euclidean geometry
Definition
Noun: - A system of geometry based on the axioms and postulates of the ancient Greek mathematician Euclid. It is the study of flat, two-dimensional planes and three-dimensional spaces where concepts like points, lines, angles, and figures (e.g., triangles, circles) behave according to Euclid's established rules.
Usage
- Euclidean geometry is used to describe the properties and relationships of shapes and spaces in a flat plane.
- It is the foundation for many principles in classical mathematics, physics, and engineering.
Examples
Advanced Usage
- "Euclidean space": A mathematical space that satisfies the axioms of Euclidean geometry. It is the generalization of two- and three-dimensional flat geometry to higher dimensions.
- The vector was analyzed in a three-dimensional Euclidean space.
Variants and Related Words
- Non-Euclidean geometry (n): A geometry based on axioms that differ from Euclid's, describing curved spaces like spheres or hyperbolic planes.
- Einstein's theory of general relativity uses non-Euclidean geometry.
Synonyms
- Parabolic geometry: A less common synonym referring to the geometry of flat space.
- Elementary geometry: Often used to describe the basic, school-level concepts derived from Euclid's work.
Related Phrases
- "Euclidean distance": The straight-line distance between two points in Euclidean space, calculated using the Pythagorean theorem.
- The algorithm calculates the Euclidean distance between the data points.
Noun
-
(mathematics) geometry based on Euclid's axioms
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