If you look closely at a sunflower, the base of a pinecone, or the shell of a snail, you will see a spiral, one of the ways nature organizes form. The math that describes the geometry of a spiral is call the Fibonacci Series. It is created by adding the two previous numbers in a series to get the next:
1 + 1 = 2
2 + 3 = 5
3 + 5 = 8
1,1, 2, 3, 5, 8, 13, 21, 34 and so on…
Discovered by Italian mathematician Leonardo of Pisa in 1225, this sequence also generates other pleasing geometries, such as the Golden Mean.
Ancient Greek philosophers used mathematical theory to discuss ways of thinking and seeing, living and learning, which I find so intriguing. Here is an example of how they applied a mathematical theory to life: the Golden Mean is the desirable middle between two extremes, one of excess and the other of deficiency. For example, in the Aristotelian view, courage is a virtue, but if one is excessively courageous, he or she would be considered reckless. And if courage is deficient, it leads to cowardice.
The Greeks believed there to be three “ingredients” to beauty: symmetry, proportion, and harmony, which they tried to reproduce in their lives: in architecture, education, and politics.
Reading about the beauty of math in nature and life, makes me think of a beautiful middle grade novel by Ellen Klages titled The Green Glass Sea, which all of us in our house read a few years ago. Here is an excerpt from the novel—a conversation between 11-year-old Dewey and her father—about math and music:
“Dews?” Papa said a few minutes later. “Remember the other night when we were talking about how much math and music are related?”
“Well, there was a quote I couldn’t quite recall, and I just found it. Listen.” He began to read, very slowly. “Music is the hidden arithmetic of the soul, which does not know that it deals with numbers. Music is the pleasure the human mind experiences from counting without being aware that it is counting.”
“Who said it?” Dewey asked.
“Leibniz. Gottfried Whilhelm Leibniz. He was an interesting guy, a mathematician and a philosopher and a musician.”
Goodreads description of The Green Glass Sea:
It is 1943, and 11-year-old Dewey Kerrigan is traveling west on a train to live with her scientist father—but no one, not her father nor the military guardians who accompany her, will tell her exactly where he is. When she reaches Los Alamos, New Mexico, she learns why: he’s working on a top-secret government program. Over the next few years, Dewey gets to know eminent scientists, starts tinkering with her own mechanical projects, becomes friends with a budding artist who is as much of a misfit as she is—and, all the while, has no idea how the Manhattan Project is about to change the world. This book’s fresh prose and fascinating subject are like nothing you’ve read before.