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Let C be a curve, let O be a fixed point (the pole), and let O^' be a second fixed point. Let P and P^' be points on a line through O meeting C at Q such that P^'Q=QP=QO^'. ...

Christoffel symbols of the second kind are the second type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

Fredholm's theorem states that, if A is an m×n matrix, then the orthogonal complement of the row space of A is the null space of A, and the orthogonal complement of the ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

Any composite number n with p|(n/p-1) for all prime divisors p of n. n is a Giuga number iff sum_(k=1)^(n-1)k^(phi(n))=-1 (mod n) (1) where phi is the totient function and ...

There are at least three theorems known as Jensen's theorem. The first states that, for a fixed vector v=(v_1,...,v_m), the function |v|_p=(sum_(i=1)^m|v_i|^p)^(1/p) is a ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...