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A vector field is a map f:R^n|->R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

Given a positive nondecreasing sequence 0<lambda_1<=lambda_2<=..., the zeta-regularized product is defined by product_(n=1)^^^inftylambda_n=exp(-zeta_lambda^'(0)), where ...

Trigonometry

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

A cube can be divided into n subcubes for only n=1, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, and n>=48 (OEIS A014544; Hadwiger 1946; Scott 1947; Gardner 1992, ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...