Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: Euclidean geometry

Bottom of Page

1 to 6 of 6

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2015
    • (edited Jul 22nd 2015)

    added the following to the References-section of the entries Euclidean geometry, synthetic geometry and Coq:

    A textbook account of the axiomatization of Euclidean geometry is

    Full formalization of this book in Coq (as synthetic geometry but following Tarski’s work) is discussed at

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJul 22nd 2015

    I think that the idea sentence including

    Euclidean geometry can be regarded as the local model for Riemannian geometry, in some sense

    is plainly wrong and misleading. Unlike the symplectic manifolds where the Darboux theorem has all such reducing to a single model locally, the Riemann geometries are locally nonisomorphic, hence Euclidean geometry can not be considered as THE local model, but just one of the very special flat cases. On the other side, Euclidean spaces have many global symmetries which play a major role in that geometry, which do not hold in Riemannian geometries which are equivalent to it locally, what also makes the statement very misleading.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2015
    • (edited Jul 22nd 2015)

    When one says, as is standard, that Klein geometries are local models for Cartan geometries, this refers to tangent spaces. The further identification over open neighbourhoods (that is possible for symplectic geometry) is an extra integrability condition.

    Maybe you would like to say “infinitesimal local model”, and feel invited to add this to the entry, but I think just “local model” here is standard terminology.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 23rd 2015

    I vote for infinitesimal local model.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2020

    added pointer to

    • Evgeny V. Ivashkevich, On Constructive-Deductive Method For Plane Euclidean Geometry (arXiv:1903.05175)

    diff, v28, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 17th 2022

    started (here) a list of links to “Basic notions and facts in Euclidean geometry”

    this is prodded by the recent creation of what seems to become a collection of such entries

    diff, v31, current

1 to 6 of 6

  1.