(mathematics) 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 preimages.
Used in a Sentence
isometry
Definition, parts of speech, synonyms, and sentence examples for isometry.
Editorial note
Inside P the pattern is periodic, and in P' the pattern is comprised of units, each of which is periodic under some isometry.
Examples16
Definitions1
Parts of speech1
Quick take
(mathematics) 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 preimages.
Meaning at a glance
The clearest senses and uses of isometry gathered in one view.
Definitions
Core meanings and parts of speech for isometry.
noun
(mathematics) 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 preimages.
Example sentences
Inside P the pattern is periodic, and in P' the pattern is comprised of units, each of which is periodic under some isometry.
To be precise, the mean curvature and metric are the same but the immersions are different (they're not related by an isometry of the ambient space).
By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry), and orientation (i.e., handedness of space).
Are there measures in ZF+DC of R^3 that are finitely (countably?) additive and isometry invariant?
Additionally, every elliptic isometry is a projective symmetry, while the other way round isn't true.
As a side issue, B-T is proof that there isn't a finitely additive, isometry-invariant measure on R^3 that's defined for all subsets.
Is there a known set theory of the form ZF+(something) which relatively consistent with ZFC in which additive, isometry invariant measures exist?
In other works, they have two immersions from the torus to R^3, whose induced metric and mean curvature are the same, and whose images are not related by an isometry of R^3.
For what it's worth, as of Terraform 1.8, you can also use functions from third-party providers like isometry/deepmerge [2] to perform a deep merge.
They don't appear to care about the images of the immersions or their complements, aside from them not being related by an isometry of R^3.
Specifically, networks train well when their input-output Jacobians exhibit dynamical isometry, namely the property that the entire distribution of singular values is close to 1.
* Measures 1 on the unit object; * Countably additive; * Isometry invariant; * Defined on all sets.
Quote examples
Actual isometry would require some 1:1 "stairs" on these lines, making them look less nice.
For example see “dynamical isometry” [1] and the evolution of those ideas which were instrumental in achieving convergence in very deep transformer models [2].
Because it expands past my normal reading FOV I keep seeing it as "I Some Try" instead of "Isometry".
"Movement" is undefined, it has to be an isometry.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use isometry in a sentence?
Inside P the pattern is periodic, and in P' the pattern is comprised of units, each of which is periodic under some isometry.
What does isometry mean?
(mathematics) 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 preimages.
What part of speech is isometry?
isometry is commonly used as noun.