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The trivial loop is the loop that takes every point to its basepoint. Formally, if X is a topological space and x in X, the trivial loop based at x is the map L:[0,1]->X ...

A polyhedron is said to be regular if its faces and vertex figures are regular (not necessarily convex) polygons (Coxeter 1973, p. 16). Using this definition, there are a ...

A square pyramid is a pyramid with a square base. It is a pentahedron. The lateral edge length e and slant height s of a right square pyramid of side length a and height h ...

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

Given a pair of orthologic triangles, the point where the perpendiculars from the vertices of the first to the sides of the second concur and the point where the ...

Two triangles DeltaABC and DeltaA^'B^'C^' are said to be perspective, or sometimes homologic, from a line if the extensions of their three pairs of corresponding sides meet ...

The Riemann tensor (Schutz 1985) R^alpha_(betagammadelta), also known the Riemann-Christoffel curvature tensor (Weinberg 1972, p. 133; Arfken 1985, p. 123) or Riemann ...

The Fields Medals are commonly regarded as mathematics' closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...