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A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can ...

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 ...

A superegg is a solid described by the equation |sqrt((x^2+y^2)/(a^2))|^n+|z/b|^n=1. (1) The special case n=2 gives a spheroid. Special cases of volume V_n are given by V_1 = ...

The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid, a fact first discovered and ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

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 hex number, also called a centered hexagonal number, is given by H_n = 1+6T_n (1) = 3n^2+3n+1, (2) where T_n=n(n+1)/2 is the nth triangular number and the indexing with ...

The number of cells in a generalized Chinese checkers board (or "centered" hexagram). Unlike the polygonal numbers, there is ambiguity in the case of the star numbers as to ...

Archimedes' spiral is an Archimedean spiral with polar equation r=atheta. (1) This spiral was studied by Conon, and later by Archimedes in On Spirals about 225 BC. Archimedes ...