如何简明地解释曲率（curvature）？ 曲率是啥，挠率（torsion）是啥，咋来的，有啥用？ 指的是对于函数 [公式] 显示全部 关注者 606

Aug 11, 2020 · How would we motivate that when speaking of curvature of the intuitive idea of curvature (how much you need to turn) as the above equatoion? And, even after all this one …

Oct 3, 2017 · The radius of curvature is the radius of the osculating circle. Curvature is the reciprocal of the radius of curvature. Once you have a formula that describes curvature, you …

Sep 16, 2018 · @RockyRock considering curvature was defined like that (definition in my textbook), a problem arises because radius of curvature is the radius of an imaginary circle of …

May 26, 2023 · The Riemann curvature tensor doesn't contain any more information than all sectional curvatures. The only intrinsic curvature we really define is Gaussian curvature of a …

For the sake of completeness and accuracy: while for a curve you can uniquely define the curvature $\kappa \in \mathbb R$ for a surface you have an infinite number of curvatures for …

Jan 30, 2020 · This can be proven rigorously. The radius of curvature is the radius of the osculating circle, the radius of a circle having the same curvature as a given curve and a point. …

Apr 23, 2015 · We call the curvature $2$-form then the differential form $\Omega = D\omega$ where $\omega$ is the connection $1$-form. Although the definition is perfectly clear I can't …

Nov 4, 2016 · I want to understand the basic conceptual idea about intrinsic and extrinsic curvature. If we consider a plane sheet of paper (whose intrinsic curvature is zero) rolled into a …

9 Intrinsic curvature comes from the parallel translation of a vector tangent to the path of translation. If a vector is translated around a loop and it fails to come back onto itself that is …