There is a significant number of identities involving Fibonacci numbers that can be proven in a sort of geometric way, as it is shown in the following picture:
However, I couldn't find any such proof that involves 3D geometry. I also couldn't find any Fibonacci identity that would be suitable for such interpretation.
Is there an inherent reason for such proofs being limited to 2D?
Is there a series (different then Fibonacci) that would be suitable for similar 3D geometric proofs?