Curves need not be smooth, for example we may consider elliptic curves over finite fields [1] or space-filling curves [2]. In general, there are various ways to

Curves need not be smooth, for example we may consider elliptic curves over finite fields [1] or space-filling curves [2]. In general, there are various ways to generalize the notion of curvature to discrete structures like graphs and programs [3] which reflects our intuitive understanding about local curvature on smooth manifolds. For example, one way to view discrete curvature is to grow a ball around a point and look at how quickly its volume deviates from a ball of the same radius embedded in a uniformly connected graph approximating a “flat” or Euclidean space. [1]: https://en.wikipedia.org/wiki/Elliptic_curve#Elliptic_curves_over_finite_fields https://en.wikipedia.org/wiki/Elliptic_curve#Elliptic_curves... [2]: https://en.wikipedia.org/wiki/Space-filling_curve https://en.wikipedia.org/wiki/Space-filling_curve [3]: https://www.maths.dur.ac.uk/users/norbert.peyerimhoff/peyerimhoff-lecture-notes.pdf https://www.maths.dur.ac.uk/users/norbert.peyerimhoff/peyeri...