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A plane curve given by the parametric equations x = cost (1) y = sintsin^m(1/2t). (2) The plots above show curves for values of m from 0 to 7. The teardrop curve has area ...

A magic square-type arrangement of the words in the Latin sentence "Sator Arepo tenet opera rotas" ("the farmer Arepo keeps the world rolling"). This square has been found in ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

A triple of three arbitrary vectors with common vertex (Altshiller-Court 1979), often called a trihedral angle since it determines three planes. The vectors are often taken ...

A figurate number which is constructed as an octahedral number with a square pyramid removed from each of the six graph vertices, TO_n = O_(3n-2)-6P_(n-1)^((4)) (1) = ...

In an integral domain R, the decomposition of a nonzero noninvertible element a as a product of prime (or irreducible) factors a=p_1...p_n, (1) is unique if every other ...

In predicate calculus, a universal formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

An ascending chain of subspaces of a vector space. If V is an n-dimensional vector space, a flag of V is a filtration V_0 subset V_1 subset ... subset V_r, (1) where all ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...