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The square knot, also called the reef knot, is a composite knot of six crossings consisting of a knot sum of a trefoil knot and its mirror image (Rolfsen 1976, p. 220). The ...

Let a Cevian PC be drawn on a triangle DeltaABC, and denote the lengths m=PA^_ and n=PB^_, with c=m+n. Then Stewart's theorem, also called Apollonius' theorem, states that ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

In the tabu search category of meta-heuristics, the essential idea is to 'forbid' search moves to points already visited in the (usually discrete) search space, at least for ...

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...

Given a doubled knot with the unknot taken as the base knot K_1, the companion knot K_2 of K_1 is called a twist knot with q twists. As illustrated above, the following knots ...

An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. It is a roulette obtained from the path described by the foci of a ...

A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces M ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...