## Interesting Fibonacci Goodness

Last year I was working on deriving a matrix based method for translating and rotating various polygons around pentagons. In the process of this I got sidetracked and started to look into the golden mean. People swoon over how it defines the most beautiful rectangles! It crops up inside pentagons and various 3-D polyhedra. It’s glorious. It’s just like how a circle has the ratio pi, and it has a name too: phi. I’ll be writing it down in Greek from here on out (it’s originally from there anyway). So learn this shape: \varphi Sometimes people write it out like this: \phi Either way it’s just a variable name. Sometimes it refers to something other than the golden mean, but here it’s the golden mean. As I found powers of \varphi , I kept noticing certain values popping up in sequence. It turns out that one can find powers of \varphi through the following formula: