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The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...

An Aztec diamond of order n is the region obtained from four staircase shapes of height n by gluing them together along the straight edges. It can therefore be defined as the ...

Let Gamma(z) be the gamma function and n!! denote a double factorial, then [(Gamma(m+1/2))/(Gamma(m))]^2[1/m+(1/2)^21/(m+1)+((1·3)/(2·4))^21/(m+2)+...]_()_(n) ...

If C_1, C_2, ...C_r are sets of positive integers and union _(i=1)^rC_i=Z^+, then some C_i contains arbitrarily long arithmetic progressions. The conjecture was proved by van ...

The Bernoulli inequality states (1+x)^n>1+nx, (1) where x>-1!=0 is a real number and n>1 an integer. This inequality can be proven by taking a Maclaurin series of (1+x)^n, ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

Any continuous function G:B^n->B^n has a fixed point, where B^n={x in R^n:x_1^2+...+x_n^2<=1} is the unit n-ball.

Calabi's triangle is the unique triangle other that the equilateral triangle for which the largest inscribed square can be inscribed in three different ways (Calabi 1997). ...

The symbol intersection , used for the intersection of sets, and sometimes also for the logical connective AND instead of the symbol ^ (wedge). In fact, for any two sets A ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...