ISO TC 211 Geographic information/Geomatics Committee site

ISO/TC 211 Geolexica

Concept Pythagorean metric <Euclidean geometry>”

Term ID

2081

source

ISO 19107:2019, (E), 3.78

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)

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info

  • status: valid
  • classification: preferred
  • date accepted: 2019-12-02

Review

last review performed:
(2019-12-02)
status:
final
decision:
accepted
decision event:
Normal ISO processing
notes:
Publication of document ISO 19107:2019(E)