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Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

Binet's first formula for the log gamma function lnGamma(z), where Gamma(z) is a gamma function, is given by for R[z]>0 (Erdélyi et al. 1981, p. 21; Whittaker and Watson ...

The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...

A set of positive integers is called weakly triple-free if, for any integer x, the set {x,2x,3x} !subset= S. For example, all subsets of {1,2,3,4,5} are weakly triple-free ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

A triple integral is a three-fold multiple integral of the form intintintf(x,y,z)dxdydz. Triple integrals arise in evaluating quantities such as the mass, volume, moment, ...

A point where a curve intersects itself along three arcs. The above plot shows the triple point at the origin of the trifolium (x^2+y^2)^2+3x^2y-y^3=0.

Dickson (1913, 2005) defined an amicable triple to be a triple of three numbers (l,m,n) such that s(l) = m+n (1) s(m) = l+n (2) s(n) = l+m, (3) where s(n) is the restricted ...

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).