euclidian
Definition
Adjective: 1. Relating to the geometry developed by the ancient Greek mathematician Euclid: Describing the classical system of geometry based on a set of axioms and postulates, primarily concerning the properties of flat, two-dimensional planes and three-dimensional space. * Euclidian geometry is the study of points, lines, planes, and figures like triangles and circles based on Euclid's axioms.
Usage
The adjective "Euclidian" is used specifically to describe concepts, principles, theorems, or spaces that conform to the traditional geometric system established by Euclid. It is often contrasted with non-Euclidian geometries.
Examples
- Adjective:
- The sum of the angles in any Euclidian triangle is always 180 degrees.
- High school mathematics typically introduces students to Euclidian geometry first.
- Parallel lines in a Euclidian plane never meet.
Advanced Usage
- "Euclidian space": A mathematical space that satisfies Euclid's axioms of geometry. It is characterized by flatness, where the rules of classical geometry apply.
- In a three-dimensional Euclidian space, the shortest distance between two points is a straight line.
Variants and Related Words
- Euclidean (adj): The more common modern spelling, identical in meaning to "Euclidian."
- Euclidean geometry is a foundational subject.
- Non-Euclidean (adj): Describing geometries that do not adhere to Euclid's parallel postulate, such as spherical or hyperbolic geometry.
- On the surface of a sphere, the geometry is non-Euclidean.
Synonyms
- Classical (in the context of geometry): Pertaining to the traditional, long-established system.
- Parabolic (in a specific mathematical context): Sometimes used to describe the flat geometry of Euclidian space.
Related Concepts
- Euclid's Elements: The foundational mathematical and geometric treatise written by Euclid.
- Parallel Postulate: A key axiom in Euclidian geometry stating that through a point not on a given line, only one line can be drawn parallel to the given line.
Adjective
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relating to geometry as developed by Euclid
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Euclidian geometry
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