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The Icosian game, also called the Hamiltonian game (Ball and Coxeter 1987, p. 262), is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the ...

The Kampyle of Eudoxus is a curve studied by Eudoxus in relation to the classical problem of cube duplication. It is given by the polar equation r=asec^2theta, (1) and the ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

The number of operations needed to effect a geometric construction as determined in geometrography. If the number of operations of the five geometrographic types are denoted ...

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 ...

A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

Diophantus's riddle is a poem that encodes a mathematical problem. In verse, it read as follows: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone ...