Some students fall in love with their teacher. Mathematician Andrew Barnes fell in love with pi. “My relationship with pi probably began when I was a schoolboy,” says Barnes, who is 44 years old and builds financial models, computes probabilities, and investigates bell curves at GE Global Research. “It started with elementary geometry and the relationship just keeps growing. Now it’s almost like being wedded to a concept.”
Pi Face: Artist Stewart Moore is painting pi to 2,500 decimal places. Ten different colors represent numbers from 0 to 9. Credit: Stewart K. Moore
Pi is the mystical ratio between the circumference and the diameter of a circle. This infinite number, which we generally round at 3.14, is celebrated every March 14 (which also happens to be Albert Einstein’s birthday.)
Barnes has been drawn to pi because of its intellectual history and philosophical implications. For example, does pi even exist? “Its existence is predicated on the fact that the ratio is the same for all circles,” he says. “They could be as small as a pea or as large as the sun, but ratio is always the same. I find that fascinating.”
Humans have known about pi since they started using wheels 4,000 years ago. Ancient Babylonians could celebrate an entire “Pi Month” since they gave pi value of 3 (as does the Old Testament).
In 300 BC, Euclid provided a path for calculating pi by “looking at the circle as a polygon with infinitely many sides,” Barnes says. Archimedes applied Euclid’s theorems to arrive at pi a few decades later. When a troop of Roman soldiers occupying his hometown Syracuse walked over his math drawings in the sand, he rebuked them and paid for pi with his life. His last words? “Do not disturb my circles.”
Barnes says that the ancient Greeks, Egyptians, Indians and other civilizations have all tried to crack pi’s mysteries. For example, they looked for a square whose area matched exactly the surface of a circle. “Squaring the circle was one of the biggest math problems of the time, kind of like our Fermat’s Last Theorem,” Barnes says. “They guessed that it was probably impossible. But the Great Pyramid in Giza contains certain ratios that involve numbers close to rational approximation of pi.”
In the 1690s, Isaac Newton and Gottfried Leibniz, the fathers of calculus, bridged the gap between algebra and geometry and used infinite series techniques to calculate pi to a then-record 15 digits.
Twentieth century mathematicians like India’s Srinivasa Ramanujan used number theory and special mathematical tools called elliptic integrals to find new ways to compute pi even further. As a result, we can now calculate 5 trillion digits of pi, but we will never be done. “These things have deep connections with other areas of mathematics,” Barnes says. “They take us to the forefront of the greatest unsolved problems.”
Algrebraic geometry is now finding applications in fields like cryptography, string theory in physics, and cosmology. “This is a fascinating journey through the intellectual history of mankind, at least for me,” Barnes says.