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Stadium billiards refers to the investigation of the path of a billiard ball on a stadium-shaped billiard table, as first investigated by Bunimovich (1974).

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

The metric g defined on a nonempty set X by g(x,x) = 0 (1) g(x,y) = 1 (2) if x!=y for all x,y in X. It follows that the open ball of radius r>0 and center at x_0 B(x_0,r)={x ...

The interior of a set is the union of all its open subsets. More informally, the interior of geometric structure is that portion of a region lying "inside" a specified ...

A topological space having a countable dense subset. An example is the Euclidean space R^n with the Euclidean topology, since it has the rational lattice Q^n as a countable ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...

Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...

There are at least two theorems known as Salmon's theorem. This first states that if P and S are two points, PX and SY are the perpendiculars from P and S to the polars of S ...

n weighings are sufficient to find a bad coin among (3^n-1)/2 coins (Steinhaus 1999, p. 61). vos Savant (1993) gives an algorithm for finding a bad ball among 12 balls in ...

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) ...