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Catalan Constant
In mathematics, Catalan's constant , is defined by : G = \beta(2) = \sum_^ \frac = \frac - \frac + \frac - \frac + \frac - \cdots, where is the Dirichlet beta function. Its numerical value is approximately : It is not known whether is irrational, let alone transcendental. has been called "arguably the most basic constant whose irrationality and transcendence (though strongly suspected) remain unproven". Catalan's constant was named after Eugène Charles Catalan, who found quickly-converging series for its calculation and published a memoir on it in 1865. Uses In low-dimensional topology, Catalan's constant is 1/4 of the volume of an ideal hyperbolic octahedron, and therefore 1/4 of the hyperbolic volume of the complement of the Whitehead link. It is 1/8 of the volume of the complement of the Borromean rings. In combinatorics and statistical mechanics, it arises in connection with counting domino tilings, spanning trees, and Hamiltonian cycles of grid graphs. In number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spanning Tree
In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see about spanning forests below). If all of the edges of ''G'' are also edges of a spanning tree ''T'' of ''G'', then ''G'' is a tree and is identical to ''T'' (that is, a tree has a unique spanning tree and it is itself). Applications Several pathfinding algorithms, including Dijkstra's algorithm and the A* search algorithm, internally build a spanning tree as an intermediate step in solving the problem. In order to minimize the cost of power networks, wiring connections, piping, automatic speech recognition, etc., people often use algorithms that gradually build a spanning tree (or many such trees) as intermediate steps in the process of finding the minimum spanning tree. The Internet and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simon Plouffe
Simon Plouffe (born June 11, 1956) is a mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the ''n''th binary digit of π, in 1995. His other 2022 formula allows extracting the ''n''th digit of in decimal. He was born in Saint-Jovite, Quebec. He co-authored ''The Encyclopedia of Integer Sequences'', made into the web site On-Line Encyclopedia of Integer Sequences dedicated to integer sequences later in 1995. In 1975, Plouffe broke the world record for memorizing digits of π by reciting 4096 digits, a record which stood until 1977. See also *Fabrice Bellard, who discovered in 1997 a faster formula to compute pi. *PiHex PiHex was a distributed computing project organized by Colin Percival to calculate specific bits of . 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. The software used for the project made use of ... Notes External links * * Plouffe website ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Whitbread Lee Glaisher
James Whitbread Lee Glaisher FRS FRSE FRAS (5 November 1848, Lewisham – 7 December 1928, Cambridge), son of James Glaisher and Cecilia Glaisher, was a prolific English mathematician and astronomer. His large collection of (mostly) English ceramics was mostly left to the Fitzwilliam Museum in Cambridge. Life He was born in Lewisham in Kent on 5 November 1848 the son of the eminent astronomer James Glaisher and his wife, Cecilia Louisa Belville. His mother was a noted photographer. He was educated at St Paul's School from 1858. He became somewhat of a school celebrity in 1861 when he made two hot-air balloon ascents with his father to study the stratosphere. He won a Campden Exhibition Scholarship allowing him to study at Trinity College, Cambridge, where he was second wrangler in 1871 and was made a Fellow of the college. Influential in his time on teaching at the University of Cambridge, he is now remembered mostly for work in number theory that anticipated later inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Clausen (mathematician)
Thomas Clausen (16 January 1801, Snogbæk, Sottrup Municipality, Duchy of Schleswig (now Denmark) – 23 May 1885, Dorpat, Imperial Russia (now Estonia)) was a Danish mathematician and astronomer. Clausen learned mathematics at home. In 1820, he became a trainee at the Munich Optical Institute and in 1824, at the Altona Observatory after he showed Heinrich Christian Schumacher his paper on calculating longitude by the occultation of stars by the moon. 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, becoming its director in 1866-1872. Works by Clausen include studies on the stability of Solar System, comet movement, ABC telegraph code and calculation of 250 decimals of pi (later, only 248 were confirmed to be correct). In 1840 he discovered the Von Staudt–Clausen theorem. Also in 1840 he also found two compass and straightedge constructions of lunes w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy & Astrophysics
''Astronomy & Astrophysics'' is a monthly peer-reviewed scientific journal covering theoretical, observational, and instrumental astronomy and astrophysics. The journal is run by a Board of Directors representing 27 sponsoring countries plus a representative of the European Southern Observatory. The journal is published by EDP Sciences and the editor-in-chief is . History Origins ''Astronomy and Astrophysics'' (A&A) was created as an answer to the publishing scenario found in Europe in the 1960s. At that time, multiple journals were being published in several countries around the continent. These journals usually had a limited number of subscribers, and published articles in languages other than English, resulting in a small number of citations compared to American and British journals. Starting in 1963, conversations between astronomers from European countries assessed the need for a common astronomical journal. On 8 April 1968, leading astronomers from Belgium, Denmark, Franc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Astrophysical Journal
''The Astrophysical Journal'', often abbreviated ''ApJ'' (pronounced "ap jay") in references and speech, is a peer-reviewed Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work (peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer review ... scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery Hale and James Edward Keeler. The journal discontinued its print edition and became an electronic-only journal in 2015. Since 1953 ''The Astrophysical Journal Supplement Series'' (''ApJS'') has been published in conjunction with ''The Astrophysical Journal'', with generally longer articles to supplement the material in the journal. It publishes six volumes per year, with two 280-page issues per volume. ''The Astrophysical Journal Letters'' (''ApJL''), established in 1967 by Subrahmanyan Chandrasekhar as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spiral Galaxy
Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''Alt URL pp. 124–151) and, as such, form part of the . Most spiral galaxies consist of a flat, rotating containing s, gas and dust, and a central concentration of stars known as the |
Mass Distribution
In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous. Astronomy In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation. Mathematical modelling A mass distribution can be modeled as a measure. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution. For example, a point mass is represented by a delta function defined in 3-dimensional space. A surface mass on a surface given by the equation may be represented by a density distribution , where g/\left, \nabla f\ is the mass per unit area. The mathematical mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau's Problems
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. They are as follows: # Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes? # Twin prime conjecture: Are there infinitely many primes ''p'' such that ''p'' + 2 is prime? # Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares? # Are there infinitely many primes ''p'' such that ''p'' − 1 is a perfect square? In other words: Are there infinitely many primes of the form ''n''2 + 1? , all four problems are unresolved. Progress toward solutions Goldbach's conjecture Goldbach's weak conjecture, every odd number greater than 5 can be expressed as the sum of three primes, is a consequence of Goldb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ulam Spiral
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's ''Mathematical Games'' column in ''Scientific American'' a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers. Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial ''x''2 − ''x'' + 41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
