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> Euclidean geometry is gone when you bend fabric? Do you just mean that everything is still Euclidean in the complete 3D space of real life? This is true but

> Euclidean geometry is gone when you bend fabric? Do you just mean that everything is still Euclidean in the complete 3D space of real life? This is true but does not make the 2D-curved-spaced analysis any less fundamental. All curved manifolds (including curved spacetimes) of dimension d can be embedded in a Euclidean space of dimension 2d such that the metric on the former is just the one you get by projecting down from the latter. Insofar as all the quantities you are working with are confined to the curved d-dimensional manifold, it's as fundamental a notion of curved space as ever exists.

chaboud 9y ago
I was arguing against the author's assertions that: 1) Euclidean geometry is a plane (though, on re-reading, she said that a plane is pure Euclidean geometry). So, to be fair to the author, that may well be me over-reading her statement (could be "within", rather than "equal to"). 2) That Burberry's dress on Ruby Rose for the 2017 Met Gala somehow meaningfully steps outside of Euclidean geometry for it's execution. It's a layered skirt composed of rectangular-ish cuts. Any apparent colinearity stems from the center-start of each panel and vertical alignment (aided, visually, by the aspect ratio of the panels). Maybe the ruching around the body? I don't see it, and to hang an argument for involvement of a field on the particulars of that dress is pretty baffling. The best I could suggest is that any dress could be called non-euclidean when cut from planar fabric due to the (general) requirement that a dress be at least a genus one manifold (or a public indecency ticket). I don't see anything in Ruby Rose's dress that implies any meaningful departure from or special knowledge of euclidean to non-euclidean considerations. Except maybe the price tag... That probably bends more than just space...

chaboud 9y ago

I was arguing against the author's assertions that: 1) Euclidean geometry is a plane (though, on re-reading, she said that a plane is pure Euclidean geometry). So, to be fair to the author, that may well be me over-reading her statement (could be "within", rather than "equal to"). 2) That Burberry's dress on Ruby Rose for the 2017 Met Gala somehow meaningfully steps outside of Euclidean geometry for it's execution. It's a layered skirt composed of rectangular-ish cuts. Any apparent colinearity stems from the center-start of each panel and vertical alignment (aided, visually, by the aspect ratio of the panels). Maybe the ruching around the body? I don't see it, and to hang an argument for involvement of a field on the particulars of that dress is pretty baffling. The best I could suggest is that any dress could be called non-euclidean when cut from planar fabric due to the (general) requirement that a dress be at least a genus one manifold (or a public indecency ticket). I don't see anything in Ruby Rose's dress that implies any meaningful departure from or special knowledge of euclidean to non-euclidean considerations. Except maybe the price tag... That probably bends more than just space...