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Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

An official chessboard is an 8×8 board containing squares alternating in color between olive green and buff (where "buff" is a color variously defined as a moderate orange ...

A curve with polar coordinates, r=b+asectheta (1) studied by the Greek mathematician Nicomedes in about 200 BC, also known as the cochloid. It is the locus of points a fixed ...

A Cunningham number is a binomial number of the form C^+/-(b,n)=b^n+/-1 with b>1 and n positive integers. Bases b^k which are themselves powers need not be considered since ...

The Dyson mod 27 identities are a set of four Rogers-Ramanujan-like identities given by A(q) = 1+sum_(n=1)^(infty)(q^(n^2)(q^3;q^3)_(n-1))/((q;q)_n(q;q)_(2n-1)) (1) = ...

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

An illusion is an object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive. Kitaoka maintains a web page of ...