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Lagrange's continued fraction theorem, proved by Lagrange in 1770, states that any positive quadratic surd sqrt(a) has a regular continued fraction which is periodic after ...

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.

The least number of crossings that occur in any projection of a link. In general, it is difficult to find the crossing number of a given link. Knots and links are generally ...

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 simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

A quartic surface named after its resemblance to the liturgical headdress worn by bishops and given by the equation 4x^2(x^2+y^2+z^2)-y^2(1-y^2-z^2)=0.

Monster-barring is a term coined by Lakatos (1976) to refer to the refining of a hypothesis to rule out nasty counterexamples (Bailey et al. 2007, p. 11).

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

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 ...

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 ...