Rewrite functions that use loops instead of numpy array

From what I can see, there are several candidate functions in at least the following modules:
- **differential_geometry.py** : gradient, triangle_gradient
- **curvature.py**

Start by reading gradient and triangle_gradient in differential_geometry.py, then inspect the candidate functions in curvature.py. Compare their loop-based behavior with the intended NumPy array approach and identify all affected functions. Done means the targeted functions use NumPy arrays without changing their results; no tests are named in the issue.

Written by the indexing model from the issue text.