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The cycloid is the locus of a point on the rim of a circle of radius a rolling along a straight line. It was studied and named by Galileo in 1599. Galileo attempted to find ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

Let there be n>=2 integers 0<a_1<...<a_n with GCD(a_1,a_2,...,a_n)=1. The values a_i represent the denominations of n different coins, where these denominations have greatest ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...