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mathworld wolfram*******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 .Examples of algebras include the algebra of real numbers, vectors and matrices, .

Learn about the fascinating world of geometry from Wolfram MathWorld, the .

Number theory is a vast and fascinating field of mathematics, sometimes called .The term "discrete mathematics" is therefore used in contrast with .Download Wolfram Notebook Topology is the mathematical study of the properties .MathWorld is the web's most extensive mathematical resource, provided as a .Calculus. In general, "a" calculus is an abstract theory developed in a purely .mathworld wolfram Iba paIn 1900, David Hilbert stated, "mathematics is the foundation of all exact knowledge .Wolfram|Alpha is a search engine that computes expert-level answers using algorithms, knowledgebase and AI technology. It covers topics such as math, science, engineering, . Calculus. 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 .

Examples of algebras include the algebra of real numbers, vectors and matrices, tensors, complex numbers , and quaternions. (Note that linear algebra, which .

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 .

In 1900, David Hilbert stated, "mathematics is the foundation of all exact knowledge of natural phenomena" and Alfred Whitehead remarked in 1911 that "all . Download Wolfram Notebook Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed.

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes .

The term "discrete mathematics" is therefore used in contrast with "continuous mathematics," which is the branch of mathematics dealing with objects that can vary . PDF -- from Wolfram MathWorld. History and Terminology. Wolfram Language Commands. Download Wolfram Notebook. A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining . A "zeroth" curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation r (theta)=1-sintheta. (1) The first heart curve is obtained by taking the y=0 cross section of the heart . Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also .

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 .Iba pa A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is equivalent to finding positive integers a, b, and c satisfying a^2+b^2=c^2. (1) The smallest and best-known Pythagorean triple is (a,b,c)=(3,4,5). The right triangle having these .Download Wolfram Notebook. The Bernoulli numbers are a sequence of signed rational numbers that can be defined by the exponential generating function. (1) These numbers arise in the series expansions of trigonometric functions, and are extremely important in number theory and analysis . There are actually two definitions for the Bernoulli numbers.

Download Wolfram Notebook. A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and .mathworld wolfram Conic Section. Download Wolfram Notebook. The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, a circle is produced. For a plane that is not perpendicular to the axis and that intersects only a single nappe, the curve .

Download Wolfram Notebook. 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 . (Press et al. 1992), sometimes known as RK4.This method is reasonably simple and robust and is a good general candidate for numerical solution of differential equations when combined with an intelligent adaptive step-size routine.with .As a result of the definition (), it is conventional to define .The Fibonacci numbers for , 2, . are 1, 1, 2, 3, 5, 8, 13, 21, .(OEIS A000045).. Fibonacci numbers can be viewed as a particular case of the Fibonacci .

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) (the coefficient a_3 of z^3 may be taken as 1 without loss of generality by dividing the entire equation through by a_3). The Wolfram Language can . Natural Logarithm. Download Wolfram Notebook. The natural logarithm is the logarithm having base e , where. (1) This function can be defined. (2) for . This definition means that e is the unique . A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P (x)=1/ (sigmasqrt (2pi))e^ (- (x-mu)^2/ (2sigma^2)) (1) on the domain x in (-infty,infty). While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists .

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 such that f(x_0)=x_0. (1) The fixed point of a function f starting from an initial value x can be computed in the Wolfram Language using FixedPoint[f, x]. Similarly, to get a list .

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular and equilateral). Only certain regular polygons are "constructible" using the classical Greek tools of the compass and straightedge. The terms equilateral triangle .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 .

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1, meaning it is a number that cannot be factored. For example, the only divisors of 13 are .

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mathworld wolfram|Iba pa