuh, the Aztec god of the sun, was usually depicted holding arrows and a shield and was closely associated with the practice of human sacrifice. The sun goddess Amaterasu is the most important deity in the Shinto religion, and she is believed to be the direct ancestor of all Japanese emperors. |
Ludwig van Beethoven | https://en.wikipedia.org/wiki?curid=17914 | 95,912 | The Beethoven Monument in Bonn was unveiled in August 1845, in honour of the 75th anniversary of his birth. It was the first statue of a composer created in Germany, and the music festival that accompanied the unveiling was the impetus for the very hasty construction of the original Beethovenhalle in Bonn (it was desig... |
ISO 4217 | https://en.wikipedia.org/wiki?curid=15403 | 100,468 | ISO 4217 is a standard published by the International Organization for Standardization (ISO) that defines alpha codes and numeric codes for the representation of currencies and provides information about the relationships between individual currencies and their minor units. This data is published in three tables: |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,259 | Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,261 | In 1919, ill health—now believed to have been hepatic amoebiasis (a complication from episodes of dysentery many years previously)—compelled Ramanujan's return to India, where he died in 1920 at the age of 32. His last letters to Hardy, written in January 1920, show that he was still continuing to produce new mathemati... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,265 | Since Ramanujan's father was at work most of the day, his mother took care of the boy, and they had a close relationship. From her, he learned about tradition and puranas, to sing religious songs, to attend pujas at the temple, and to maintain particular eating habits—all part of Brahmin culture. At Kangayan Primary Sc... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,269 | In 1910, after a meeting between the 23-year-old Ramanujan and the founder of the Indian Mathematical Society, V. Ramaswamy Aiyer, Ramanujan began to get recognition in Madras's mathematical circles, leading to his inclusion as a researcher at the University of Madras. On 14 July 1909, Ramanujan married Janaki (Janakia... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,275 | I was struck by the extraordinary mathematical results contained in [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department. Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends in Madras. Some of them looked at his work and gave h... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,280 | Mr. Ramanujan's methods were so terse and novel and his presentation so lacking in clearness and precision, that the ordinary [mathematical reader], unaccustomed to such intellectual gymnastics, could hardly follow him. Ramanujan later wrote another paper and also continued to provide problems in the "Journal". In earl... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,285 | The first two professors, H. F. Baker and E. W. Hobson, returned Ramanujan's papers without comment. On 16 January 1913, Ramanujan wrote to G. H. Hardy. Coming from an unknown mathematician, the nine pages of mathematics made Hardy initially view Ramanujan's manuscripts as a possible fraud. Hardy recognised some of Ram... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,289 | While he was engaged as a research student, Ramanujan continued to submit papers to the "Journal of the Indian Mathematical Society." In one instance, Iyer submitted some of Ramanujan's theorems on summation of series to the journal, adding, "The following theorem is due to S. Ramanujan, the mathematics student of Madr... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,293 | Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood, and published part of his findings there. Hardy and Ramanujan had highly contrasting personalities. Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades, the foundations of ... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,298 | A 1994 analysis of Ramanujan's medical records and symptoms by Dr. D. A. B. Young concluded that his medical symptoms—including his past relapses, fevers, and hepatic conditions—were much closer to those resulting from hepatic amoebiasis, an illness then widespread in Madras, than tuberculosis. He had two episodes of d... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,303 | This result is based on the negative fundamental discriminant with class number . Further, and , which is related to the fact that Ramanujan's series for converges extraordinarily rapidly and forms the basis of some of the fastest algorithms currently used to calculate . Truncating the sum to the first term also gives ... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,311 | While still in Madras, Ramanujan recorded the bulk of his results in four notebooks of looseleaf paper. They were mostly written up without any derivations. This is probably the origin of the misapprehension that Ramanujan was unable to prove his results and simply thought up the final result directly. Mathematician Br... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,319 | When asked about the methods Ramanujan employed to arrive at his solutions, Hardy said they were "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account." He also said that he had "never met his equal, and can compare him only with Euler or Ja... |
Srinivasa Ramanujan | https://en.wikipedia.org/wiki?curid=47717 | 103,324 | In 2011, on the 125th anniversary of his birth, the Indian government declared that 22 December will be celebrated every year as "National Mathematics Day". Then Indian Prime Minister Manmohan Singh also declared that 2012 would be celebrated as National Mathematics Year. Ramanujan IT City is an information technology ... |
World Wide Web | https://en.wikipedia.org/wiki?curid=33139 | 105,967 | HTML can embed programs written in a scripting language such as JavaScript, which affects the behavior and content of web pages. Inclusion of CSS defines the look and layout of content. The World Wide Web Consortium (W3C), maintainer of both the HTML and the CSS standards, has encouraged the use of CSS over explicit pr... |
Aristotle | https://en.wikipedia.org/wiki?curid=308 | 106,256 | Near the end of his life, Alexander and Aristotle became estranged over Alexander's relationship with Persia and Persians. A widespread tradition in antiquity suspected Aristotle of playing a role in Alexander's death, but the only evidence of this is an unlikely claim made some six years after the death. Following Ale... |
