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The 21 assumptions which underlie the geometry published in Hilbert's classic text Grundlagen der Geometrie. The eight incidence axioms concern collinearity and intersection ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

Let a chord of constant length be slid around a smooth, closed, convex curve C, and choose a point on the chord which divides it into segments of lengths p and q. This point ...

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

Home plate in the game of baseball is an irregular pentagon with two parallel sides, each perpendicular to a base. It seems reasonable to dub such a figure (i.e., a rectangle ...

A linear ordinary differential equation of order n is said to be homogeneous if it is of the form a_n(x)y^((n))+a_(n-1)(x)y^((n-1))+...+a_1(x)y^'+a_0(x)y=0, (1) where ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

The solid cut from a horizontal cylinder of length L and radius R by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal ...

Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...