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In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that ...

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 ...

Cayley's cubic surface is the unique cubic surface having four ordinary double points (Hunt), the maximum possible for cubic surface (Endraß). The Cayley cubic is invariant ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

Cospectral graphs, also called isospectral graphs, are graphs that share the same graph spectrum. The smallest pair of isospectral graphs is the graph union C_4 union K_1 and ...