Euclidean

American  

[yoo-klid-ee-uhn] / yuˈklɪd i ən /

Or Euclidian

adjective

1. of or relating to Euclid, or adopting his postulates.

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Euclidean Scientific  

/ yo̅o̅-klĭd′ē-ən /

1. 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.

2. Compare non-Euclidean

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Etymology

Origin of Euclidean

1650–60; < Latin Euclīdē ( us ) of Euclid (< Greek Eukleídeios ) + -an

Example Sentences

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

Wordsworth imagined that Euclidean geometry “wedded soul to soul in purest bond / Of reason, undisturbed by space or time.”

From New York Times • May 18, 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

To avoid the technical difficulties in actually performing the sum over histories, these curved space-times must be taken to be Euclidean.

From "A Brief History of Time: And Other Essays" by Stephen Hawking