What does "isometry" mean?
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.
Isometry
noun
noun ·Rare ·Advanced level
Meaning at a glance
- Primary sense: 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.
- Grammar: isometry is listed as noun.
- Nearest alternatives: congruence-preserving map, distance-preserving map, distance-preserving transformation, isometric growth.
- Useful contrasts: allometry, nonisometry, skewing.
- Usage evidence: A distance-preserving diffeomorphism between two Riemannian manifolds is called an isometry.
How to use "isometry"
- Start with the primary definition, then check the part of speech before placing the word in a sentence.
- Compare nearby synonyms to make sure "isometry" carries the exact meaning, tone, and strength you need.
- Use the example sentence as a context check. If your sentence uses the word differently, confirm that the grammar still fits.
Meaning check
- Does the word fit the sentence's grammar?
- Does it match the intended tone rather than only the dictionary definition?
- Would a simpler synonym be clearer for the reader?
- Is there enough surrounding context to prevent ambiguity?
Source and review context
This entry combines structured lexical data with WordToolSet review checks. Definitions, examples, synonyms, and usage notes may come from different source tables, so the page is designed to show evidence from more than one angle before you rely on "isometry" in a final draft.
If a word has several senses, prefer the sense that matches your sentence's grammar and surrounding context. A correct definition can still be the wrong choice when the sentence needs a different register, emphasis, or level of specificity.
Before you rely on this definition
Read the first definition as a starting point, then check the example, synonyms, and part of speech before treating "isometry" as the right word for your sentence.
If your draft is formal, technical, persuasive, or sensitive, compare "isometry" with a nearby alternative so the final choice matches both meaning and reader expectation.
Compare nearby meanings
- Use synonyms when you need a softer, stronger, simpler, or more specific word.
- Use antonyms to check the boundary of the meaning and avoid accidental contrast.
- Use the example sentence to confirm the word behaves naturally in context.
- Keep the original wording when a replacement adds complexity without improving precision.
Definition decision workflow
1. Identify the role
Check whether "isometry" is acting as noun in your sentence. A definition is only useful when the grammar matches the way the word is being used.
2. Test the nearest option
Compare it with "congruence-preserving map" and other nearby choices to see whether the sentence needs a softer, stronger, or more familiar word.
3. Confirm with context
Use the example sentence below as an evidence check, then read your own sentence out loud to catch tone or rhythm problems.
Review note: Definition pages are checked for source coverage, sentence evidence, synonym support, and editorial insight before they are treated as approval-ready pages. If the evidence is too thin, the page remains available to users but is kept out of the approval-facing indexed inventory.
Final meaning check
Before publishing a sentence with "isometry", ask whether the word helps the reader understand the idea faster. A precise word should reduce confusion, not simply make the sentence look more polished.
When the definition, synonym evidence, and example context point in the same direction, the word is usually a safer choice. When they conflict, revise the sentence or choose a clearer alternative.
Definitions
Noun
- 1 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.
"Isometry is to metric spaces what isomorphism is to groups."
- 2 equality of measure (e.g., equality of height above sea level or equality of loudness etc.) wordnet
- 3 equality of elevation above sea level wordnet
- 4 a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points wordnet
- 5 the growth rates in different parts of a growing organism are the same wordnet
Synonyms
All synonyms congruence-preserving mapdistance-preserving mapdistance-preserving transformationisometric growthisometricsproportional growth
Antonyms
Example
"A distance-preserving diffeomorphism between two Riemannian manifolds is called an isometry."
Common questions
What is a synonym for "isometry"?
Common synonyms include: congruence-preserving map, distance-preserving map, distance-preserving transformation, isometric growth, isometrics, proportional growth.
How do you use "isometry" in a sentence?
A distance-preserving diffeomorphism between two Riemannian manifolds is called an isometry.
Etymology
From New Latin isometria, from Ancient Greek ἰσομετρία (isometría), from ἰσο- (iso-) + -μετρία (-metría), from ἴσος (ísos, “equal”) and μέτρον (métron, “measurement”) + -ια (-ia, “-y”). Equivalent to iso- + -metry.