Differential geometry of curves and surfaces
by Manfredo Perdigão do Carmo · first published 1976
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…linking the geometry and topology of manifolds. For a more classical introduction to differential geometry requiring only multivariate calculus and some real analysis/point set topology, Do Carmo's "Differential Geometry of Curves and Surfaces" is a great textbook. I put together a summary (key definitions/theorems) from an undergraduate course following Do Carmo at [2]. [1]: http://www.amazon.com/Differential-Geometry-Curves-Surfaces-...…
on “Functional Differential Geometry (2012) [pdf]” ↗Never read it, but the preview pages look pretty neat. I might pick it up for a fun read. Might want to pair it with something like do Carmo's Differential Geometry of Curves and Surfaces (which is quite accessible) for the mathematical side.
on “Ask HN: What are you learning?” ↗One book that I've read recently that really stands out is Differential Geometry of Curves and Surfaces by Manfredo do Carmo. It's a bit outdated, and at times hard to read, but it has a lot gems that aren't well know (there is a bit at the beginning on estimating the length of a curve by counting the…
on “Ask HN: Books you read in 2016?” ↗Differential geometry of curves and surfaces by Do Carmo
on “Ask HN: Older textbooks/papers you consider classics still worth studying today?” ↗…in the rest of it. I think both our roads are eventually going to lead us to differential geometry, and the only thing I know about that is that there appears to be a very good book on Amazon (Tapp, Differential Geometry of Curves and Surfaces), and that you may want to avoid older books that use the older notation for it. I have heard great things about the book Gravitation, but I'm totally afraid of it, not ready to go there yet. Also check…
on “Ask HN: How do I learn math/physics in my thirties?” ↗See https://en.wikipedia.org/wiki/Crofton_formula Also see page 41 of Differential Geometry of Curves and Surfaces by Manfredo Do Carmo
on “Steinhaus Longimeter” ↗