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Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...

Consider the family of ellipses (x^2)/(c^2)+(y^2)/((1-c)^2)-1=0 (1) for c in [0,1]. The partial derivative with respect to c is -(2x^2)/(c^3)+(2y^2)/((1-c)^3)=0 (2) ...

The result of a matrix multiplication.

The breaking up of self-intersecting polygons into simple polygons (illustrated above) is also called tessellation (Woo et al. 1999).

A Smarandache-like function which is defined where S_k(n) is defined as the smallest integer for which n|S_k(n)^k. The Smarandache S_k(n) function can therefore be obtained ...

A partial differential diffusion equation of the form (partialU)/(partialt)=kappadel ^2U. (1) Physically, the equation commonly arises in situations where kappa is the ...

The Beatty sequence is a spectrum sequence with an irrational base. In other words, the Beatty sequence corresponding to an irrational number theta is given by |_theta_|, ...

A lossless data compression algorithm which uses a small number of bits to encode common characters. Huffman coding approximates the probability for each character as a power ...