elementary geometry
Definition
Noun: - The branch of mathematics dealing with the properties and relations of points, lines, surfaces, and solids based on the axioms and theorems established by Euclid. It is the traditional, foundational form of geometry that does not involve more advanced concepts like calculus or non-Euclidean systems.
Usage
- As a subject of study: "Elementary geometry" is typically taught in middle school or high school.
- To distinguish from advanced geometry: The term is used to specify the classical, Euclidean foundation of the subject.
Examples
- Noun:
- Students must master the principles of elementary geometry before moving on to trigonometry.
- The proof relies on concepts from elementary geometry, such as congruent triangles and the Pythagorean theorem.
Advanced Usage
- "Euclidean geometry": This is a direct synonym for "elementary geometry," emphasizing its basis in Euclid's postulates.
- In elementary geometry, also known as Euclidean geometry, the sum of angles in a triangle is always 180 degrees.
Variants and Related Words
- Euclidean geometry (n): A synonym for elementary geometry.
- Plane geometry (n): A major subset of elementary geometry dealing with two-dimensional figures on a plane.
- Solid geometry (n): A subset of elementary geometry dealing with three-dimensional figures.
Synonyms
- Euclidean geometry: The geometry based on Euclid's axioms.
- Parabolic geometry: A less common technical term.
Related Phrases
- Foundations of geometry: Often refers to the axiomatic system underlying elementary geometry.
- Classical geometry: Another term emphasizing its historical and traditional roots, largely synonymous with elementary geometry.
Noun
-
(mathematics) geometry based on Euclid's axioms
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