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Pi Algorithms
The number (; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining , to avoid relying on the definition of the length of a curve. The number is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as \tfrac are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of appear to be randomly distributed, but no proof of thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constant
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an Letter (alphabet), alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as and pi, occurring in such diverse contexts as geometry, number theory, statistics, and calculus. Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (). Other constants are notable more for historical reasons than for their mathematical properties. The more popular constants have been studied throughout the ages and computed to many decimal places. All named mathematical constants are Definable real number, definable numbers, and usually are also computable numbers (Chaitin's constant being a significant exception). Basic mathematical constants These a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supercomputer
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2022, supercomputers have existed which can perform over 1018 FLOPS, so called Exascale computing, exascale supercomputers. For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013). Since November 2017, all of the TOP500, world's fastest 500 supercomputers run on Linux-based operating systems. Additional research is being conducted in the United States, the European Union, Taiwan, Japan, and China to build faster, more powerful and technologically superior exascale supercomputers. Supercomputers play an important role in the field of computational science, and are used for a wide range of computationally intensive tasks in various fields, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PRIMARY
Primary or primaries may refer to: Arts, entertainment, and media Music Groups and labels * Primary (band), from Australia * Primary (musician), hip hop musician and record producer from South Korea * Primary Music, Israeli record label Works * ''Primary'' (album) by Rubicon (2002) * "Primary" (song) by The Cure * "Primary", song by Spoon from the album '' Telephono'' Other uses in arts, entertainment, and media * Primaries or primary beams, in E. E. Smith's science-fiction series '' Lensman'' * ''Primary'' (film), American political documentary (1960) Computing * PRIMARY, an X Window selection * Primary data storage, computer technology used to retain digital data * Primary server, main server on the server farm Education * Primary education, the first stage of compulsory education * Primary FRCA, academic examination for anaesthetists in the U.K. * Primary school, school providing primary education Mathematics * ''p''-group of prime power order * Primary decom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable. Infinitesimal calculus was formulated separately ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Jones (mathematician)
William Jones, FRS (16751 July 1749) was a Welsh mathematician best known for his use of the symbol (the Greek letter '' Pi'') to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November 1711, Jones became a fellow of the Royal Society, and later served as the Royal Society's vice-president. Early life William Jones was born as the son of Siôn Siôr (John George Jones) and Elizabeth Rowland in the parish of Llanfihangel Tre'r Beirdd, about west of Benllech on the Isle of Anglesey in Wales. He attended a charity school at Llanfechell, also on the Isle of Anglesey, where his mathematical talents were spotted by the local landowner Lord Bulkeley, who arranged for him to work in a merchant's counting-house in London. His main patrons were the Bulkeley family of north Wales, and later the Earl of Macclesfield. Early mathematical career Jones initially served at sea, teaching mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi (letter)
Pi (; Ancient Greek or , uppercase Π, lowercase π, cursive ϖ; ) is the sixteenth letter of the Greek alphabet, representing the voiceless bilabial plosive . In the system of Greek numerals it has a value of 80. It was derived from the Phoenician alphabet, Phoenician letter Pe (Semitic letter), Pe (). Letters that arose from pi include Latin alphabet, Latin P, Cyrillic script, Cyrillic Pe (Cyrillic), Pe (П, п), Coptic alphabet, Coptic pi (Ⲡ, ⲡ), and Gothic alphabet, Gothic pairthra (𐍀). Uppercase Pi The uppercase letter Π is used as a symbol for: * In textual criticism, ''Codex Petropolitanus (New Testament), Codex Petropolitanus'', a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia. * In legal shorthand, it represents a plaintiff. * In Mathematical finance, it represents a portfolio. Greek letters used in mathematics, science, and engineering, In science and engineering: * The product (mathematics), product operator in mathematics, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series (mathematics)
In mathematics, a series is, roughly speaking, an addition of Infinity, infinitely many Addition#Terms, terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical properties of infinite series make them widely applicable in other quantitative disciplines such as physics, computer science, statistics and finance. Among the Ancient Greece, Ancient Greeks, the idea that a potential infinity, potentially infinite summation could produce a finite result was considered paradoxical, most famously in Zeno's paradoxes. Nonetheless, infinite series were applied practically by Ancient Greek mathematicians including Archimedes, for instance in the Quadrature of the Parabola, quadrature of the parabola. The mathematical side of Zeno's paradoxes was resolved using the concept of a limit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava of Sangamagrama, Madhava. The Decimal, decimal number system in use today: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own." was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of 0 (number), ze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Mathematics
Mathematics emerged independently in China by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2, binary and base 10, decimal), algebra, geometry, number theory and trigonometry. Since the Han dynasty, as diophantine approximation being a prominent numerical method, the Chinese made substantial progress on polynomial evaluation. Algorithms like regula falsi and expressions like simple continued fractions are widely used and have been well-documented ever since. They deliberately find the principal nth root, ''n''th root of positive numbers and the zero of a function, roots of equations. The major texts from the period, ''The Nine Chapters on the Mathematical Art'' and the ''Book on Numbers and Computation'' gave detailed processes for solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archimedes
Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenistic Sicily, Sicily. Although few details of his life are known, based on his surviving work, he is considered one of the leading scientists in classical antiquity, and one of the greatest mathematicians of all time. Archimedes anticipated modern calculus and mathematical analysis, analysis by applying the concept of the Cavalieri's principle, infinitesimals and the method of exhaustion to derive and rigorously prove many geometry, geometrical theorem, theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Archimedes' other math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
