1.
Euclid
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Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the father of geometry. He was active in Alexandria during the reign of Ptolemy I, in the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, Euclid is the anglicized version of the Greek name Εὐκλείδης, which means renowned, glorious. Very few original references to Euclid survive, so little is known about his life, the date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, the few historical references to Euclid were written centuries after he lived by Proclus c.450 AD and Pappus of Alexandria c.320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements, Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclids Elements, Euclid replied there is no royal road to geometry. This anecdote is questionable since it is similar to a story told about Menaechmus, a detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be completely fictitious, however, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The only reference that historians rely on of Euclid having written the Elements was from Proclus, although best known for its geometric results, the Elements also includes number theory. The geometrical system described in the Elements was long known simply as geometry, today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day and they follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of information in geometrical problems. On Divisions of Figures, which only partially in Arabic translation. It is similar to a first-century AD work by Heron of Alexandria, catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor, phaenomena, a treatise on spherical astronomy, survives in Greek, it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective, in its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth, Things seen under a greater angle appear greater, proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Other works are attributed to Euclid, but have been lost
2.
Electronic Frontier Foundation
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The Electronic Frontier Foundation is an international non-profit digital rights group based in San Francisco, California. In April 1990, Barlow had been visited by a U. S. Federal Bureau of Investigation agent in relation to the theft, Barlow described the visit as complicated by fairly complete unfamiliarity with computer technology. I realized right away that before I could demonstrate my innocence, Barlow felt that his experience was symptomatic of a great paroxysm of governmental confusion during which everyones liberties would become at risk. Barlow posted an account of experience to The WELL online community and was contacted by Mitch Kapor. The pair agreed that there was a need to defend civil liberties on the Internet and this generated a large amount of publicity which led to offers of financial support from John Gilmore and Steve Wozniak. This generated further reaction and support for the ideas of Barlow, in late June, Barlow held a series of dinners in San Francisco with major figures in the computer industry to develop a coherent response to these perceived threats. Barlow considered that, The actions of the FBI and Secret Service were symptoms of a social crisis. America was entering the Information Age with neither laws nor metaphors for the appropriate protection, Barlow felt that to confront this a formal organization would be needed, he hired Cathy Cook as press coordinator, and began to set up what would become the Electronic Frontier Foundation. The Electronic Frontier Foundation was formally founded on July 10,1990, by Kapor and Barlow, who soon after elected Gilmore, Wozniak. Initial funding was provided by Kapor, Wozniak, and an anonymous benefactor, in 1990, Mike Godwin joined the organization as its first staff counsel. Then in 1991, Esther Dyson and Jerry Berman joined the EFF board of directors. C, the creation of the organization was motivated by the massive search and seizure on Steve Jackson Games executed by the United States Secret Service early in 1990. Similar but officially unconnected law-enforcement raids were being conducted across the United States at about time as part of a state–federal task force called Operation Sundevil. However, the Steve Jackson Games case, which became EFFs first high-profile case, was the rallying point around which EFF began promoting computer-. In 1993, their offices moved to 1001 G Street in Washington, more recently, the organization has been involved in defending Edward Felten, Jon Lech Johansen and Dmitry Sklyarov. The organization was located at Mitch Kapors Kapor Enterprises offices in Cambridge. By the fall of 1993, the main EFF offices were consolidated into an office, in Washington. During this time, some of EFFs attention focused on influencing national policy, in 1994, Berman parted ways with EFF and formed the Center for Democracy and Technology, while Drew Taubman briefly took the reins as executive director. There, it took up residence at John Gilmores Toad Hall
3.
