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There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible ...

A Mongolian tent graph is defined as the graph obtained from the grid graph P_m square P_n for odd n by adding an extra vertex above the graph and joining every other vertex ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

From the point of view of coordinate charts, the notion of tangent space is quite simple. The tangent space consists of all directions, or velocities, a particle can take. In ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...

The Markov numbers m are the union of the solutions (x,y,z) to the Markov equation x^2+y^2+z^2=3xyz, (1) and are related to Lagrange numbers L_n by L_n=sqrt(9-4/(m^2)). (2) ...

The Miller Institute knot is the 6-crossing prime knot 6_2. It is alternating, chiral, and invertible. A knot diagram of its laevo form is illustrated above, which is ...

Let K_1 be a knot inside a torus, and knot the torus in the shape of a second knot (called the companion knot) K_2, with certain additional mild restrictions to avoid trivial ...