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The ending of a game in which neither of two players wins, sometimes also called a "tie." A game in which no draw is possible is called a categorical game.

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

A relation between compact boundaryless manifolds (also called closed manifolds). Two closed manifolds are bordant iff their disjoint union is the boundary of a compact ...

In a lattice, any two elements a and b have a greatest lower bound. This greatest lower bound is often called the meet of a and b, and is denoted by a ^ b. One can also speak ...

In elliptic n-space, the pole of an (n-1)-flat is a point located at an arc length of pi/2 radians away from each point of the (n-1)-flat.

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

The contact triangle of a triangle DeltaABC, also called the intouch triangle, is the triangle DeltaC_AC_BC_C formed by the points of tangency of the incircle of DeltaABC ...

Two adjoined cupolas.

Two adjoined rotundas.