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Continuum percolation can be thought of as a continuous, uncountable version of percolation theory-a theory which, in its most studied form, takes place on a discrete, ...

The Earls sequence gives the starting position in the decimal digits of pi (or in general, any constant), not counting digits to the left of the decimal point, at which a ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

A map projection obtained by projecting points P on the surface of sphere from the sphere's north pole N to point P^' in a plane tangent to the south pole S (Coxeter 1969, p. ...

Feynman (1997, p. 116) noticed the curious fact that the decimal expansion 1/(243)=0.004115226337448559... (1) repeats pairs of the digits 0, 1, 2, 3, ... separated by the ...

Let x_0 be a rational number in the closed interval [0,1], and generate a sequence using the map x_(n+1)=2x_n (mod 1). (1) Then the number of periodic map orbits of period p ...

A method of solving combinatorial problems by means of an algorithm which is allowed to run forward until a dead end is reached, at which point previous steps are retraced ...

The attractor of the iterated function system given by the set of "fern functions" f_1(x,y) = [0.85 0.04; -0.04 0.85][x; y]+[0.00; 1.60] (1) f_2(x,y) = [-0.15 0.28; 0.26 ...

The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Define the angles theta and phi by letting a=cos(theta/2) and ...