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The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

The Penrose tiles are a pair of shapes that tile the plane only aperiodically (when the markings are constrained to match at borders). These two tiles, illustrated above, are ...

A Greek cross, also called a square cross, is a cross in the shape of a plus sign. It is a non-regular dodecagon. A square cross appears on the flag of Switzerland, and also ...

A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

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 word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

A binomial coefficient (N; k) is said to be exceptional if lpf(N; k)>N/k. The following table gives the exception binomial coefficients which are also good binomial ...

Let X be a normed space and X^(**)=(X^*)^* denote the second dual vector space of X. The canonical map x|->x^^ defined by x^^(f)=f(x),f in X^* gives an isometric linear ...

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...