Properties of Fibonacci numbers are often proved by induction. Although
this results in technically correct proofs, I find that proofs by
induction usually give me very little insight. Over the years I've found
various alternative definitions of the Fibonacci numbers that I can try
out when I'm trying to understand a result. I recently realized that the
sequence of Fibonacci numbers can be viewed as the projection of a two
dimensional geometric sequence, and I'm writing about it here.
The final sections aren't done, but the draft has been sitting on my
hard disk for over a year, so I'm posting an incomplete version to
provide myself with motivation to finish.
It's at
<http://www.gbbservices.com/math/fib.html>
Hope you enjoy it,
Walter