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Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is ...

A well-formed formula B is said to be true for the interpretation M (written |=_MB) iff every sequence in Sigma (the set of all denumerable sequences of elements of the ...

A function of more than one variable.

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...

The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

The Pell constant is the infinite product P = 1-product_(k=0)^(infty)(1-1/(2^(2k+1))) (1) = 1-(1/2;1/4)_infty (2) = 0.58057755820489... (3) (OEIS A141848), where (a,q)_infty ...

Given a regular pentagon of unit area, mean triangle area of a triangle picked at random inside it is given by the n=5 case of polygon triangle picking, A^_ = ...

An ideal I of a ring R is called principal if there is an element a of R such that I=aR={ar:r in R}. In other words, the ideal is generated by the element a. For example, the ...

The ratio of two numbers r and s is written r/s, where r is the numerator and s is the denominator. The ratio of r to s is equivalent to the quotient r/s. Betting odds ...