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/* Idea for presenting this */
::::Sure, I'll work on [[curvature]] (pretty sure I can improve what's on there now!). I'm thinking I'll start off talking about curvature of hypersurfaces in R^3 and the idea of parallel transport (illustrated on the round 2-sphere, probably), then define the Riemann curvature tensor (roughly -- we'll see about actually defining tensors) via holonomy. My thinking is that it probably then makes most sense to define sectional curvatures next and then say a bit about scalar and Ricci curvature. This all comes with the disclaimer that my expository abilities aren't really up to par, but I'll try to at least get the groundwork in place. I probably won't really start until Monday, but I'll see if I can't get a start tomorrow. --[[User:MarkGall|MarkGall]] 20:23, 14 November 2009 (EST)
::::: HA! Yeah, I'd say we can do better than that for [[curvature]]. ;-) If it were me writing it (and I'm glad it's not; thank you) from the perspective of a physicist, the point I'd emphasize is that it is ''not'' possible to put a consistent set of Cartesian coordinates onto a curved surface. If the surface is curved, then it cannot be flattened by a coordinate transform, period. So you ''have'' to deal with the curvature. That's the point I emphasize when I do "differential geometry for dummies." But of course, your article won't be for budding physicists, it'll be for budding mathematicians or anybody who's interested. So I'll support whatever choice you make. --[[User:KSorenson|KSorenson]] 20:46, 14 November 2009 (EST)
