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It is possible to place 7 cigarettes in such a way that each touches every other if l/d>7sqrt(3)/2 (Gardner 1959, p. 115).

An arrangement of overlapping circles which cover the entire plane. A lower bound for a covering using equivalent circles is 2pi/sqrt(27) (Williams 1979, p. 51).

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...

A sphere with four punctures occurring where a knot passes through the surface.

A fractal curve of infinite length which bounds an area twice that of the original square.

A set S of positive integers is said to be Diophantine iff there exists a polynomial Q with integral coefficients in m>=1 indeterminates such that ...

The Eisenstein units are the Eisenstein integers +/-1, +/-omega, +/-omega^2, where omega = 1/2(-1+isqrt(3)) (1) omega^2 = 1/2(-1-isqrt(3)). (2)

The problem of determining (or counting) the set of all solutions to a given problem.

A polygon whose vertex angles are equal (Williams 1979, p. 32).

An equilateral polygon is a polygon whose edges are all of equal length (Williams 1979, pp. 31-32). The most prominent examples of equilateral polygons are the regular ...