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Given a function f(x), its inverse f^(-1)(x) is defined by f(f^(-1)(x))=f^(-1)(f(x))=x. (1) Therefore, f(x) and f^(-1)(x) are reflections about the line y=x. In the Wolfram ...

An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be computed. The method of steepest descent, also ...

The topology on the Cartesian product X×Y of two topological spaces whose open sets are the unions of subsets A×B, where A and B are open subsets of X and Y, respectively. ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

The set of all lines through a point. The term was first used by Desargues (Cremona 1960, p. x). The six angles of any pencils of four rays O{ABCD} are connected by the ...

In the plane, the reflection property can be stated as three theorems (Ogilvy 1990, pp. 73-77): 1. The locus of the center of a variable circle, tangent to a fixed circle and ...

A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore ...

A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...