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The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a ...

Consider two mutually tangent (externally) spheres A and B together with a larger sphere C inside which A and B are internally tangent. Then construct a chain of spheres each ...

The fibonorial n!_F, also called the Fibonacci factorial, is defined as n!_F=product_(k=1)^nF_k, where F_k is a Fibonacci number. For n=1, 2, ..., the first few fibonorials ...

Let x be a positive number, and define lambda(d) = mu(d)[ln(x/d)]^2 (1) f(n) = sum_(d)lambda(d), (2) where the sum extends over the divisors d of n, and mu(n) is the Möbius ...

Let F_n be the nth Fibonacci number, and let (p|5) be a Legendre symbol so that e_p=(p/5)={1 for p=1,4 (mod 5); -1 for p=2,3 (mod 5). (1) A prime p is called a Wall-Sun-Sun ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

The matrix decomposition of a square matrix A into so-called eigenvalues and eigenvectors is an extremely important one. This decomposition generally goes under the name ...

Euler conjectured that there do not exist Euler squares of order n=4k+2 for k=1, 2, .... In fact, MacNeish (1921-1922) published a purported proof of this conjecture (Bruck ...

A class formed by sets in R^n which have essentially the same structure, regardless of size, shape and dimension. The "essential structure" is what a set keeps when it is ...

There are several statistical quantities called means, e.g., harmonic mean, geometric mean, arithmetic-geometric mean, and root-mean-square. When applied to two elements a ...