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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:

enter image description here

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?

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Actually, there is one 3D proof of a Fibonacci identity:

enter image description here

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  • $\begingroup$ Brilliant interception. $\endgroup$ – Vim Jan 23 '15 at 19:06

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