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
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
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
Every theorem in Euclidean geometry can be dualized in projective geometry, setting up a whole set of new theorems in the parallel universe of projective geometry.
From "Zero: The Biography of a Dangerous Idea" by Charles Seife
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