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Euclidean
[ yoo-klid-ee-uhn ]
adjective
- of or relating to Euclid, or adopting his postulates.
Euclidean
/ ̅̅-ĭ′ŧ-ə /
- 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.
- Compare non-Euclidean
yvlog History and Origins
Origin of Euclidean1
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.
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.
What I find so creepy about OpenAI’s bots is not that they seem to exhibit creativity; computers have been doing creative tasks such as generating original proofs in Euclidean geometry since the 1950s.
I used to be a mathematician, and I’m not suggesting that there’s some kind of Euclidean geometric proof that this is the right way to go.
Manifolds are objects that on a zoomed-in, ‘local’ scale appear indistinguishable from the plane or higher-dimensional space described by Euclidean geometry.
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