Fibonacci Spiral's End

Fibonacci Spiral's End

I believe, you have heard about Fibonacci numbers, which form a respective sequence, where each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

The sequence may be shown as a tiling with squares whose side lengths are successive Fibonacci numbers. For this mission we use exactly this position of squares:

If you follow numbers, you see that they form a spiral. Indeed, on the next image the Fibonacci spiral is build: an approximation of the golden spiral, created by drawing circular arcs, connecting the opposite corners of squares in the Fibonacci tiling: ...

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