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The tesseract is the hypercube in R^4, also called the 8-cell or octachoron. It has the Schläfli symbol {4,3,3}, and vertices (+/-1,+/-1,+/-1,+/-1). The figure above shows a ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...

Calculus II

A series is said to be conditionally convergent iff it is convergent, the series of its positive terms diverges to positive infinity, and the series of its negative terms ...

A power series sum^(infty)c_kx^k will converge only for certain values of x. For instance, sum_(k=0)^(infty)x^k converges for -1<x<1. In general, there is always an interval ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

There are many mathematical and recreational problems related to folding. Origami, the Japanese art of paper folding, is one well-known example. It is possible to make a ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

A set of functions {f_1(n,x),f_2(n,x)} is termed a complete biorthogonal system in the closed interval R if, they are biorthogonal, i.e., int_Rf_1(m,x)f_1(n,x)dx = ...