Search Results for ""

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 ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

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 ...

The 24-cell is a finite regular four-dimensional polytope with Schläfli symbol {3,4,3}. It is also known as the hyperdiamond or icositetrachoron, and is composed of 24 ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

The Steinmetz solid is the solid common to two (or three) right circular cylinders of equal radii intersecting at right angles is called the Steinmetz solid. Two cylinders ...