How did Fibonacci beat the Solitaire army?

From a channel Lumen includes in full: Mathologer, run by mathematician Burkard Polster, gives detailed visual proofs of classic and surprising results (Ramanujan identities, magic squares, Fermat, infinite series), with the full argument rather than just the picture.

A 23-minute video from Mathologer's catalogue; the title names its topic.

Video by Mathologer, played through YouTube's embedded player.