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E. Pegg Jr. (pers. comm., Nov. 8, 2004) found an approximation to Apéry's constant zeta(3) given by zeta(3) approx 10+zeta(16)-sqrt(96), (1) which is good to 6 digits. M. ...

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

A factorization of the form 2^(4n+2)+1=(2^(2n+1)-2^(n+1)+1)(2^(2n+1)+2^(n+1)+1). (1) The factorization for n=14 was discovered by Aurifeuille, and the general form was ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...

The apodization function f(x)=1-(|x|)/a (1) which is a generalization of the one-argument triangle function. Its full width at half maximum is a. It has instrument function ...

The numbers three and four appear prominently in the game of baseball. There are three strikes for an out, three outs per half-inning (i.e., teams switch after three outs, ...

A class of curve defined at integer values which hops from one value to another. Their name derives from the Greek word betaalphataurhoalphachiiotaomicronnu batrachion, which ...

A transformation formula for continued fractions (Lorentzen and Waadeland 1992) which can, for example, be used to prove identities such as ...

Let T(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Define f_m(x)=product_(t in T(m))(x-t). (1) Then a ...

The Baum-Sweet sequence is the sequence of numbers {b_n} such that b_n=1 if the binary representation of n contains no block of consecutive 0s of odd length, and b_n=0 ...