parabolic geometry

Thân thiện

A student draws a diagram of parabolic geometry on a chalkboard.

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.

Học thuật

Noun

1. (mathematics) geometry based on Euclid's axioms

Từ đồng nghĩa

• elementary geometry
• Euclidean geometry