euclidean
- Adjective:
- Relating to the geometry or mathematical system developed by the ancient Greek mathematician Euclid. This describes concepts, principles, or spaces that conform to the axioms and postulates set out in Euclid's Elements, which form the basis of classical or "flat" geometry.
The adjective "Euclidean" is used to modify nouns related to geometry, mathematics, and physics to specify that they adhere to the classical system. It is often contrasted with non-Euclidean geometries.
- Adjective:
- In Euclidean geometry, the angles of a triangle always sum to 180 degrees.
- The concept of parallel lines is fundamental to Euclidean space.
- We studied Euclidean constructions using only a compass and straightedge.
"Euclidean algorithm": A specific, efficient method for computing the greatest common divisor (GCD) of two integers, described by Euclid.
- The Euclidean algorithm is a classic example of an ancient, yet still vital, computational procedure.
"Euclidean distance": In mathematics and data science, the straight-line distance between two points in Euclidean space, calculated using the Pythagorean theorem.
- The k-nearest neighbors algorithm often uses Euclidean distance to measure similarity between data points.
"Euclidean norm": The length of a vector in Euclidean space, also known as the L² norm.
- The Euclidean norm of a vector is the square root of the sum of the squares of its components.
Euclidian (adj): An alternative, less common spelling with identical meaning.
- Euclidian geometry is another term for Euclidean geometry.
Non-Euclidean (adj): Describing geometries that do not adhere to Euclid's parallel postulate, such as spherical or hyperbolic geometry.
- The surface of a sphere is an example of a non-Euclidean space.
- Classical (in the context of geometry).
- Planar (when referring specifically to flat, two-dimensional Euclidean geometry).
- Euclidean geometry: The specific system of geometry based on Euclid's axioms.
- Euclidean space: A mathematical space where Euclid's axioms hold, typically referring to two-dimensional (plane) or three-dimensional space.
- Euclidean plane: The two-dimensional Euclidean space.
-
relating to geometry as developed by Euclid
-
Euclidian geometry
-
Khám phá thêm
Các từ liên quan
Từ đồng nghĩa
Từ gần giống
Từ chứa "euclidean"
Từ có nhắc đến "euclidean"
