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The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

The unknot, also called the trivial knot (Rolfsen 1976, p. 51), is a closed loop that is not knotted. In the 1930s Reidemeister first proved that knots exist which are ...

A Heronian tetrahedron, also called a perfect tetrahedron, is a (not necessarily regular) tetrahedron whose sides, face areas, and volume are all rational numbers. It ...

The 6.1.2 equation A^6=B^6+C^6 (1) is a special case of Fermat's last theorem with n=6, and so has no solution. No 6.1.n solutions are known for n<=6 (Lander et al. 1967; Guy ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

Combinatorial topology is a subset of algebraic topology that uses combinatorial methods. For example, simplicial homology is a combinatorial construction in algebraic ...

When f:A->B is a ring homomorphism and b is an ideal in B, then f^(-1)(b) is an ideal in A, called the contraction of b and sometimes denoted b^c. The contraction of a prime ...

The triangle DeltaA^'B^'C^' formed by the points of pairwise intersection of the three intangents. It is not in perspective with DeltaABC. It has trilinear vertex matrix ...

A lag system, introduced by Wang (1963), is a sort of opposite to a tag system. Lag systems allow dependence on more than just the first element, but remove only the first ...