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
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
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
For example, some of you might recall that in good old high school Euclidean geometry there are five axioms, one of which is the “parallel axiom.”
From Slate ● Aug. 6, 2018
A space-time in which events have imaginary values of the time coordinate is said to be Euclidean, after the ancient Greek Euclid, who founded the study of the geometry of two-dimensional surfaces.
From "A Brief History of Time: And Other Essays" by Stephen Hawking
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