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Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups C_2 and D_1 are ...

Two partially ordered sets are said to be isomorphic if their "structures" are entirely analogous. Formally, partially ordered sets P=(X,<=) and Q=(X^',<=^') are isomorphic ...

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...

Let a plane figure have area A and perimeter p. Then Q=(4piA)/(p^2)<=1, where Q is known as the isoperimetric quotient. The equation becomes an equality only for a circle.

Of all convex n-gons of a given perimeter, the one which maximizes area is the regular n-gon.

An isosceles trapezoid (called an isosceles trapezium by the British; Bronshtein and Semendyayev 1997, p. 174) is trapezoid in which the base angles are equal and therefore ...

A parameterization is isothermal if, for zeta=u+iv and phi_k(zeta)=(partialx_k)/(partialu)-i(partialx_k)/(partialv), the identity phi_1^2(zeta)+phi_2^2(zeta)+phi_3^2(zeta)=0 ...

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

The isotomic transform of a geometric object is the object obtained by collectively taking the isotomic conjugates of all its points.

A homotopy from one embedding of a manifold M in N to another such that at every time, it is an embedding. The notion of isotopy is category independent, so notions of ...