Leonhard Euler
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He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, Euler was one of the most eminent mathematicians of the 18th century, and is held to be one of the greatest in history. He is also considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field and he spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Eulers influence on mathematics, Read Euler, read Euler, Leonhard Euler was born on 15 April 1707, in Basel, Switzerland to Paul III Euler, a pastor of the Reformed Church, and Marguerite née Brucker, a pastors daughter. He had two sisters, Anna Maria and Maria Magdalena, and a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, Paul Euler was a friend of the Bernoulli family, Johann Bernoulli was then regarded as Europes foremost mathematician, and would eventually be the most important influence on young Leonhard. Eulers formal education started in Basel, where he was sent to live with his maternal grandmother. In 1720, aged thirteen, he enrolled at the University of Basel, during that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupils incredible talent for mathematics. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono, at that time, he was unsuccessfully attempting to obtain a position at the University of Basel. In 1727, he first entered the Paris Academy Prize Problem competition, Pierre Bouguer, who became known as the father of naval architecture, won and Euler took second place. Euler later won this annual prize twelve times, around this time Johann Bernoullis two sons, Daniel and Nicolaus, were working at the Imperial Russian Academy of Sciences in Saint Petersburg. In November 1726 Euler eagerly accepted the offer, but delayed making the trip to Saint Petersburg while he applied for a physics professorship at the University of Basel. Euler arrived in Saint Petersburg on 17 May 1727 and he was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he worked in close collaboration. Euler mastered Russian and settled life in Saint Petersburg. He also took on a job as a medic in the Russian Navy. The Academy at Saint Petersburg, established by Peter the Great, was intended to improve education in Russia, as a result, it was made especially attractive to foreign scholars like Euler
4.
Electronic delay storage automatic calculator
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Electronic delay storage automatic calculator was an early British computer. EDSAC was the electronic digital stored-program computer to go into regular service. Later the project was supported by J. Lyons & Co. Ltd. a British firm, work on EDSAC started during 1947, and it ran its first programs on 6 May 1949, when it calculated a table of squares and a list of prime numbers. EDSAC1 was finally shut down on 11 July 1958, having been superseded by EDSAC2, as soon as EDSAC was operational, it began serving the Universitys research needs. It used mercury delay lines for memory, and derated vacuum tubes for logic, cycle time was 1.5 ms for all ordinary instructions,6 ms for multiplication. Input was via five-hole punched tape and output was via a teleprinter, initially registers were limited to an accumulator and a multiplier register. In 1953, David Wheeler, returning from a stay at the University of Illinois, a magnetic tape drive was added in 1952 but never worked sufficiently well to be of real use. Until 1952, the main memory was only 512 18-bit words. The delay lines were arranged in two batteries providing 512 words each, the second battery came into operation in 1952. The full 1024-word delay line store was not available until 1955 or early 1956, the EDSACs main memory consisted of 1024 locations, though only 512 locations were initially installed. Each contained 18 bits, but the topmost bit was always due to timing problems. An instruction consisted of a five-bit instruction code, one bit, a ten bit operand. Numbers were either 17 bits or 35 bits long, unusually, the multiplier was designed to treat numbers as fixed-point fractions in the range −1 ≤ x <1, i. e. the binary point was immediately to the right of the sign. The accumulator could hold 71 bits, including the sign, allowing two long numbers to be multiplied without losing any precision, there was no division instruction and no way to directly load a number into the accumulator. There was no unconditional jump instruction, nor was there a call instruction - it had not yet been invented. The initial orders were hard-wired on a set of uniselector switches, by May 1949, the initial orders provided a primitive relocating assembler taking advantage of the mnemonic design described above, all in 31 words. This was the worlds first assembler, and arguably the start of the software industry. There is a simulation of EDSAC available and a description of the initial orders
5.
Time (magazine)
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Time is an American weekly news magazine published in New York City. It was founded in 1923 and for decades was dominated by Henry Luce, a European edition is published in London and also covers the Middle East, Africa and, since 2003, Latin America. An Asian edition is based in Hong Kong, the South Pacific edition, which covers Australia, New Zealand and the Pacific Islands, is based in Sydney, Australia. In December 2008, Time discontinued publishing a Canadian advertiser edition, Time has the worlds largest circulation for a weekly news magazine, and has a readership of 26 million,20 million of which are based in the United States. As of 2012, it had a circulation of 3.3 million making it the eleventh most circulated magazine in the United States reception room circuit, as of 2015, its circulation was 3,036,602. Richard Stengel was the editor from May 2006 to October 2013. Nancy Gibbs has been the editor since October 2013. Time magazine was created in 1923 by Briton Hadden and Henry Luce, the two had previously worked together as chairman and managing editor respectively of the Yale Daily News. They first called the proposed magazine Facts and they wanted to emphasize brevity, so that a busy man could read it in an hour. They changed the name to Time and used the slogan Take Time–Its Brief and it set out to tell the news through people, and for many decades the magazines cover depicted a single person. More recently, Time has incorporated People of the Year issues which grew in popularity over the years, notable mentions of them were Barack Obama, Steve Jobs, Matej Turk, etc. The first issue of Time was published on March 3,1923, featuring Joseph G. Cannon, the retired Speaker of the House of Representatives, on its cover, a facsimile reprint of Issue No. 1, including all of the articles and advertisements contained in the original, was included with copies of the February 28,1938 issue as a commemoration of the magazines 15th anniversary. The cover price was 15¢ On Haddens death in 1929, Luce became the dominant man at Time, the Intimate History of a Publishing Enterprise 1923–1941. In 1929, Roy Larsen was also named a Time Inc. director, J. P. Morgan retained a certain control through two directorates and a share of stocks, both over Time and Fortune. Other shareholders were Brown Brothers W. A. Harriman & Co. the Intimate History of a Changing Enterprise 1957–1983. According to the September 10,1979 issue of The New York Times, after Time magazine began publishing its weekly issues in March 1923, Roy Larsen was able to increase its circulation by utilizing U. S. radio and movie theaters around the world. It often promoted both Time magazine and U. S. political and corporate interests, Larsen next arranged for a 30-minute radio program, The March of Time, to be broadcast over CBS, beginning on March 6,1931
6.
