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In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states e^(ix)=cosx+isinx, (1) where i is the imaginary unit. Note that Euler's ...

A dissection of a rectangle into smaller rectangles such that the original rectangle is not divided into two subrectangles. Rectangle dissections into 3, 4, or 6 pieces ...

In mathematics, a formal language is normally defined by an alphabet and formation rules. The alphabet of a formal language is a set of symbols on which this language is ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...

The continued fraction of A is [1; 3, 1, 1, 5, 1, 1, 1, 3, 12, 4, 1, 271, 1, ...] (OEIS A087501). A plot of the first 256 terms of the continued fraction represented as a ...

The n-hypercube graph, also called the n-cube graph and commonly denoted Q_n or 2^n, is the graph whose vertices are the 2^k symbols epsilon_1, ..., epsilon_n where ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...