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A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

The word "class" has many specialized meanings in mathematics in which it refers to a group of objects with some common property (e.g., characteristic class or conjugacy ...

A colossally abundant number is a positive integer n for which there is a positive exponent epsilon such that (sigma(n))/(n^(1+epsilon))>=(sigma(k))/(k^(1+epsilon)) for all ...

If a discrete group of displacements in the plane has more than one center of rotation, then the only rotations that can occur are by 2, 3, 4, and 6. This can be shown as ...

There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly ...

The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

The Darboux integral, also called a Darboux-Stieltjes integral, is a variant of the Stieltjes integral that is defined as a common value for the lower and upper Darboux ...

The initially palindromic numbers 1, 121, 12321, 1234321, 123454321, ... (OEIS A002477). For the first through ninth terms, the sequence is given by the generating function ...