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Lagrange's continued fraction theorem, proved by Lagrange in 1770, states that any positive quadratic surd sqrt(a) has a regular continued fraction which is periodic after ...

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...

The operation of multiplication, i.e., a times b. Various notations are a×b, a·b, a*b, ab, and (a)(b). The "multiplication sign" × is based on Saint Andrew's cross (Bergamini ...

Consider a two-dimensional tessellation with q regular p-gons at each polygon vertex. In the plane, (1-2/p)pi=(2pi)/q (1) 1/p+1/q=1/2, (2) so (p-2)(q-2)=4 (3) (Ball and ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

The tetrahedral group T_d is the point group of symmetries of the tetrahedron including the inversion operation. It is one of the 12 non-Abelian groups of order 24. The ...

There are two curves known as the butterfly curve. The first is the sextic plane curve given by the implicit equation y^6=x^2-x^6 (1) (Cundy and Rollett 1989, p. 72; left ...

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...