A curve in the plane is determined, up to orientation-preserving Euclidean motions, by its curvature function, $\kappa(s)$. Here is one of my favorite examples, from Alfred Gray's book, Modern
Differential Geometry: Lecture 12 part 1: surfaces in R3
PDF) Non-existence of orthogonal complex structures on the round 6
Distance distributions and inverse problems for metric measure
Differential Geometry: Lecture 21 part 2: total Gaussian curvature
Distance distributions and inverse problems for metric measure
Differential Geometry: Lecture 16: calculation of K and H
introduction.html
What are applications of convex sets and the notion of convexity
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry
Curvature of a surface, only using calculus
Visual Differential Geometry & Forms
CS 15-458/858: Discrete Differential Geometry – CARNEGIE MELLON