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A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the ...

A hexagon is a six-sided polygon. Several special types of hexagons are illustrated above. In particular, a hexagon with vertices equally spaced around a circle and with all ...

A symbol of the form {p,q,r,...} used to describe regular polygons, polyhedra, and their higher-dimensional counterparts. The symbol {p} denotes a regular polygon for integer ...

Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...

If the knot K is the boundary K=f(S^1) of a singular disk f:D->S^3 which has the property that each self-intersecting component is an arc A subset f(D^2) for which f^(-1)(A) ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

A generalization of the Wilcoxon rank sum test.

There are least two Bang's theorems, one concerning tetrahedra (Bang 1897), and the other with widths of convex domains (Bang 1951). The theorem of Bang (1897) states that ...