eng

### Pythagorean metric <Euclidean geometry>

distance measure on a 𝔼n coordinate space using a root-mean sum of the differences between the individual coordinate offsets

Note to entry: `P = (p_i), Q = (q_i), "distance"(P,Q) = sqrt( sum_{i=1}^n (p_i - q_i)^2)`. The proofs of the Pythagorean metrics all depend on the local "flatness" of the space. Cartesian coordinate space which have Pythagorean metrics are called Euclidean spaces (`bbb"E"^n`). In the realm of coordinate reference systems, only "Engineering Coordinate Systems" are Euclidean. Any CRS using a curved Datum are by definition non-Euclidean, and cannot "truthfully" use Pythagorean metrics except for approximation. These approximations are valid for topological statements, but not for real world measures without adjustments.

ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)