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﹃Wolfram MathWorld: The Web's Most Extensive Mathematics Resource﹄
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人気
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すべて
6users
mathworld.wolfram.com
The BBP (named after Bailey-Borwein-Plouffe) is a formula for calculating pi discovered by Simon Plouffe in 1995, Amazingly, this formula is a digit-extraction algorithm for in base 16. Following the discovery of this and related formulas, similar formulas in other bases were investigated. This class of formulas are now known as BBP-type formulas. ReferencesAdamchik, V. and Wagon, S. "A Simple For
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学び
●2022/06/09 13:22
4users
mathworld.wolfram.com
Created, developed & nurtured by Eric Weisstein with contributions from the world's mathematical community
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学び
●2020/04/04 00:38
●数学
3users
mathworld.wolfram.com
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学び
●2012/01/15 18:17
●数学
3users
mathworld.wolfram.com
is the logarithmic integral. Gauss did not publish this result, which he first mentioned in an 1849 letter to Encke. It was subsequently posthumously published in 1863 (Gauss 1863; Havil 2003, pp. 174-176). Note that has the asymptotic series about of and taking the first three terms has been shown to be a better estimate than alone (Derbyshire 2004, pp. 116-117). The statement (4) is often known
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学び
●2010/12/20 07:26
●math
3users
mathworld.wolfram.com
A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because of this ambiguity, two different notations are sometimes (but not always) used, with
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学び
●2010/12/12 01:43
3users
mathworld.wolfram.com
An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an "anchor ring." It can be constructed from a rectangle by gluing both pairs of opposite edges together with no twists (right figure; Gardner 1971, pp. 15-17; Gray 1997, pp. 323-324). The usual torus embedded in three-dimensional
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学び
●2010/01/22 12:01
5users
mathworld.wolfram.com
There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation The first heart curve is obtained by taking the cross section of the heart surface and relabeling the -coordinates as , giving the order-6 algebraic equation
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学び
●2009/11/17 17:32
●math
●数学
●科学
3users
mathworld.wolfram.com
Rodrigues' rotation formula gives an efficient method for computing the rotation matrix corresponding to a rotation by an angle about a fixed axis specified by the unit vector . Then is given by
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学び
●2009/09/03 11:45
3users
mathworld.wolfram.com
A map projection obtained by projecting points on the surface of sphere from the sphere's north pole to point in a plane tangent to the south pole (Coxeter 1969, p. 93). In such a projection, great circles are mapped to circles, and loxodromes become logarithmic spirals. Stereographic projections have a very simple algebraic form that results immediately from similarity of triangles. In the above
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学び
●2009/08/10 09:36
●数学
●メモ
5users
mathworld.wolfram.com
is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by Note that some authors (e.g., Whittaker and Watson 1990, p. 341) define without the leading factor of . Erf is implemented in the Wolfram Language as Erf[z]. A two-argument form giving is also implemented as Erf[z0, z1]. Erf satisfies
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学び
●2009/08/06 13:39
●数学
●研究
3users
mathworld.wolfram.com
Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to the first, the circles form a Steiner chain. The simplest way to construct a Steiner chain is to perform an inversion on a symmetrical arrangement on circles packed between a central circle of radius and an outer concentric c
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テクノロジー
●2009/06/11 09:24
●programming
3users
mathworld.wolfram.com
A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired. von Neumann was one of the first people to consider such a model, and incorporated a cellular model into his "universa
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テクノロジー
●2008/11/17 02:51
3users
mathworld.wolfram.com
Barycentric coordinates are triples of numbers corresponding to masses placed at the vertices of a reference triangle . These masses then determine a point , which is the geometric centroid of the three masses and is identified with coordinates . The vertices of the triangle are given by , , and . Barycentric coordinates were discovered by Möbius in 1827 (Coxeter 1969, p. 217; Fauvel et al. 1993).
