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A definition assigns properties to some sort of mathematical object. For example, Euclid's Elements starts with a number of definitions, such as "a line is a breadthless ...

Two manifolds are said to be diffeomorphic if there exists a diffeomorphism between them.

A set S of positive integers is said to be Diophantine iff there exists a polynomial Q with integral coefficients in m>=1 indeterminates such that ...

The length of the largest-sized square contained within the Ferrers diagram of a partition. Its size can be determined using DurfeeSquare[f] in the Wolfram Language package ...

A Padé approximant perturbed with a Chebyshev polynomial of the first kind to reduce the leading coefficient in the error.

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

A distribution of error such that the error remaining is always given approximately by the last term dropped.

The bias of an estimator theta^~ is defined as B(theta^~)=<theta^~>-theta. (1) It is therefore true that theta^~-theta = (theta^~-<theta^~>)+(<theta^~>-theta) (2) = ...

The excentral-hexyl ellipse is the ellipse passing through vertices of the excentral and hexyl triangles (P. Moses, pers. comm., Jan. 29, 2005). It has center at the ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...