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Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

A rotation group is a group in which the elements are orthogonal matrices with determinant 1. In the case of three-dimensional space, the rotation group is known as the ...

If the sides of a triangle are divided in the ratios lambda:1, mu:1, and nu:1, the cevians form a central triangle whose area is ...

The vector space generated by the rows of a matrix viewed as vectors. The row space of a n×m matrix A with real entries is a subspace generated by n elements of R^m, hence ...

A usually simple algorithm or identity. The term is frequently applied to specific orders of Newton-Cotes formulas. The designation "rule n" is also given to the nth ...

Rule 126 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Rule 182 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Rule 250 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

The time required for a given principal to double (assuming n=1 conversion period) for compound interest is given by solving 2P=P(1+r)^t, (1) or t=(ln2)/(ln(1+r)), (2) where ...