PRO

# Golden yucca

This is a Fibonacci spiral; the linear size of each square is a Fibonacci number. Let F_{n} denote the n'th Fibonacci number. Then it is clear from this figure that F_{n} = F_{n-1} + F_{n-2}; the length of each side is the sum of the lengths of the previous two sides. It is also clear the areas of all the squares add up the the area of the large rectangle; that is: (F_1)^2 + (F_2)^2 + ... + (F_n)^2 = F_{n}*F_{n-1}.

You can read more about the Fibonacci spiral, and it's cousin the Golden spiral, on wikipedia.

You won't be surprised that I also wrote a Gimp script to make these things automatically. You would be surprised (or appalled) to know how long it took me to finally debug it...

Now available at the Gimp registry.