Euclidean

or Eu·clid·i·an

[ yoo-klid-ee-uhn ]

adjective

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

Euclidean

/ 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

Word History and Origins

Origin of Euclidean¹

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

Example Sentences

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

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

The boom of interest stemmed in part from frustration with more than two millennia of Euclidean orthodoxy.

From Literature

The emergence in the early nineteenth century of “non-Euclidean” geometry was a watershed for mathematics in that it described a theory of physical space that totally contradicted our experience of the world and therefore was hard to imagine, but nevertheless contained no mathematical contradictions, and so was as mathematically valid as the Euclidean system that came before.

From Literature

Perhaps the most stunning result in Euclidean geometry, though, is one that reveals an astonishing property about triangles.

From Literature