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A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

Every real number is negative, 0, or positive. The law is sometimes stated as "For arbitrary real numbers a and b, exactly one of the relations a<b, a=b, a>b holds" (Apostol ...

The Chern number is defined in terms of the Chern class of a manifold as follows. For any collection Chern classes such that their cup product has the same dimension as the ...

Given algebraic numbers a_1, ..., a_n it is always possible to find a single algebraic number b such that each of a_1, ..., a_n can be expressed as a polynomial in b with ...

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...

A figurate number of the form 4n^2-3n. The first few are 1, 10, 27, 52, 85, ... (OEIS A001107). The generating function giving the decagonal numbers is ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...