Oct 11, 2014 · 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 607

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 …

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 …

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 …

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 …

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 …

The Gaussian curvature is the ratio of the solid angle subtended by the normal projection of a small patch divided by the area of that patch. The fact that this ratio is based totally on the …

What are you taking as your definition of curvature? Typically it is defined as the magnitude of the derivative of the unit tangent vector with respect to arc length, right?

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 …