2,147,483,647
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The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 −1. It is one of four known double Mersenne primes. The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772, Euler used trial division, improving on Cataldis method, so that at most 372 divisions were needed. It thus improved upon the previous record-holding prime,6,700,417, also discovered by Euler, the number 2,147,483,647 remained the largest known prime until 1867. He repeated this prediction in his 1814 work A New Mathematical and Philosophical Dictionary, in fact a larger prime was discovered in 1855 by Thomas Clausen, though a proof was not provided. Furthermore,3,203,431,780,337 was proven to be prime in 1867, the number 2,147,483,647 is the maximum positive value for a 32-bit signed binary integer in computing. It is therefore the value for variables declared as integers in many programming languages. The appearance of the number often reflects an error, overflow condition, google later admitted that this was a joke. The data type time_t, used on operating systems such as Unix, is a signed integer counting the number of seconds since the start of the Unix epoch, and is often implemented as a 32-bit integer. The latest time that can be represented in this form is 03,14,07 UTC on Tuesday,19 January 2038 and this means that systems using a 32-bit time_t type are susceptible to the Year 2038 problem. Also, this number is in most browsers the highest to accept positive or negative z-index in Cascading Style Sheets, power of two Prime curios,2147483647
7.
Pietro Cataldi
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Pietro Antonio Cataldi was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems and his work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclids fifth postulate, Cataldi discovered the sixth and seventh primes later to acquire the designation Mersenne primes by 1588. Although Cataldi also claimed that p=23,29,31 and 37 all also generate Mersenne primes, oConnor, John J. Robertson, Edmund F. Pietro Cataldi, MacTutor History of Mathematics archive, University of St Andrews
8.
Thomas Clausen (mathematician)
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For the Louisiana educator, see Thomas Clausen. Thomas Clausen was a Danish mathematician and astronomer and he eventually returned to Munich, where he conceived and published his best known works on mathematics. In 1842 Clausen was hired by the staff of the Tartu Observatory, works by Clausen include studies on the stability of Solar system, comet movement, ABC telegraph code and calculation of 250 decimals of Pi. In 1840 he discovered the Von Staudt–Clausen theorem, in 1854 he factored the sixth Fermat number as 264+1 =67280421310721 ×274177. Von Staudt–Clausen theorem Clausens formula Clausen function Biermann, Kurt-R, edward, Euler at 300, MAA Spectrum, Washington, DC, Math. America, pp. 217–225, ISBN 978-0-88385-565-2, MR2349552 Biography
9.
