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Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...

Given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, known as the Weill point, ...

Let L be a nontrivial bounded lattice (or a nontrivial complemented lattice, etc.). If every nonconstant lattice homomorphism defined on L is 0,1-separating, then L is a ...

The set theory symbol aleph_0 refers to a set having the same cardinal number as the "small" infinite set of integers. The symbol aleph_0 is often pronounced "aleph-null" ...

Aleph-1 is the set theory symbol aleph_1 for the smallest infinite set larger than aleph_0 (Aleph-0), which in turn is equal to the cardinal number of the set of countable ...

Let X be an alphabet (i.e., a finite and nonempty set), and call its member letters. A word on X is a finite sequence of letters a_1...a_n, where a_1,...,a_n in X. Denote the ...

An algebraic set is the locus of zeros of a collection of polynomials. For example, the circle is the set of zeros of x^2+y^2-1 and the point at (0,0) is the set of zeros of ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines. A connection between automata theory ...