Associations to the word «Euclidean»

EUCLIDEAN, adjective. (geometry) Adhering to the principles of traditional geometry, in which parallel lines are equidistant.

EUCLIDEAN, adjective. Of or relating to Euclid's Elements, especially to Euclidean geometry.

EUCLIDEAN, adjective. Of or relating to Euclidean zoning.

EUCLIDEAN, adjective. (rare) Alternative spelling of Euclidean

EUCLIDEAN ALGORITHM, noun. (algebra) A method based on the division algorithm for finding the greatest common divisor (gcd) of two given integers.

EUCLIDEAN ALPHABET, noun. The classical Greek alphabet, a modified form of the Ionic alphabet adopted by Athens in 403 BC following its defeat in the Peloponnesian War.

EUCLIDEAN DISTANCE, noun. (geometry) The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (ax, ay) and b = (bx, by) is defined as:

EUCLIDEAN DOMAIN, noun. (algebra) a principal ideal domain in which division with remainder is possible

EUCLIDEAN GEOMETRY, noun. (geometry) The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line.

EUCLIDEAN GROUP, noun. (mathematics) the set of rigid motions that are also affine transformations.

EUCLIDEAN GROUPS, noun. Plural of Euclidean group

EUCLIDEAN METRIC, noun. (analysis) In the space \(\mathbb{R}^n\), the metric \( d(\vec x, \vec y) = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + ... + (x_n - y_n)^2} \) where \( \vec x = (x_1, ..., x_n) \) and \( \vec y = (y_1, ..., y_n)\).

EUCLIDEAN NORM, noun. (mathematics) A norm of an ordinary Euclidean space, for which the Pythagorean theorem holds, defined by \(\| x \| = \sqrt{\sum_j {x_j}^2}\)

EUCLIDEAN PLANE, noun. (mathematics) Two-dimensional Euclidean space.

EUCLIDEAN PLANES, noun. Plural of Euclidean plane

EUCLIDEAN SPACE, noun. Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.

EUCLIDEAN SPACE, noun. (mathematics) Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.

EUCLIDEAN SPACES, noun. Plural of Euclidean space

EUCLIDEAN, adjective. Relating to geometry as developed by Euclid; "Euclidian geometry".