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The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

17 is a Fermat prime, which means that the 17-sided regular polygon (the heptadecagon) is constructible using compass and straightedge (as proved by Gauss).

Specifying two adjacent angles A and B and the side between them c uniquely (up to geometric congruence) determines a triangle with area K=(c^2)/(2(cotA+cotB)). (1) The angle ...

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

A stereogram made of two pictures, one red and one blue, taken from offset positions. When the pictures are viewed through glasses with one lens of each color, the picture ...

Inference of the truth of an unknown result obtained by noting its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a ...

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...