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The Hadamard product is a representation for the Riemann zeta function zeta(s) as a product over its nontrivial zeros rho, ...

The Mertens constant B_1, also known as the Hadamard-de la Vallee-Poussin constant, prime reciprocal constant (Bach and Shallit 1996, p. 234), or Kronecker's constant ...

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

There are a great many beautiful identities involving q-series, some of which follow directly by taking the q-analog of standard combinatorial identities, e.g., the ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a ...

Specifying three sides uniquely determines a triangle whose area is given by Heron's formula, K=sqrt(s(s-a)(s-b)(s-c)), (1) where s=1/2(a+b+c) (2) is the semiperimeter of the ...

The point of coincidence of P and P^' in Fagnano's theorem.

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle ...

Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area K = (a^2sinBsinC)/(2sinA) (1) = (a^2sinBsin(pi-A-B))/(2sinA). (2) The third ...