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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 ...

A region in a knot or link projection plane surrounded by a circle such that the knot or link crosses the circle exactly four times. Two tangles are equivalent if a sequence ...

The de Longchamps point L is the reflection of the orthocenter H about the circumcenter O of a triangle. It has triangle center function alpha=cosA-cosBcosC, (1) and is ...

Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

A circle-preserving transformation composed of an odd number of inversions.

The inverse function of the logarithm, defined such that log_b(antilog_bz)=z=antilog_b(log_bz). The antilogarithm in base b of z is therefore b^z.

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

If two quantities A and B are approximately equal, this is written A approx B.

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 group in which any decreasing chain of distinct subgroups terminates after a finite number.