What does "euclidean" mean?
Adhering to the principles of traditional geometry, in which parallel lines are equidistant.
Euclidean
/juːˈklɪd.i.ən/ adj
adj ·Uncommon ·Advanced level
Meaning at a glance
- Primary sense: Adhering to the principles of traditional geometry, in which parallel lines are equidistant.
- Grammar: euclidean is listed as adj.
- Nearest alternatives: algebraic euclidean property, classical geometry, division domain property, euclid geometry.
- Useful contrasts: non-Euclidean, hyperbolic, non-Euclidean domain.
- Usage evidence: The surface of a balloon is not an Euclidean space, and therefore does not follow the rules of Euclidean geometry.
How to use "euclidean"
- Start with the primary definition, then check the part of speech before placing the word in a sentence.
- Compare nearby synonyms to make sure "euclidean" 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 "euclidean" 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 "euclidean" as the right word for your sentence.
If your draft is formal, technical, persuasive, or sensitive, compare "euclidean" 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 "euclidean" is acting as adj 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 "algebraic euclidean property" 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 "euclidean", 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
Adjective
- 1 Adhering to the principles of traditional geometry, in which parallel lines are equidistant. not-comparable
- 2 Of or relating to Euclidean zoning. not-comparable
- 3 Alternative spelling of Euclidean. alt-of, alternative, not-comparable, rare
"If (#92;alpha#95;1,#92;dots,#92;alpha#95;n) is an orthonormal basis of a euclidean space V, then for all #92;alpha,#92;beta in V#92;alpha#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;i)#92;alpha#95;i#92;quad#92;text#123;and#125;#92;quad(#92;alpha#92;vert#92;beta)#61;#92;sum#95;#123;i#61;1#125;ⁿ(#92;alpha#92;vert#92;alpha#95;i)(#92;beta#92;vert#92;alpha#95;i).We turn now to a somewhat more profound matter. Suppose that we partially order by inclusion the collection of all orthonormal sets of vectors in a euclidean space V. A maximal element of this set is called a maximal orthonormal set."
- 4 Of or relating to Euclid's Elements, especially to Euclidean geometry. not-comparable
Adjective
- 1 relating to geometry as developed by Euclid wordnet
Synonyms
All synonyms algebraic euclidean propertyclassical geometrydivision domain propertyeuclid geometryeuclid's geometryeuclidian
Antonyms
Example
"The surface of a balloon is not an Euclidean space, and therefore does not follow the rules of Euclidean geometry."
Common questions
What is a synonym for "euclidean"?
Common synonyms include: algebraic euclidean property, classical geometry, division domain property, euclid geometry, euclid's geometry, euclidian.
How do you use "euclidean" in a sentence?
The surface of a balloon is not an Euclidean space, and therefore does not follow the rules of Euclidean geometry.
How do you pronounce "euclidean"?
Pronounced /juːˈklɪd.i.ən/.
Etymology
Etymology 1
Named after Euclid, who established the principles of plane geometry.
Etymology 2
Named after the landmark U.S. Supreme Court case Village of Euclid v. Ambler Realty Co., which in turn refers to the city of Euclid, Ohio.