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A variate is a generalization of the concept of a random variable that is defined without reference to a particular type of probabilistic experiment. It is defined as the set ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A limiting value of a holonomic function near a singular point. Holonomic constants include Apéry's constant, Catalan's constant, Pólya's random walk constants for d>2, and ...

A plot of y_i versus the estimator e_i=y^^_i-y_i. Random scatter indicates the model is probably good. A pattern indicates a problem with the model. If the spread in e_i ...

Consider the average volume of a tetrahedron picked at random inside an octahedron of unit volume. The answer is difficult to compute analytically (Zinani 2003), but the mean ...

A sequence of random variates X_0, X_1, ... with finite means such that the conditional expectation of X_(n+1) given X_0, X_1, X_2, ..., X_n is equal to X_n, i.e., ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...