Computer Laboratory, University of Cambridge
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The Computer Laboratory is the computer science department of the University of Cambridge. As of 2007, it employs 35 academic staff,25 support staff,35 affiliated research staff, the current head of department is Professor Andy Hopper. The new laboratory was housed in the North Wing of the former Anatomy School, upon its foundation, it was intended to provide a computing service for general use, and to be a centre for the development of computational techniques in the University. The Cambridge Diploma in Computer Science was the world’s first postgraduate course in computing, starting in 1953. It inspired the world’s first business computer, LEO and it was replaced by EDSAC2, the first microcoded and bitsliced computer, in 1958. In 1961, David Hartley developed Autocode, one of the first high-level programming languages, also in that year, proposals for Titan, based on the Ferranti Atlas machine, were developed. Titan became fully operational in 1964 and EDSAC2 was retired the following year, in 1967, a full multi-user time-shared service for up to 64 users was inaugurated on Titan. In 2002, the Computer Laboratory launched the Cambridge Computer Lab Ring, the Computer Laboratory built and operated the world’s first fully operational practical stored program computer and offered the world’s first postgraduate taught course in computer science in 1953. It currently offers a 3-year undergraduate course and a 1-year masters course, members of the Computer Laboratory have been involved in the creation of many successful UK IT companies such as Acorn, ARM, nCipher and XenSource. A number of companies have been founded by staff and graduates and their names were featured in the new laboratory entrance in 2012. Some cited examples of companies are ARM, Autonomy, Aveva, CSR. One common factor they share is that key staff or founder members are drenched in university training, the Cambridge Computer Lab Ring was praised for its tireless work by Andy Hopper in 2012, at its tenth anniversary dinner. Ian Pratt Simon Crosby David L Tennenhouse Michael Burrows Andy Harter Andy Hopper
10.
Prime number
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A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a number is called a composite number. For example,5 is prime because 1 and 5 are its only positive integer factors, the property of being prime is called primality. A simple but slow method of verifying the primality of a number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and n, algorithms much more efficient than trial division have been devised to test the primality of large numbers. Particularly fast methods are available for numbers of forms, such as Mersenne numbers. As of January 2016, the largest known prime number has 22,338,618 decimal digits, there are infinitely many primes, as demonstrated by Euclid around 300 BC. There is no simple formula that separates prime numbers from composite numbers. However, the distribution of primes, that is to say, many questions regarding prime numbers remain open, such as Goldbachs conjecture, and the twin prime conjecture. Such questions spurred the development of branches of number theory. Prime numbers give rise to various generalizations in other domains, mainly algebra, such as prime elements. A natural number is called a number if it has exactly two positive divisors,1 and the number itself. Natural numbers greater than 1 that are not prime are called composite, among the numbers 1 to 6, the numbers 2,3, and 5 are the prime numbers, while 1,4, and 6 are not prime. 1 is excluded as a number, for reasons explained below. 2 is a number, since the only natural numbers dividing it are 1 and 2. Next,3 is prime, too,1 and 3 do divide 3 without remainder, however,4 is composite, since 2 is another number dividing 4 without remainder,4 =2 ·2. 5 is again prime, none of the numbers 2,3, next,6 is divisible by 2 or 3, since 6 =2 ·3. The image at the right illustrates that 12 is not prime,12 =3 ·4, no even number greater than 2 is prime because by definition, any such number n has at least three distinct divisors, namely 1,2, and n
11.
Fast Fourier transform
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A fast Fourier transform algorithm computes the discrete Fourier transform of a sequence, or its inverse. Fourier analysis converts a signal from its domain to a representation in the frequency domain. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse factors. As a result, it manages to reduce the complexity of computing the DFT from O, which if one simply applies the definition of DFT, to O. Fast Fourier transforms are used for many applications in engineering, science. The basic ideas were popularized in 1965, but some algorithms had been derived as early as 1805, the DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields but computing it directly from the definition is too slow to be practical. The difference in speed can be enormous, especially for data sets where N may be in the thousands or millions. In practice, the time can be reduced by several orders of magnitude in such cases. The best-known FFT algorithms depend upon the factorization of N, but there are FFTs with O complexity for all N, even for prime N. Since the inverse DFT is the same as the DFT, but with the sign in the exponent. The development of fast algorithms for DFT can be traced to Gausss unpublished work in 1805 when he needed it to interpolate the orbit of asteroids Pallas and Juno from sample observations. His method was similar to the one published in 1965 by Cooley and Tukey. While Gausss work predated even Fouriers results in 1822, he did not analyze the computation time, between 1805 and 1965, some versions of FFT were published by other authors. Yates in 1932 published his version called interaction algorithm, which provided efficient computation of Hadamard, yates algorithm is still used in the field of statistical design and analysis of experiments. In 1942, Danielson and Lanczos published their version to compute DFT for x-ray crystallography, Cooley and Tukey published a more general version of FFT in 1965 that is applicable when N is composite and not necessarily a power of 2. To analyze the output of these sensors, a fast Fourier transform algorithm would be needed, garwin gave Tukeys idea to Cooley for implementation. Cooley and Tukey published the paper in a short six months