Fibonacci has been studied a lot and has many (surprising) applications like in trading (finance)!

I don't suppose you have any references to those uses?

Aside from those exploring the purely theoretical properties of Fib, does anyone use anything much beyond say fib(1000)?:

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+541794905189040387984007925516929592259308032263477520968962323987332
+247116164299644090653318793829896964992851600370447613779516684922887
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Not really, but the following list gives an idea: petals on a flower, leaves, branching plants, Fibonacci spiral (e.g. Cauliflour), Music, Phi (golden ratio), the human body, finance (mainly for traders, like for example retracement), etc. There several books on the application of Fibonacci. I think for most practical purposes the number is big enough!

Thank you the retracement link. I was aware of the link to the Golden Ratio and many of places in the natural world and artistic endeavours where it crops up.

As a teenager I was fascinated by the GR for several years. I wrote my first recursive Fib routine when I was 15 in an interpreted assembler-like teaching language called BBCX (that was itself implemented in an interpreted BASIC and ran on a TOPS-20 mainframe at a Uni miles away).

Runtime was strictly limited, so I had to get special permission to have the program run over a weekend in order for it to calculate the first 23 terms (16-bit signed integer limit). I don't remember how many hours it ran, but it was a looong time.

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