Fibonacci

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... is commonly called the Fibonacci Sequence, named after Leonardo Fibonacci, who dabbled in such things in the 13th century. This particular sequence of numbers can be generated by starting with 0 and 1, and then adding the previous two terms together to get the next term.
0
1
0+1 = 1
1+1=2
1+2=3
2+3=5
and so on.

The tiling below is formed with squares having side lengths of successive Fibonacci numbers. The spiral then consists of 90 degree arcs connected along adjacent squares' opposite vertices. 

The 20th Fibonacci number is 6765.



The coolest thing is this: the ratio of any two consecutive Fibonacci numbers is approximately 1.618, commonly known as the Golden Ratio. :-)

Look at the sunflower model to see the Fibonacci curves