The famous astronomer Galileo Galilei once said that, “The Book of Nature is written in the language of mathematics.” I can say with confidence that he was right.
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The world that we live in is a beautiful sight, and the natural world a spectacle. If beauty can be found in nature, and if nature can be written in mathematical statements, then can there be a mathematical explanation for what we perceive as beauty? The answer is most likely yes.
A wonderful illustration of this is the Fibonacci sequence. Named after the mathematician Leonardo of Pisa (c. 1170 – c. 1250), this sequence begins with:
1, 1, 2, 3, 5, 8, 13, 21, …
Except for the first two, each number in the sequence is the sum of the previous two. (For example, 3=1+2 and 5=3+2.) Fibonacci stumbled on this sequence when thinking about how to count the offspring produced by a pair of rabbits. Not very exciting (or beautiful), I admit. But a hidden pattern emerges when you visualize the numbers differently. The image on the left creates squares whose side lengths are the successive Fibonacci numbers; the image on the right draws circular arcs connecting opposite edges of those squares:
The rectangle on the left is called the golden rectangle. The beautiful blue spiral on the right is called the golden spiral. I can almost guarantee that you’ve seen these in your everyday life (albeit sometimes hidden in plain view):
This connection between the Fibonacci numbers and the many beautiful objects containing patterns describable by the numbers is why I, along with most other mathematicians, think that the Fibonacci numbers are beautiful.
There is also an underlying mathematical pattern in the beautiful faces that we see. Check out the article over at Psychology Today.
(Image Credit: Draw Paint Academy)