Thus, rather than speaking of a concrete Euclidean metric, one may use sets to describe points close to " x ".
22.
In the applications of mathematics, there are often situations where an affine plane without the Euclidean metric is used instead of the Euclidean plane.
23.
In fact, a " metric " is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance.
24.
In fact, the notion of " metric " is a generalization of the Euclidean metric arising from the four long known properties of the Euclidean distance.
25.
For instance, the Euclidean metric measures the distance between points in the Euclidean plane, while the hyperbolic metric measures the distance in the hyperbolic plane.
26.
Operators preserving the Euclidean metric on such a space form the isometry group, and those that fix the origin form a subgroup known as the orthogonal group.
27.
Equivalently, the Fubini Study metric can be understood as the metric on complex projective Hilbert space that is induced by the complex extension of the flat Euclidean metric.
28.
In the case of the Euclidean metric for " k " = 1, it is known as the smallest enclosing sphere problem or 1-center problem.
29.
Here Hausdorff dimension is relative to the Euclidean metric on "'R " "'n " ( or any metric Lipschitz equivalent to it ).
30.
In finite dimensional spaces, all metrics induced by the p-norm, including the euclidean metric, the taxicab metric, and the Chebyshev distance, are strongly equivalent.
