Euclidean
Americanadjective
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Relating to geometry of plane figures based on the five postulates (axioms) of Euclid, involving the derivation of theorems from those postulates. The five postulates are: 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment, a circle can be drawn having the line segment as radius and an endpoint as center. 4. All right angles are congruent. 5. (Also called the parallel postulate.) If two lines are drawn that intersect a third in such a way that the sum of inner angles on one side is less than the sum of two right triangles, then the two lines will intersect each other on that side if the lines are extended far enough.
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Compare non-Euclidean
Etymology
Origin of Euclidean
1650–60; < Latin Euclīdē ( us ) of Euclid (< Greek Eukleídeios ) + -an
Example Sentences
Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.
The method is not limited to familiar flat, or Euclidean, spaces.
From Science Daily • Jan. 7, 2026
Manifolds are objects that on a zoomed-in, ‘local’ scale appear indistinguishable from the plane or higher-dimensional space described by Euclidean geometry.
From Scientific American • Mar. 28, 2022
In the ultra-stylized portraits of this Brooklyn-based painter, flesh resolves into Euclidean shapes and decorative patterning: eyes and breasts appear as little half-moons, foreheads and shoulders as perfect semicircles of pink and powder blue.
From New York Times • Oct. 28, 2021
Well, for centuries mathematicians tried to prove that this statement actually followed from the other four axioms of Euclidean geometry—but as it turned out, the parallel axiom is actually independent of them.
From Slate • Aug. 6, 2018
What we now call Euclidean space-time is very similar except that it has four dimensions instead of two.
From "A Brief History of Time: And Other Essays" by Stephen Hawking
Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023
Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
