What does isometry mean?

Definitions for isometry
aɪˈsɒm ɪ triisom·e·t·ry

This dictionary definitions page includes all the possible meanings, example usage and translations of the word isometry.

Princeton's WordNet

  1. isometrynoun

    the growth rates in different parts of a growing organism are the same

  2. isometrynoun

    a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points

    "the isometries of the cube"

  3. isometrynoun

    equality of elevation above sea level

  4. isometrynoun

    equality of measure (e.g., equality of height above sea level or equality of loudness etc.)

Wiktionary

  1. isometrynoun

    A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their pre-images.

  2. Etymology: From iso- and -metry.

Wikipedia

  1. Isometry

    In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure".

ChatGPT

  1. isometry

    An isometry is a transformation of a geometric space that preserves distances between every pair of points. It is often described as a rigid motion, involving rotation, reflection, translation or their combination without changing the shape and size of the figure. In other words, the preimage and image of a figure under an isometric transformation are congruent. Isometries are used in fields such as geometry, physics, and computer graphics.

Wikidata

  1. Isometry

    In mathematics, an isometry is a distance-preserving map between metric spaces. Given a metric space, or a set and scheme for assigning distances between elements of the set, an isometry is a transformation which maps elements to another metric space such that the distance between the elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional space, two geometric figures are congruent if they are related by an isometry: related by either a rigid motion, or a composition of a rigid motion and a reflection. Up to a relation by a rigid motion, they are equal if related by a direct isometry. Isometries are often used in constructions where one space is embedded in another space. For instance, the completion of a metric space M involves an isometry from M into M', a quotient set of the space of Cauchy sequences on M. The original space M is thus isometrically isomorphic to a subspace of a complete metric space, and it is usually identified with this subspace. Other embedding constructions show that every metric space is isometrically isomorphic to a closed subset of some normed vector space and that every complete metric space is isometrically isomorphic to a closed subset of some Banach space.

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Numerology

  1. Chaldean Numerology

    The numerical value of isometry in Chaldean Numerology is: 9

  2. Pythagorean Numerology

    The numerical value of isometry in Pythagorean Numerology is: 7

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"isometry." Definitions.net. STANDS4 LLC, 2024. Web. 29 Mar. 2024. <https://www.definitions.net/definition/isometry>.

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