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テクノロジー
●2008/10/27 17:51
●Programming
3users
mathworld.wolfram.com
The cycloid is the locus of a point on the rim of a circle of radius rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find the area by weighing pieces of metal cut into the shape of the cycloid. Torricelli, Fermat, and Descartes all found the area. The cycloid was also studied by Roberval in 1634, Wren in 1658, Huygens in 1673, and Johann Bernoulli i
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学び
●2008/10/09 00:49
6users
mathworld.wolfram.com
A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list into a one-to-one correspondence with itself. The number of permutations on a set of elements is given by ( factorial; Uspensky 1937, p. 18). For example, there are permutations of , namely and , and permutations of , namely , , , , , and . The permutations of a list can be found in
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テクノロジー
●2008/09/11 18:21
●*プログラミング
●*ネタ
3users
mathworld.wolfram.com
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学び
●2008/02/23 05:53
8users
mathworld.wolfram.com
A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability , much greater than the expected 11.1% (i.e., one digit out of 9). Benford's law can be observed, for instance, by examining tables of logarithms and noting that the first pages ar
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テクノロジー
●2007/08/21 16:30
●Algorithm
●数学
●統計
●科学
●science
●Programming
3users
mathworld.wolfram.com
Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions on a sphere or spheroid. Define to be the azimuthal angle in the -plane from the x-axis with (denoted when referred to as the longitude), to be the polar angle (also known as the zenith angle and colatitude, with where is the l
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学び
●2007/06/20 17:14
8users
mathworld.wolfram.com
where is the floor function and is the mod function, which, when graphed over and with gives the self-referential "plot" illustrated above. Tupper's formula can be generalized to other desired outcomes. For example, L. Garron (pers. comm.) has constructed generalizations for to 29. ReferencesBailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mat
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おもしろ
●2007/05/14 23:08
●数学
●math
●ネタ
●これはすごい
3users
mathworld.wolfram.com
Consider an -digit number . Square it and add the right digits to the left or digits. If the resultant sum is , then is called a Kaprekar number. For example, 9 is a Kaprekar number since
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学び
●2007/01/17 01:23
5users
mathworld.wolfram.com
A self-avoiding walk is a path from one point to another which never intersects itself. Such paths are usually considered to occur on lattices, so that steps are only allowed in a discrete number of directions and of certain lengths. Consider a self-avoiding walk on a two-dimensional square grid (i.e., a lattice path which never visits the same lattice point twice) which starts at the origin, take
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学び
●2006/11/21 15:35
●数学
●科学
3users
mathworld.wolfram.com
By Eric W. Weisstein September 4, 2006--Less than a year after the 43rd Mersenne prime was reported (MathWorld headline news: December 25, 2005), Great Internet Mersenne Prime Search (GIMPS) project organizer George Woltman is reporting in a Sep. 4 email to the GIMPS mailing list that a new Mersenne number has been flagged as prime and reported to the project's server. If verified, this would be t
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学び
●2006/09/05 19:58
●math
6users
mathworld.wolfram.com
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学び
●2006/01/25 04:08
●数学
●画像
●study
●science
●design
3users
mathworld.wolfram.com
The constant is base of the natural logarithm. is sometimes known as Napier's constant, although its symbol () honors Euler. is the unique number with the property that the area of the region bounded by the hyperbola , the x-axis, and the vertical lines and is 1. In other words, With the possible exception of , is the most important constant in mathematics since it appears in myriad mathematical c
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学び
●2006/01/07 03:11
4users
mathworld.wolfram.com
The (complete) gamma function is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by a slightly unfortunate notation due to Legendre which is now universally used instead of Gauss's simpler (Gauss 1812; Edwards 2001, p. 8). It is analytic everywhere except at , , , ..., and the residue at is There are no points at which . The gamma fu
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学び
●2005/12/27 17:24
●数学
3users
mathworld.wolfram.com
To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates and from uniform distributions and , since the area element is a function of , and hence points picked in this way will be "bunched" near the poles (left figure above). random points can be picked on a unit sphere in the Wolfram Language using the function RandomPoint[Sphere[], n]. To obtain poi
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学び
●2005/12/26 23:15
6users
mathworld.wolfram.com
By Eric W. Weisstein December 25, 2005--Less than a year after the 42nd Mersenne prime was reported (MathWorld headline news: February 26, 2005), the Great Internet Mersenne Prime Search (GIMPS) project has discovered the 43rd known Mersenne prime. The candidate prime was flagged prime by Drs. Curtis Cooper and Steven Boone, professors at Central Missouri State University. Additional details can b
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テクノロジー
●2005/12/26 22:32
●math
4users
mathworld.wolfram.com
The BBP (named after Bailey-Borwein-Plouffe) is a formula for calculating pi discovered by Simon Plouffe in 1995, Amazingly, this formula is a digit-extraction algorithm for in base 16. Following the discovery of this and related formulas, similar formulas in other bases were investigated. This class of formulas are now known as BBP-type formulas. ReferencesAdamchik, V. and Wagon, S. "A Simple For
●
暮らし
●2005/04/21 01:39
●Math
211 users
mathworld.wolfram.com
A free resource from Wolfram Research built with Mathematica/Wolfram Language technology Created, developed & nurtured by Eric Weisstein with contributions from the world's mathematical community
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暮らし
●2005/03/05 21:46
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