Software | https://en.wikipedia.org/wiki?curid=5309 | 112,362 | Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists of machine language instructions supported by an individual processor—typically a ... |
Software | https://en.wikipedia.org/wiki?curid=5309 | 112,368 | Programming tools are also software in the form of programs or applications that developers use to create, debug, maintain, or otherwise support software. Software is written in one or more programming languages; there are many programming languages in existence, and each has at least one implementation, each of which ... |
Software | https://en.wikipedia.org/wiki?curid=5309 | 112,375 | The software's license gives the user the right to use the software in the licensed environment, and in the case of free software licenses, also grants other rights such as the right to make copies. Open-source software comes with a free software license, granting the recipient the rights to modify and redistribute the... |
Software | https://en.wikipedia.org/wiki?curid=5309 | 112,381 | Data structures such as hash tables, arrays, and binary trees, and algorithms such as quicksort, can be useful for creating software. Computer software has special economic characteristics that make its design, creation, and distribution different from most other economic goods. A person who creates software is called ... |
Maslow's hierarchy of needs | https://en.wikipedia.org/wiki?curid=163131 | 113,496 | At the time of its original publication in 1943, there was no empirical evidence to support the theory. In a 1976 review of Maslow's hierarchy of needs, little evidence was found for the specific ranking of needs that Maslow described or for the existence of a definite hierarchy at all. This refutation was claimed to b... |
Neil Armstrong | https://en.wikipedia.org/wiki?curid=21247 | 114,313 | Armstrong's regular commission was terminated on February 25, 1952, and he became an ensign in the United States Navy Reserve. On completion of his combat tour with "Essex", he was assigned to a transport squadron, VR-32, in May 1952. He was released from active duty on August 23, 1952, but remained in the reserve, and... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,155 | The number (; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integ... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,159 | The symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase Greek letter, sometimes spelled out as "pi." In English, is pronounced as "pie" ( ). In mathematical use, the lowercase letter is distinguished from its capitalized and enlarged counterpart , which deno... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,166 | is an irrational number, meaning that it cannot be written as the ratio of two integers. Fractions such as and are commonly used to approximate , but no common fraction (ratio of whole numbers) can be its exact value. Because is irrational, it has an infinite number of digits in its decimal representation, and does not... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,171 | Like all irrational numbers, cannot be represented as a common fraction (also known as a simple or vulgar fraction), by the very definition of irrational number (i.e., not a rational number). But every irrational number, including , can be represented by an infinite series of nested fractions, called a continued fracti... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,179 | In the Shulba Sutras of Indian mathematics, dating to an oral tradition from the first or second millennium BC, approximations are given which have been variously interpreted as approximately 3.08831, 3.08833, 3.004, 3, or 3.125. The first recorded algorithm for rigorously calculating the value of was a geometrical app... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,182 | The Indian astronomer Aryabhata used a value of 3.1416 in his "Āryabhaṭīya" (499 AD). Fibonacci in c. 1220 computed 3.1418 using a polygonal method, independent of Archimedes. Italian author Dante apparently employed the value . The Persian astronomer Jamshīd al-Kāshī produced 9 sexagesimal digits, roughly the equivale... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,185 | In 1593, François Viète published what is now known as Viète's formula, an infinite product (rather than an infinite sum, which is more typically used in calculations): In the 1660s, the English scientist Isaac Newton and German mathematician Gottfried Wilhelm Leibniz discovered calculus, which led to the development o... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,194 | An infinite series for (published by Nilakantha in the 15th century) that converges more rapidly than the Gregory–Leibniz series is: After five terms, the sum of the Gregory–Leibniz series is within 0.2 of the correct value of , whereas the sum of Nilakantha's series is within 0.002 of the correct value. Nilakantha's s... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,200 | Euler started using the single-letter form beginning with his 1727 "Essay Explaining the Properties of Air", though he used , the ratio of periphery to radius, in this and some later writing. Euler first used in his 1736 work "Mechanica", and continued in his widely-read 1748 work (he wrote: "for the sake of brevity we... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,204 | The iterative algorithms were widely used after 1980 because they are faster than infinite series algorithms: whereas infinite series typically increase the number of correct digits additively in successive terms, iterative algorithms generally "multiply" the number of correct digits at each step. For example, the Bren... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,208 | It produces about 14 digits of per term, and has been used for several record-setting calculations, including the first to surpass 1 billion (10) digits in 1989 by the Chudnovsky brothers, 10 trillion (10) digits in 2011 by Alexander Yee and Shigeru Kondo, and 100 trillion digits by Emma Haruka Iwao in 2022. For simila... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,219 | Another spigot algorithm, the BBP digit extraction algorithm, was discovered in 1995 by Simon Plouffe: This formula, unlike others before it, can produce any individual hexadecimal digit of without calculating all the preceding digits. Individual binary digits may be extracted from individual hexadecimal digits, and oc... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,226 | Definite integrals that describe circumference, area, or volume of shapes generated by circles typically have values that involve . For example, an integral that specifies half the area of a circle of radius one is given by: In that integral the function represents the height over the formula_30-axis of a semicircle (t... