My professor asked us to find and make a list of things/facts from real life which have a differential geometry interpretation or justification. One example is this older question of mine. Another example my teacher presented is proving that on a soccer ball which is made of regular pentagons and regular hexagons, the number of pentagons is fixed, as a consequence of Euler's polyhedral formula. I guess that there are many more of these.
The idea is to find things/facts whose explanation is a theorem in differential geometry and eventually give a reference to a book/article where these connections are explained.
My teacher wants us to make such a list and then each to pick a subject and make a project which presents the theorem which is applied (with proof, if the proof is not too long) and then present the application itself.
Any reference or book on the subject is more than welcome.