Euclidean

American  

[yoo-klid-ee-uhn] / juˈklɪd 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

See Examples For:

Euclidean

The method is not limited to familiar flat, or Euclidean, spaces.

From Science Daily ● Jan. 7, 2026

Within the realm of two dimensions, geometry deals with properties of points, lines, figures, surfaces: The Euclidean plane is flat and therefore displays zero curvature.

From New York Times ● Jan. 15, 2024

It’s almost a circle, with a small but significant deviation from Euclidean perfection that actually makes Earth’s orbit a slightly squashed oval—that is, an ellipse.

From Scientific American ● Jun. 30, 2023

Does democracy follow from the Constitution like a proof of Euclidean geometry?

From Slate ● Aug. 6, 2018

To do this, we must perform the sum over histories for all possible Euclidean space-times that have no boundary.

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