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,234 | The number serves appears in similar eigenvalue problems in higher-dimensional analysis. As mentioned above, it can be characterized via its role as the best constant in the isoperimetric inequality: the area enclosed by a plane Jordan curve of perimeter satisfies the inequality Ultimately, as a consequence of the isop... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,244 | The factor of formula_47 makes the area under the graph of equal to one, as is required for a probability distribution. This follows from a change of variables in the Gaussian integral: The central limit theorem explains the central role of normal distributions, and thus of , in probability and statistics. This theorem... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,252 | Special cases include Coulomb's law and Newton's law of universal gravitation. Gauss' law states that the outward flux of the field through any smooth, simple, closed, orientable surface containing the origin is equal to : It is standard to absorb this factor of into the constant , in which case it appears in the numer... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,260 | The general form of Cauchy's integral formula establishes the relationship between the values of a complex analytic function on the Jordan curve and the value of at any interior point of : provided is analytic in the region enclosed by and extends continuously to . Cauchy's integral formula is a special case of the res... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,270 | This probability can be used in conjunction with a random number generator to approximate using a Monte Carlo approach. The solution to the Basel problem implies that the geometrically derived quantity is connected in a deep way to the distribution of prime numbers. This is a special case of Weil's conjecture on Tamaga... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,278 | which is a kind of modular form called a Jacobi form. This is sometimes written in terms of the nome formula_88. The constant is the unique constant making the Jacobi theta function an automorphic form, which means that it transforms in a specific way. Certain identities hold for all automorphic forms. An example is wh... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,286 | The fact that is approximately equal to 3 plays a role in the relatively long lifetime of orthopositronium. The inverse lifetime to lowest order in the fine-structure constant is The field of fluid dynamics contains in Stokes' law, which approximates the frictional force exerted on small, spherical objects of radius , ... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,293 | A few authors have used the digits of to establish a new form of constrained writing, where the word lengths are required to represent the digits of . The "Cadaeic Cadenza" contains the first 3835 digits of in this manner, and the full-length book "Not a Wake" contains 10,000 words, each representing one digit of . Per... |
Pi | https://en.wikipedia.org/wiki?curid=23601 | 115,300 | In 1958 Albert Eagle proposed replacing by (tau), where , to simplify formulas, but this use of is otherwise unknown. Some propose , arguing that , as the number of radians in one turn or the ratio of a circle's circumference to its radius, is more natural than and simplifies many formulas. This use of has not made its... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,766 | A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the eve... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,770 | On 11 February 2016, the LIGO Scientific Collaboration and the Virgo collaboration announced the first direct detection of gravitational waves, representing the first observation of a black hole merger. On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made ... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,774 | In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at ) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who arg... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,778 | In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged. Through the work of Werner Israel, Brandon Carter, and David Ro... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,783 | In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler; Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on, leading some to credit Wheeler with coining the phrase. The no-hair theorem postulates that, once it achieves a stable condit... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,788 | Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,796 | To a distant observer, clocks near a black hole would appear to tick more slowly than those farther away from the black hole. Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it. At the same... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,802 | The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,808 | In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole. The... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,814 | If the mass of the remnant exceeds about (the Tolman–Oppenheimer–Volkoff limit), either because the original star was very heavy or because the remnant collected additional mass through accretion of matter, even the degeneracy pressure of neutrons is insufficient to stop the collapse. No known mechanism (except possibl... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,818 | Despite the early universe being extremely dense—far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for the gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expandi... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,822 | A stellar black hole of has a Hawking temperature of 62 nanokelvins. This is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of ... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,827 | On 10 April 2019, an image was released of a black hole, which is seen magnified because the light paths near the event horizon are highly bent. The dark shadow in the middle results from light paths absorbed by the black hole. The image is in false color, as the detected light halo in this image is not in the visible ... |
Black hole | https://en.wikipedia.org/wiki?curid=4650 | 116,831 | In 2015, the EHT detected magnetic fields just outside the event horizon of Sagittarius A* and even discerned some of their properties. The field lines that pass through the accretion disc were a complex mixture of ordered and tangled. Theoretical studies of black holes had predicted the existence of magnetic fields. O... |
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