I recently watched a video about the Gömböc, a shape with one stable and one unstable point of equilibrium. Dr. Gábor Domokos proved the existence of this shape. Domokos originally looked at pebbles when trying to find the shape, although this approach was ultimately unsuccessful. Later on, some turtles were found to have a similar shape to the Gömböc.
I am looking for some other examples of when researchers have drawn inspiration (or completely copied) from nature in order to find solutions to math/engineering problems. To clarify, I am not looking for examples of explaining nature using math, as there are many examples of that (e.g. the Fibonacci spiral, arrangement of electrons in atoms/molecules, normal distribution, etc), but instead for examples of explaining math/engineering using nature.
I wasn't able to come up with or find any more examples myself, only the Gömböc.
Edit: I feel like there must have been some instance of when researchers have used the natural positioning of electrons to model something else, but I can't think of anything off the top of my head.