Question

What are fibonacci numbers? What is the golden ratio? How do fibonacci numbers and the golden ratios relate to each other?

Answer 1

Also, where does the golden ratio appear?

Answer 2

The Fibonacci sequence is a sequence generated by adding the number before itself:
1,1,2,3,5,8,13,21,...
because 1+0=2
and 1+1=2
1+2=3
2+3=5
etc.
the Golden ratio appears as the limit of succesive terms in the Fibonacci sequence:
\[\lim_{n \rightarrow \infty}n/(n+1)\]
where n is the nth term in the sequence.
In nature it appears everywhere from plants to crystals. It even plays an integral role in the latest Nobel Prize awarded for chemistry:
http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/sciback_2011.pdf

Answer 3

sorry n=2 int the sequence is
1+0=1

Answer 4

the height of a human divided by the height of their navel is very close to golden ratio -believe it or not its true!!)