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Some kids crave cake, but mathematician Andrew Barnes couldn’t get enough of pi. “My relationship with pi probably began when I was a schoolboy,” says Barnes, who is now 45 years old and builds financial models and computes probabilities 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, like love, is an abstract notion. Although it’s defined as the ratio between the circumference and the diameter of a circle, it’s also an irrational number that, maddeningly, cannot be expressed as a fraction and runs into infinity.
We generally round it at 3.14. That way we can also throw pi a party and celebrate March 14 as Pi Day. (The date also happens to be Albert Einstein’s birthday.) This year calls for extra champagne, since on Saturday 3/14/15 at 9.26:53am, the date and time will spell the first 10 digits of pi, an occurrence that won’t happen again for another century.
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Above: Pi Face: Artist Stewart Moore is working on a painting of pi with 2,500 decimal places. Ten different colors represent numbers from 0 to 9. Image credit: Stewart K. Moore Top GIF: Pi is everywhere! Animation credit: Cindy Suen
Barnes says he has been drawn to pi because of its intellectual history and philosophical implications. “Its existence is predicated on the fact that the ratio is the same for all circles,” he says. “They can 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 someone invented the wheel 4,000 years ago. Ancient Babylonians could celebrate an entire “Pi Month” since they assigned pi the value of 3 (as did the Old Testament).
In 300 BC, Euclid provided a path for calculating pi by “looking at the circle as a polygon with infinite number of sides,” Barnes says.
Archimedes applied Euclid’s theorems to arrive at a more precise value of 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.”
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Death of Archimedes by Giammaria Mazzuchelli. Image source: Wikimedia Commons
Barnes says that ancient Greek, Egyptian, Indian 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 bridged the gap between algebra and geometry and used calculus to figure out pi’s first 15 digits, a new record.
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We can’t get enough of pi.
The 20th century mathematician Srinivasa Ramanujan used even more powerful tools like number theory and elliptic integrals to find new ways to compute pi further.
We now know circumference v. diameter ratio to the 5 trillionth digit, and keep counting. 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, for example, is now finding applications in fields like cryptography, string theory in physics, and cosmology.
Says Barnes: “This is a fascinating journey through the intellectual history of mankind, at least for me.”
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Happy Pi Day! GIF by Tyler Dibiasio