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A game played with two heaps of counters in which a player may take any number from either heap or the same number from both. The player taking the last counter wins. The rth ...

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three ...

The de Longchamps circle is defined as the radical circle of the power circles of a given reference triangle. It is defined only for obtuse triangles. It is the complement of ...

Given a real number q>1, the series x=sum_(n=0)^inftya_nq^(-n) is called the q-expansion, or beta-expansion (Parry 1957), of the positive real number x if, for all n>=0, ...

Let sopfr(n) be the sum of prime factors (with repetition) of a number n. For example, 20=2^2·5, so sopfr(20)=2+2+5=9. Then sopfr(n) for n=1, 2, ... is given by 0, 2, 3, 4, ...

A bicubic spline is a special case of bicubic interpolation which uses an interpolation function of the form y(x_1,x_2) = sum_(i=1)^(4)sum_(j=1)^(4)c_(ij)t^(i-1)u^(j-1) (1) ...

The central factorials x^([k]) form an associated Sheffer sequence with f(t) = e^(t/2)-e^(-t/2) (1) = 2sinh(1/2t), (2) giving the generating function ...

Gieseking's constant is defined by G = int_0^(2pi/3)ln(2cos(1/2x))dx (1) = Cl_2(1/3pi) (2) = (3sqrt(3))/4[1-sum_(k=0)^(infty)1/((3k+2)^2)+sum_(k=1)^(infty)1/((3k+1)^2)] (3) = ...

The cosecant cscz is the function defined by cscz = 1/(sinz) (1) = (2i)/(e^(iz)-e^(-iz)), (2) where sinz is the sine. The cosecant is implemented in the Wolfram Language as ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...