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A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...

The expected value B_n(s) of r^s from a fixed vertex of a unit n-cube to a point picked at random in the interior of the hypercube is given by B_n(s) = ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

Picking two independent sets of points x and y from a unit uniform distribution and placing them at coordinates (x,y) gives points uniformly distributed over the unit square. ...

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

An n-dimensional open disk of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Krantz (1999, p. 3) uses the symbol D(x,r) ...

Pick two points at random in a circular sector of radius 1 and central angle theta, and consider the length s of the line joining them. The following table summarizes ...

A disk algebra is an algebra of functions which are analytic on the open unit disk in C and continuous up to the boundary. A representative measure for a point x in the ...

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 ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...