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For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

A Proth number that is prime, i.e., a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. Factors of Fermat numbers are of this form as long as they ...

The box fractal is a fractal also called the anticross-stitch curve which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 0 ...

Cantor dust is a fractal that can be constructed using string rewriting beginning with a cell [0] and iterating the rules {0->[0 0 0; 0 0 0; 0 0 0],1->[1 0 1; 0 0 0; 1 0 1]}. ...

A Lindenmayer system, also known as an L-system, is a string rewriting system that can be used to generate fractals with dimension between 1 and 2. Several example fractals ...

The Peano-Gosper curve is a plane-filling function originally called a "flowsnake" by R. W. Gosper and M. Gardner. Mandelbrot (1977) subsequently coined the name Peano-Gosper ...

A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a ...

If f_1(x), ..., f_s(x) are irreducible polynomials with integer coefficients such that no integer n>1 divides f_1(x), ..., f_s(x) for all integers x, then there should exist ...

A fractal curve of infinite length which bounds an area twice that of the original square.

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...