Supplesomething forwarded me an interesting NPR piece on Manjul Bhargava, 28, a professor of number theory at Princeton who discusses how the Fibonacci series pops up not just in mathematics but also in the arts.
The Fibonacci series is the set of numbers beginning with 1, 1 where every number is the sum of the previous two numbers. The series begins with 1, 1, 2, 3, 5, 8, 13, and so on. They were known in India before Fibonacci as the Hemachandra numbers. And the ratio of any two successive Fibonacci numbers approximates a ratio, ~1.618, called the golden section or golden mean.
It's long been known that the Fibonacci series turns up frequently in nature. The numbers of petals on a daisy and the dimensions of a section of a spiral nautilus shell are usually Fibonacci numbers. For plants, this is because the fractional part of the golden mean, a constant called phi (0.618), is the rotation fraction (222.5 degrees) which yields the most efficient and scalable packing of circular objects such as seeds, petals and leaves.
But Bhargava points out that the series also shows up in the arts. Sanksrit poetry, tabla compositions and tango, to name a few examples, use the series to find the number of possible combinations of single and double-length beats within a stanza.
For example, the eighth Fibonacci number is 34, assuming we number the series starting from 0. There are 34 ways to combine single and double-syllable words in a stanza with eight beats. Similarly, there are 34 ways to combine fast and slow tango steps over eight beats. It's classic Zen and the Art of Motorcycle Maintenance: the beauty in logic, the logic in beauty.
If Hemachandra were alive today, no doubt he'd apply his series to how many Indian bureaucrats it takes to sell a railway ticket. In the first year, one; in the ninth, 55, and so on.
