More Fibonnaci Connections

See Braids, Permutations, Representations, Continued Fraction Expansions and Models of Typed Lambda Calculus and Sophie Maclean on Euclid's Algorithm. 

Pythagorean triples have an intimate connection with both Fibonacci series and the rationals. 

See the links in the video description which include: 

At 26:07 there is a nice bit of joining-up. 

I think the real joining up would be to find the ideas in their most abstract form which explain these connections in the most economical way. Of course, what "most economical" means depends upon where on where you want to start. Different cultures started in different ways, but all these different slices of the space will have quite precise correspondences between them.

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