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C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

A busy beaver is an n-state, 2-color Turing machine which writes a maximum number Sigma(n) of 1s before halting (Rado 1962; Lin and Rado 1965; Shallit 1998). Alternatively, ...

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...

There exists an integer N such that every string in the look and say sequence "decays" in at most N days to a compound of "common" and "transuranic elements." The table below ...

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...