This is a fascinating YouTube clip about the Fibonacci series, the Golden Ratio, and how both of the above appear in nature. I explained the topic briefly on Facebook for a couple of friends who seemed to like the explanation. So here it is:
The Fibonacci series is a set of numbers where each one is the sum of the previous two. So: 1 1 2 3 5 8 13 21 34 55 etc. The first part of the video shows how the escalating sizes of these numbers relate to th…e golden ratio.
The golden ratio is 1.618—”golden” because a rectangle of proportions 1 x 1.618 is said to be the most pleasing to the eye.
If you take a “golden” rectangle and divide off an exact square, the piece that’s left is another, smaller golden rectangle. If you divide a square off this piece you get another, even smaller one. You can do this forever.
If you draw an arc through each of the squares you made, you get a “golden spiral”—which occurs LOTS of places in nature, most obviously seashells, but also in other places, some of which are shown in the video.