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Knuth's up-arrow notation is a notation invented by Knuth (1976) to represent large numbers in which evaluation proceeds from the right (Conway and Guy 1996, p. 60): m^n ...

A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

A notation is a set of well-defined rules for representing quantities and operations with symbols.

The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...

The pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(31). The unit pentagonal gyrobicupola has volume V=1/3(5+4sqrt(5)) (1) and Dehn invariant D ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

The regular nonagon is the regular polygon with nine sides and Schläfli symbol {9}. The regular nonagon cannot be constructed using the classical Greek rules of geometric ...

A Størmer number is a positive integer n for which the greatest prime factor p of n^2+1 is at least 2n. Every Gregory number t_x can be expressed uniquely as a sum of t_ns ...