……将流形的几何与拓扑联系起来。如果需要更经典的微分几何入门，且只需要多元微积分和一些实分析/点集拓扑基础的话，多卡莫（Do Carmo）的《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces）是一本极好的教材。我在 [2] 里整理了一份本科跟读多卡莫课程的总结（核心定义/定理）。[1]: http://www.amazon.com/Differential-Geometry-Curves-Surfaces-...…
…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-...…
没读过，但预览页面看起来挺赞的。我可能会找来读读当消遣。数学方面也许可以搭配多卡莫的《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces，这本书相当好懂）一起看。
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.
我最近读过的一本真正脱颖而出的书是曼弗雷多·多卡莫的《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces）。它有点过时，有时读起来也费劲，但里面有很多不为人知的干货（开头有一小节讲通过计数来估算曲线长度……
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 It's a bit outdated, and at times hard to read, but it has a lot gems that aren't well know (there is a bit at the beginning on estimating the length of a curve by counting the…
……在剩下的内容里。我觉得我们俩的探索路线最终都会通向微分几何，而对此我唯一知道的是，亚马逊上似乎有一本很好的书（塔普，《曲线与曲面的微分几何》/Differential Geometry of Curves and Surfaces），而且你可能想避开那些使用老旧记号的老书。我听过很多关于《引力论》（Gravitation）这书的极高评价，但我完全被它吓退了，还没准备好去啃它。另外去看看……
…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…
……将流形的几何与拓扑联系起来。如果需要更经典的微分几何入门，且只需要多元微积分和一些实分析/点集拓扑基础的话，多卡莫（Do Carmo）的《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces）是一本极好的教材。我在 [2] 里整理了一份本科跟读多卡莫课程的总结（核心定义/定理）。[1]: http://www.amazon.com/Differential-Geometry-Curves-Surfaces-...…
…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-...…
没读过，但预览页面看起来挺赞的。我可能会找来读读当消遣。数学方面也许可以搭配多卡莫的《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces，这本书相当好懂）一起看。
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.
我最近读过的一本真正脱颖而出的书是曼弗雷多·多卡莫的《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces）。它有点过时，有时读起来也费劲，但里面有很多不为人知的干货（开头有一小节讲通过计数来估算曲线长度……
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…
多卡莫的《曲线与曲面的微分几何》（Differential geometry of curves and surfaces）
Differential geometry of curves and surfaces by Do Carmo
……在剩下的内容里。我觉得我们俩的探索路线最终都会通向微分几何，而对此我唯一知道的是，亚马逊上似乎有一本很好的书（塔普，《曲线与曲面的微分几何》/Differential Geometry of Curves and Surfaces），而且你可能想避开那些使用老旧记号的老书。我听过很多关于《引力论》（Gravitation）这书的极高评价，但我完全被它吓退了，还没准备好去啃它。另外去看看……
…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…
参见 https://en.wikipedia.org/wiki/Crofton_formula 也可以看看曼弗雷多·多卡莫《曲线与曲面的微分几何》（Differential Geometry of Curves and Surfaces）第41页
See https://en.wikipedia.org/wiki/Crofton_formula Also see page 41 of Differential Geometry of Curves and Surfaces by Manfredo Do Carmo