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Given a point P, the pedal triangle of P is the triangle whose polygon vertices are the feet of the perpendiculars from P to the side lines. The pedal triangle of a triangle ...

An affine geometry is a geometry in which properties are preserved by parallel projection from one plane to another. In an affine geometry, the third and fourth of Euclid's ...

The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a ...

A module having dual properties with respect to a free module, as enumerated below. 1. Every free module is projective; every cofree module is injective. 2. For every module ...

A notation for polyhedra which begins by specifying a "seed" polyhedron using a capital letter. The Platonic solids are denoted T (tetrahedron), O (octahedron), C (cube), I ...

A set is denumerable iff it is equipollent to the finite ordinal numbers. (Moore 1982, p. 6; Rubin 1967, p. 107; Suppes 1972, pp. 151-152). However, Ciesielski (1997, p. 64) ...

The total angular defect is the sum of the angular defects over all polyhedron vertices of a polyhedron, where the angular defect delta at a given polyhedron vertex is the ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...

The intersection Fl of the Gergonne line and the Soddy line. In the above figure, D^', E^', and F^' are the Nobbs points, I is the incenter, Ge is the Gergonne point, and S ...