isomorphism

[ ahy-suh-mawr-fiz-uhm ]

noun

1. the state or property of being isomorphous or isomorphic.
2. Mathematics. a one-to-one relation onto the map between two sets, which preserves the relations existing between elements in its domain.

isomorphism

/ ˌaɪsəʊˈmɔːfɪzəm /

noun

1. biology similarity of form, as in different generations of the same life cycle
2. chem the existence of two or more substances of different composition in a similar crystalline form
3. maths a one-to-one correspondence between the elements of two or more sets, such as those of Arabic and Roman numerals, and between the sums or products of the elements of one of these sets and those of the equivalent elements of the other set or sets

isomorphism

/ ī′sə-môr′fĭz′əm /

1. Similarity in form, as in organisms of different ancestry.
2. A one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.
3. A close similarity in the crystalline structure of two or more substances of different chemical composition. Isomorphism is seen, for example, in the group of minerals known as garnets, which can vary in chemical composition but always have the same crystal structure.

Word History and Origins

Origin of isomorphism¹

First recorded in 1820–30; isomorph(ous) + -ism

Example Sentences

We can define the notion of isomorphism in any category, which allows us to transport this concept between mathematical contexts.

From Scientific American

A professor of physics at Dartmouth College and a lifelong student of jazz, Dr. Alexander has taken on “the challenge to find an isomorphism between jazz and cosmology.”

From New York Times

“Institutional isomorphism,” explained Mason President Ángel Cabrera, a former business school dean.

From Washington Post

Graph isomorphism is known to be in NP, which contains some problems that are believed to take a long time to solve.

From Nature

In the "graph isomorphism problem," the challenge is to determine whether two graphs are really the same or not.

From Science Magazine