isomorphism

American  

[ahy-suh-mawr-fiz-uhm] / ˌaɪ səˈmɔr fɪz əm /

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.

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isomorphism British  

/ 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

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isomorphism Scientific  

/ 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.

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Etymology

Origin of isomorphism

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

Example Sentences

An isomorphism of the Isomorphism of a group with itself. group with itself, established in this way, is called an inner isomorphism.

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various

Isomorphism, ī-so-morf′izm, n. a term applied by chemists to those substances which are not only similar in their crystalline form, but are also analogous in their chemical composition.—adj.

From Chambers's Twentieth Century Dictionary (part 2 of 4: E-M) by Various

Finally, Isomorphism, or the equality of form of many chemical compounds having a different composition, tends to prove that matter consists of atoms the mere arrangement of which produces all the properties of bodies.

From Familiar Letters on Chemistry by Liebig, Justus, Freiherr von

Isomorphism is most clearly discerned between elements of analogous chemical properties; and from the wide generality of such observations attempts have been made to form a classification of elements based on isomorphous replacements.

From Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1 "Châtelet" to "Chicago" by Various

Who will explain to us the laws of Isomorphism?

From Reflections on the Decline of Science in England by Babbage, Charles