mathworld wolfram|Great Icosahedron

mathworld wolfram,MathWorld is the web's most extensive mathematics resource, with 13,000 detailed entries on various topics, created and updated by Eric Weisstein and the world's .Examples of algebras include the algebra of real numbers, vectors and matrices, .

Geometry is the study of figures in a space of a given number of dimensions and of .

Number theory is a vast and fascinating field of mathematics, sometimes called .Discrete mathematics is the branch of mathematics dealing with objects that .A set for which a topology has been specified is called a topological space .MathWorld is the web's most extensive mathematical resource, provided as a .In 1900, David Hilbert stated, "mathematics is the foundation of all exact knowledge .An ellipse can be specified in the Wolfram Language using Circle [ x, y, a , b ]. If .Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, .

Learn about algebra, a branch of mathematics that studies number systems, operations, and structures. Explore different types of algebras, their properties, examples, and .mathworld wolfram Learn about the history, terminology, and foundations of mathematics from Wolfram MathWorld, a web-based encyclopedia of mathematics. Explore various branches of . Learn about the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Explore topics such as curves, surfaces, manifolds, homotopy, and more with .

MathWorld is the web's most extensive mathematical resource, assembled by Eric W. Weisstein and others for over 25 years. It covers all levels of mathematics and uses . An ellipse can be specified in the Wolfram Language using Circle [ x, y, a , b ]. If the endpoints of a segment are moved along two intersecting lines, a fixed point on the segment (or on the line that prolongs it) describes an arc .

The gamma function is implemented in the Wolfram Language as Gamma [ z ]. There are a number of notational conventions in common use for indication of a power of a gamma functions.MathWorld is a comprehensive and free online encyclopedia of mathematics, created and written by Eric W. Weisstein. It is sponsored by Wolfram Research, Inc. and has a history of legal . The great icosahedron can be constructed from an icosahedron with unit edge lengths by taking the 20 sets of vertices that are mutually spaced by a distance , the golden ratio. The solid therefore consists of 20 equilateral . A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A is uniquely associated with an object f(a) in B. A function is therefore a many-to-one (or sometimes one-to-one) relation. The set A of values at which a function is defined is called its .(OEIS A000796). Pi's digits have many interesting properties, although not very much is known about their analytic properties. However, spigot (Rabinowitz and Wagon 1995; Arndt and Haenel 2001; Borwein and Bailey 2003, pp. 140-141) and digit-extraction algorithms (the BBP formula) are known for . A brief history of notation for pi is given by Castellanos (1988ab).A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate polynomial) with constant coefficients is given by a_nx^n+.+a_2x^2+a_1x+a_0. (1) The individual summands with the coefficients (usually) included are called monomials (Becker and Weispfenning 1993, p. . A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative distribution function for a continuous uniform distribution on the interval [a,b] are P(x) = {0 for xb (1) D(x) = {0 for xb. (2) . A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle. The equation of a plane with nonzero normal vector n=(a,b,c) through the point x_0=(x_0,y_0,z_0) is n

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at the large end of the distribution), the function is said to have negative skewness. If the reverse is true, it has positive skewness. If the two are equal, it has zero skewness. Several types of skewness .

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta function zeros, i.e., the values of s other than -2, -4, -6, . such that zeta(s)=0 (where zeta(s) is the Riemann zeta function) all lie on the "critical line" sigma=R[s]=1/2 (where R[s] denotes the .

A schematic diagram used in logic theory to depict collections of sets and represent their relationships. The Venn diagrams on two and three sets are illustrated above. The order-two diagram (left) consists of two intersecting circles, producing a total of four regions, A, B, A intersection B, and emptyset (the empty set, represented by none of the regions occupied). .

The pedal curve of a conic section with pedal point at a focus is either a circle or a line.In particular the ellipse pedal curve and hyperbola pedal curve are both circles, while the parabola pedal curve is a line (Hilbert and Cohn-Vossen 1999, pp. 25-27).. Five points in a plane determine a conic (Coxeter and Greitzer 1967, p. 76; Le Lionnais 1983, p. 56; Wells 1991), as .

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.. (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e is the unique number with the property that the area of the region bounded by the hyperbola y=1/x, the x-axis, and the vertical lines x=1 and x=e is 1. In other words, .

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first type of curvature to be studied historically, culminating in the Frenet formulas, which describe a space curve entirely in terms of its "curvature," torsion, and the initial starting point and direction. .

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects like the point, line, circle, triangle, and polygon), solid geometry (dealing with objects like the line, sphere, and polyhedron), and spherical geometry (dealing with objects like the spherical . A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. Twice the radius is known as the diameter d=2r. The .

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational tool for computation and tabulation of quantities, it has blossomed into an extremely rich and diverse set of tools, terminologies, and approaches which range from the purely .mathworld wolfram Great Icosahedron due to an anonymous source and obtained from the log files of Wolfram|Alpha in early February 2010. Each half of this heart curve is a portion of an algebraic curve of order 12, so the entire curve is a portion of an algebraic curve of order 24.. A fifth heart curve can be defined parametrically as In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, infinitesimal analysis), is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects. The calculus is .Great Icosahedron A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a matrix, and every matrix corresponds to a unique linear transformation. The matrix, and its close relative the determinant, are extremely important concepts in linear algebra, and were first formulated . Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular coordinates. The two axes of two-dimensional Cartesian coordinates, conventionally denoted the x- and y-axes (a notation due to Descartes), are chosen to be linear and mutually perpendicular. .

mathworld wolfram|Great Icosahedron

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