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Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

The inversive distance is the natural logarithm of the ratio of two concentric circles into which the given circles can be inverted. Let c be the distance between the centers ...

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

The Jackson-Slater identity is the q-series identity of Rogers-Ramanujan-type given by sum_(k=0)^(infty)(q^(2k^2))/((q)_(2k)) = ...

The Janko groups are the four sporadic groups J_1, J_2, J_3 and J_4. The Janko group J_2 is also known as the Hall-Janko group. The Janko groups are implemented in the ...

Jessen's orthogonal icosahedron is a concave shaky polyhedron constructed by replacing six pairs of adjacent triangles in an icosahedron (whose edges form a skew ...

A planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is ...

The signature s(K) of a knot K can be defined using the skein relationship s(unknot)=0 (1) s(K_+)-s(K_-) in {0,2}, (2) and 4|s(K)<->del (K)(2i)>0, (3) where del (K) is the ...

Given an m×n matrix A and a p×q matrix B, their Kronecker product C=A tensor B, also called their matrix direct product, is an (mp)×(nq) matrix with elements defined by ...