Tuesday, January 3, 2012

Brahmagupta and Fibonacci

I am reading a book called The Man of Numbers: Fibonacci’s Arithmetic Revolution, by Keith Devlin.

So far, it is fascinating. I didn’t know anything about the history of mathematics, so it is all new and exciting to me. I liked Chapter 1 so much, I cajoled my kids into letting me read it aloud to them. There was some concealed eye-rolling, but they were interested once I began reading.

First, we learned about how the earliest known tally marks date back to Swaziland, circa 35,000 BC. Twenty-nine notches were carved into a baboon’s fibula. It hadn’t occurred to me that Roman numerals are really a more sophisticated version of tally marks. Devlin points out that, while it is easy to add Roman numerals, multiplication becomes problematic. Multiplying is best done with repeated addition when using Roman numerals, so anything involving two large numbers is impractical. Calculations were done using complicated finger arithmetic systems and abacus. It sounds like only a few people could do that sort of thing, and you just had to trust that the answer was correct (ahem).

The Hindu-Arabic system we use today dates back to 700 A.D. in India. My kids were surprised to hear that the symbols chosen to represent numerals may have been designed so that the number of angles match the quantity represented. You have to write the numerals in a certain, Flintstonian way for this to work.

The best part of our reading was learning about the invention of zero. The other nine numerals were well-established when an Indian named Brahmagupta entered the scene. Brahmagupta (fun to pronounce) created the number zero in the year 628. Before Brahmagupta and his gigantic book entitled Brahmasphutasiddhanta (which means “the opening of the universe”), folks were simply circling the blank spots in numbers. Brahmagupta wrote about zeroes in elliptic verse, which appeals to my sense of rhythm and brevity:

A debt minus zero is a debt.
A fortune minus zero is a fortune.
Zero minus zero is a zero.
A debt subtracted from zero is a fortune.
A fortune subtracted from zero is a debt.

The zero revolutionized the Hindu-Arabic system, making it possible to perform calculations much easier than before. I was definitely taking zero for granted before reading this book.

Now, on to Fibonacci. There was no one really named Fibonacci, but there was a guy named Leonardo de Pisa who lived in Italy in the 12th century. He brought math to the masses. I haven’t gotten to the part of the book yet that tells the history of the famed Fibonacci sequence, so I’ll have to keep reading. In the meantime, Vi Hart has released a new video entitled Doodling in Math: Spirals, Fibonacci, and Being a Plant which does an excellent job of explaining Fibonacci numbers and simultaneously making math seem young, cool, and beautiful even for those who didn't previously think so. It is worth finding 6 minutes to watch it with your students!