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There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

The volume of a solid body is the amount of "space" it occupies. Volume has units of length cubed (i.e., cm^3, m^3, in^3, etc.) For example, the volume of a box (cuboid) of ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

Cayley's cubic surface is the unique cubic surface having four ordinary double points (Hunt), the maximum possible for cubic surface (Endraß). The Cayley cubic is invariant ...

Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. The group is most commonly N, R, R-+, ...

The Euler-Lagrange differential equation is the fundamental equation of calculus of variations. It states that if J is defined by an integral of the form J=intf(t,y,y^.)dt, ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...