Fibonacci, golden rectangle and chaos theory, how are these related to each other and nature?

Answer 1

The limit of the ratio of successive numbers in the F sequence IS the golden ratio. That is: from 1,2,3,5,8,13,21 . . . that 2/1=2 is a poor approximation of the golden ratio, 21/13=1.615, not bad. Keep going and this would be the "exact" golden ratio. It has self-similar scaling properties, e.g. the golden spiral, so it is of interest in chaos.

Answer 2

Fibonacci is simply a number sequence, Chaos Theory is the theory that something with the same circumstances will come out differently, and the golden rectangular theory, which is simply a geometry term, are completely unrelated, except for the fact that they include mathematics. Chaos Theory is quantum physics (which has nothing to do with mathematics, quite technically), Fibonacci is actually technically Algebra, and Golden Rectangle is geometry. Fibonacci represents phi, 1.615, aka DaVinci's golden ratio, which everything in nature is 1.615. A snail's shell's spiral, between one line to the next, the ratio is 1.615.