isometries
|i-so-met-ry|
🇺🇸
/aɪˈsɑːmətri/
🇬🇧
/aɪˈsɒmətri/
(isometry)
preserve distance
Etymology
'isometry' originates from Greek, specifically the words 'isos' and 'metron', where 'isos' meant 'equal' and 'metron' meant 'measure'.
'isometry' was formed in modern mathematical usage (attested in the 19th century), via French 'isométrie' and other European mathematical terminology, and was adopted into English as 'isometry'.
Initially it meant 'equal measure' from the Greek roots, but over time it evolved into its current technical meaning of 'a distance-preserving mapping'.
Meanings by Part of Speech
Noun 1
a mapping between metric spaces that preserves distances (for any two points x and y, the distance between f(x) and f(y) equals the distance between x and y).
Translations, rotations and reflections are common examples of isometries in Euclidean geometry.
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Noun 2
an element of the group of transformations of a space that preserves the metric (often used in group-theoretic or geometric contexts: 'the group of isometries of the plane').
The group of isometries of the plane includes all combinations of translations, rotations and reflections.
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Noun 3
a linear map between normed vector spaces (or inner-product spaces) that preserves norms (or inner products); e.g., unitary or orthogonal operators are linear isometries.
Unitary operators on a Hilbert space are examples of linear isometries.
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Last updated: 2026/01/02 20:35