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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 subset A of a larger set, the characteristic function chi_A, sometimes also called the indicator function, is the function defined to be identically one on A, and is ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

A Chen prime is a prime number p for which p+2 is either a prime or semiprime. Chen primes are named after Jing Run Chen who proved in 1966 that there are infinitely many ...

The Chu-Vandermonde identity _2F_1(-n,b;c;1)=((c-b)_n)/((c)_n) (1) (for n in Z^+) is a special case of Gauss's hypergeometric theorem _2F_1(a,b;c;1) = ((c-b)_(-a))/((c)_(-a)) ...

A prime number p is called circular if it remains prime after any cyclic permutation of its digits. An example in base-10 is 1,193 because 1,931, 9,311, and 3,119 are all ...

A circumhyperbola is a circumconic that is a hyperbola. A rectangular circumhyperbola always passes through the orthocenter H and has center on the nine-point circle ...

Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

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 ...