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The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation x = (asin[(m+n)t])/(sin[(m-n)t]) (1) y = ...

The only stellations of Platonic solids which are uniform polyhedra are the three dodecahedron stellations and the great icosahedron.

Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

An upper semicontinuous function whose restrictions to all complex lines are subharmonic (where defined). These functions were introduced by P. Lelong and Oka in the early ...

The first and second Pöschl-Teller differential equations are given by y^('')-{a^2[(kappa(kappa-1))/(sin^2(ax))+(lambda(lambda-1))/(cos^2(ax))]-b^2}y=0 and ...

The system of partial differential equations u_(xx)-u_(yy)+/-sinucosu+(cosu)/(sin^3u)(v_x^2-v_y^2)=0 (v_xcot^2u)_x=(v_ycot^2u)_y.

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

A nonsimply connected 3-manifold, also called a dodecahedral space.

Let {y^k} be a set of orthonormal vectors with k=1, 2, ..., K, such that the inner product (y^k,y^k)=1. Then set x=sum_(k=1)^Ku_ky^k (1) so that for any square matrix A for ...

Solutions to holomorphic differential equations are themselves holomorphic functions of time, initial conditions, and parameters.