parabolic geometry
Definition
Noun: 1. A system of geometry based on Euclid's axioms: Parabolic geometry is the classical system of geometry, also known as Euclidean geometry. It is characterized by axioms that describe a flat, two-dimensional plane where, for example, parallel lines never meet and the sum of angles in a triangle is always 180 degrees.
Usage Examples
- The principles of parabolic geometry are fundamental to architectural design and engineering.
- In parabolic geometry, the shortest distance between two points is a straight line.
- Students often first encounter parabolic geometry in their high school math classes.
Advanced Usage
- The term "parabolic geometry" is used in advanced mathematical discourse to distinguish classical Euclidean geometry from non-Euclidean geometries (elliptic and hyperbolic). It is less common in everyday speech than "Euclidean geometry."
Variants and Related Words
- Euclidean geometry (n): The more common synonym for parabolic geometry.
- Elliptic geometry (n): A non-Euclidean geometry where parallel lines do not exist (e.g., geometry on a sphere).
- Hyperbolic geometry (n): A non-Euclidean geometry where through a point not on a given line, there are infinitely many lines parallel to the given line.
Synonyms
- Euclidean geometry
Related Terms and Concepts
- Parallel postulate: A key axiom in parabolic geometry stating that through a point not on a given line, there is exactly one line parallel to the given line.
- Flat space: A term describing the type of space modeled by parabolic geometry, in contrast to curved spaces.
Noun
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(mathematics) geometry based on Euclid's axioms
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