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The altitudes of a triangle are the Cevians A_iH_i that are perpendicular to the legs A_jA_k opposite A_i. The three altitudes of any triangle are concurrent at the ...

The orthic axis of the excentral triangle, which is central line L_1 (Casey 1888, p. 177; Kimberling 1998, p. 150) and therefore has trilinear equation alpha+beta+gamma=0. It ...

The Archimedean solids in general have many stellations. Examples of Archimedean solid stellations include the dodecadodecahedron and great icosidodecahedron. The following ...

Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...

The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

A Barker code is a string of digits a_i=+/-1 of length l>=2 such that |sum_(i=1)^(l-k)a_ia_(i+k)|<=1 for all 1<=k<l. Barker codes are used for pulse compression of radar ...

Barnette's conjecture asserts that every 3-connected bipartite cubic planar graph is Hamiltonian. The only graph on nine or fewer vertices satisfying Barnette's conditions is ...