Another interesting occurrence of Fibonacci numbers in nature is the relationship to proportional squares. Taking an example, we draw a series of squares starting with the size of the first numbers in the Fibonacci sequence.
Continuing to draw squares with a size equal to the next Fibonacci number in the sequence we end up with a picture of squares all placed together to from a larger rectangle. The following steps illustrate this concept:
1. Start with two squares of size 1 and 1 (the first numbers in the Fibonacci sequence)
2. Add a square of size 2 on top of these two squares, then add a square of size three to the right side of this square. The shape which is produced by the group of squares is known as the Fibonacci rectangle.
3. The process continues with a square representing the size of the next Fibonacci number being added to the Fibonacci rectangle, the new square will reside on the next clockwise face of the rectangle. This process continues indefinitely. The following picture shows the Fibonacci rectangle produced up to the 13 number.
The Fibonacci Spiral in nature
When a circle is drawn in each square in the Fibonacci rectangle so that a quarter circle appears in each square it produces a spiral. This is shown in the picture above on the right.
This spiral formation occurs in many places in nature. You may have seen this shape in various sea shells.
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