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Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

Milnor (1956) found more than one smooth structure on the seven-dimensional hypersphere. Generalizations have subsequently been found in other dimensions. Using surgery ...

In general, an extremal graph is the largest graph of order n which does not contain a given graph G as a subgraph (Skiena 1990, p. 143). Turán studied extremal graphs that ...

Fermat's spiral, also known as the parabolic spiral, is an Archimedean spiral with m=2 having polar equation r^2=a^2theta. (1) This curve was discussed by Fermat in 1636 ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

A graph is a forbidden minor if its presence as a graph minor of a given graph means it is not a member of some family of graphs. More generally, there may be a family of ...

The squared norm of a four-vector a=(a_0,a_1,a_2,a_3)=a_0+a is given by the dot product a^2=a_mua^mu=(a^0)^2-a·a, (1) where a·a is the usual vector dot product in Euclidean ...

There are a number of slightly different definitions of the Fresnel integrals. In physics, the Fresnel integrals denoted C(u) and S(u) are most often defined by C(u)+iS(u) = ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

Gelfond's theorem, also called the Gelfond-Schneider theorem, states that a^b is transcendental if 1. a is algebraic !=0,1 and 2. b is algebraic and irrational. This provides ...