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The outer Soddy circle is the solution to the four coins problem. It has circle function l=((-a+b+c)^2[f(a,b,c)+16g(a,b,c)rs])/(4bc[(a^2+b^2+c^2)-2(ab+bc+ca)+8rs]^4), (1) ...

Consider the problem of comparing two real numbers x and y based on their continued fraction representations. Then the mean number of iterations needed to determine if x<y or ...

Eternity is a puzzle devised by Christopher Monckton and consisting of 209 pieces, each of which is a 12-polydrafter (i.e., a compound of 30-60-90 triangles). The puzzle was ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

The conjecture that the maximum local density is given by rho_(dodecahedron).

Let graph G have p points v_i and graph H have p points u_i, where p>=3. Then if for each i, the subgraphs G_i=G-v_i and H_i=H-u_i are isomorphic, then the graphs G and H are ...

A holyhedron is polyhedron whose faces and holes are all finite-sided polygons and that contains at least one hole whose boundary shares no point with a face boundary. D. ...

Given a sequence S_i as input to stage i, form sequence S_(i+1) as follows: 1. For k in [1,...,i], write term i+k and then term i-k. 2. Discard the ith term. 3. Write the ...

A generalization of Fermat's last theorem which states that if a^x+b^y=c^z, where a, b, c, x, y, and z are any positive integers with x,y,z>2, then a, b, and c have a common ...

Erdős offered a $3000 prize for a proof of the proposition that "If the sum of reciprocals of a set of integers diverges, then that set contains arbitrarily long arithmetic ...