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A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

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 ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

Eternity is a puzzle devised by Christopher Monckton and consisting of 209 pieces, each of which is a 12-polydrafter (i.e., a compound of 30-60-90 triangles). The puzzle was ...

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 board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the Egyptian mathematician and pedagogist Caleb ...