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An algorithm which allows digits of a given number to be calculated without requiring the computation of earlier digits. The BBP formula for pi is the best-known such ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

An illusion studied by the psychologist Walter Ehrenstein in which the sides of a square placed inside a pattern of concentric circles take an apparent curved shape. The name ...

The E_n(x) function is defined by the integral E_n(x)=int_1^infty(e^(-xt)dt)/(t^n) (1) and is given by the Wolfram Language function ExpIntegralE[n, x]. Defining t=eta^(-1) ...

The case of the Weierstrass elliptic function with invariants g_2=0 and g_3=1. The corresponding real half-period is given by omega_2 = (Gamma^3(1/3))/(4pi) (1) = ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...

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 ...

Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

Given three coins of possibly different sizes which are arranged so that each is tangent to the other two, find the coin which is tangent to the other three coins. The ...