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The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

The molecular topological index is a graph index defined by MTI=sum_(i=1)^nE_i, where E_i are the components of the vector E=(A+D)d, with A the adjacency matrix, D the graph ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...

The pentagonal wedge graph is the skeleton of the pentagonal wedge. It is a has 8 vertices, 12 edges, and 6 faces. The pentagonal wedge graph is implemented in the Wolfram ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...