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A general system of fourth-order curvilinear coordinates based on the cyclide in which Laplace's equation is separable (either simply separable or R-separable). Bôcher (1894) ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

A tetractys, also called a tetraktys or decad, is an arrangement of 10 points in the form of a triangle with 1 point in the first row, two in the second, three in the third, ...

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.

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the incircle (with center I) and the A-excircle (with center J_A). Of these, three correspond to the ...

A multimagic square such that the first, second, third, fourth, and fifth powers of the elements all yield magic squares is known as a pentamagic square. The first known ...

Let J_nu(z) be a Bessel function of the first kind, Y_nu(z) a Bessel function of the second kind, and K_nu(z) a modified Bessel function of the first kind. Also let R[z]>0 ...

Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...