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"Part of the process of becoming a mathematics writer is, it appears, learning that you cannot refer to the golden ratio without following the first mention by a phrase that goes something like "which the ancient Greeks and others believed to have divine and mystical properties." Almost as compulsive is the urge to add a second factoid along the lines of "Leonardo Da Vinci believed that the human form displays the golden ratio."
There is not a shred of evidence to back up either claim, and every reason to assume they are both false. Yet both claims, along with various others in a similar vein, live on..."
I was surprised about the nautilus shell part. I've heard that so many times. It would be interesting to see if there was a preferred rectangle, that people choose more ofte than others. Maybe if you did enough tests you could find the Preferred Ratio?