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Consider the Euclid numbers defined by E_k=1+p_k#, where p_k is the kth prime and p# is the primorial. The first few values of E_k are 3, 7, 31, 211, 2311, 30031, 510511, ... ...

A board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the Egyptian mathematician and pedagogist Caleb ...

Let the difference of successive primes be defined by d_n=p_(n+1)-p_n, and d_n^k by d_n^k={d_n for k=1; |d_(n+1)^(k-1)-d_n^(k-1)| for k>1. (1) N. L. Gilbreath claimed that ...

The Heesch number of a closed plane figure is the maximum number of times that figure can be completely surrounded by copies of itself. The determination of the maximum ...

The Ouchi illusion, illustrated above, is an illusion named after its inventor, Japanese artist Hajime Ouchi. In this illusion, the central disk seems to float above the ...

A pentomino is a 5-polyomino. There are 12 free pentominoes, 18 one-sided pentominoes, and 63 fixed pentominoes. The twelve free pentominoes are known by the letters of the ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

The first strong law of small numbers (Gardner 1980, Guy 1988, 1990) states "There aren't enough small numbers to meet the many demands made of them." The second strong law ...

An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, inversion, or more ...

Synergetics deals with systems composed of many subsystems which may each be of a very different nature. In particular, synergetics treats systems in which cooperation among ...