Symplectic Geometry in 2D – Points, Lines, Circles

Re:Symplectic Geometry in 2D – Points, Lines, Circles by ReleaseCandidat on Monday February 21, 2022 @10:59AM (#30417289)

Interesting definition of 'Euclidian geometry'. I am used to call 'something' Euclidean, if the parallel postulate of Euclid holds (that is, there exists exactly one parallel line to a given line through a point (which does not lie on the given line)).

[ Parent | on HN ]

Re:Symplectic Geometry in 2D – Points, Lines, Circles by Koshkin on Monday February 21, 2022 @11:53AM (#30417888)

To be fair, the term they are using is "Euclidean structure," which, strictly speaking, is more algebraic than (purely) geometric. The notion of the "angle" (and from there that of parallelism) logically follows from it.

[ Parent | on HN ]

Re:Symplectic Geometry in 2D – Points, Lines, Circles by pfortuny on Monday February 21, 2022 @11:43AM (#30417768)

I guess he isnusing it in the metric sense (Euclidean metric).

[ Parent | on HN ]