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A braid with M strands and R components with P positive crossings and N negative crossings satisfies |P-N|<=2U+M-R<=P+N, where U is the unknotting number. While the second ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

A valuation for which |x|<=1 implies |1+x|<=C for the constant C=1 (independent of x). Such a valuation does not satisfy the strong triangle inequality |x+y|<=max(|x|,|y|).

A mathematical statement of the equivalence of two quantities. The equality "A is equal to B" is written A=B.

A strong inequality in which a is not only less than b, but much less (by some convention) is denoted a<<b.

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

The (first) rhombic dodecahedron is the dual polyhedron of the cuboctahedron A_1 (Holden 1971, p. 55) and Wenninger dual W_(11). Its sometimes also called the rhomboidal ...

The pentaflake is a fractal with 5-fold symmetry. As illustrated above, five pentagons can be arranged around an identical pentagon to form the first iteration of the ...

The small triambic icosahedron is the dual polyhedron of the small ditrigonal icosidodecahedron with Maeder index 30 (Maeder 1997), Weinninger index 70 (Wenninger 1971, p. ...

If f has no spectrum in [-lambda,lambda], then ||f||_infty<=pi/(2lambda)||f^'||_infty (1) (Bohr 1935). A related inequality states that if A_k is the class of functions such ...