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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 ...

The area of a surface or lamina is the amount of material needed to "cover" it completely. The area of a surface or collection of surfaces bounding a solid is called, not ...

A polygon which has both a circumcircle (which touches each vertex) and an incircle (which is tangent to each side). All triangles are bicentric with R^2-x^2=2Rr, (1) where R ...

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

The triangle DeltaN_1N_2N_3 formed by joining a set of three Neuberg centers (i.e., centers of the Neuberg circles) obtained from the edges of a given triangle DeltaA_1A_2A_3 ...

Although the rigidity theorem states that if the faces of a convex polyhedron are made of metal plates and the polyhedron edges are replaced by hinges, the polyhedron would ...

A minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v) (1) y(u,v) = ...

The meeting point of lines that connect corresponding points from homothetic figures. In the above figure, O is the homothetic center of the homothetic figures ABCDE and ...