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Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

Solid partitions are generalizations of plane partitions. MacMahon (1960) conjectured the generating function for the number of solid partitions was ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

In three dimensions, the spherical harmonic differential equation is given by ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

The square knot, also called the reef knot, is a composite knot of six crossings consisting of a knot sum of a trefoil knot and its mirror image (Rolfsen 1976, p. 220). The ...

There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles ...

Given a set of n men and n women, marry them off in pairs after each man has ranked the women in order of preference from 1 to n, {w_1,...,w_n} and each women has done ...

A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter 2n+4 ...

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).