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From the feet H_A, H_B, and H_C of each altitude of a triangle DeltaABC, draw lines (H_AP_A,H_AQ_A), (H_BP_B,H_BQ_B), (H_CP_C,H_CQ_C) perpendicular to the adjacent sides, as ...

Let DeltaABC be a triangle and D a point on the side BC. Let I be the incenter, P the center of the circle tangent to the circumcircle and segments AD and BD, Q the center of ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...

Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

There are two types of squares inscribing reference triangle DeltaABC in the sense that all vertices lie on the sidelines of ABC. The first type has two adjacent vertices of ...

The 14-faced Archimedean solid with faces 8{3}+6{8}. It is also the uniform polyhedron with Maeder index 9 (Maeder 1997), Wenninger index 8 (Wenninger 1989), Coxeter index 21 ...

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A zebra graph is a graph formed by all possible moves of a hypothetical chess piece called a "zebra" which moves analogously to a knight except that it is restricted to moves ...

Discrete Mathematics

An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom ...