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A method of numerically integrating ordinary differential equations by using a trial step at the midpoint of an interval to cancel out lower-order error terms. The ...

The sample variance m_2 (commonly written s^2 or sometimes s_N^2) is the second sample central moment and is defined by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ the ...

Let K_1 be a knot inside a torus, and knot the torus in the shape of a second knot (called the companion knot) K_2, with certain additional mild restrictions to avoid trivial ...

Set theory is the mathematical theory of sets. Set theory is closely associated with the branch of mathematics known as logic. There are a number of different versions of set ...

A correction which must be applied to the measured moments m_k obtained from normally distributed data which have been binned in order to obtain correct estimators mu^^_i for ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

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^'. ...

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 ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...