From the Archives: Today is Pi Day. Detractors say pi really is half-baked
Today is Pi Day. Math nerds and geometry aficionados will be celebrating the mathematical constant that describes the relationship between the circumference of a circle and its diameter.
For those who need a refresher: Take a circle that is 1 inch across. Then measure the length of the circle itself. When you’ve gone all the way around, you’ll have covered a distance of slightly more than 3.14 inches. That’s pi. (And that’s why Pi Day is observed on March 14.)
Pi (represented by the Greek letter Π) has many uses. In addition to using it to calculate the circumference of a circle (2Πr, where “r” is the circle’s radius), it will also tell you the area (Πr2).
But that’s just the beginning. You can use it to calculate the surface area and volume of a sphere. You need it for trigonometric functions that repeat periodically, like sine and cosine. And it is essential for calculating the normal distribution for probability and statistics.
Pi hides out in the famous fractal known as the Mandelbrot set. It also appears in the equation for Heisenberg’s uncertainty principle and Einstein’s field equations. On a more practical level, pi is necessary to determine your location with GPS.
In short, pi has been helping humans do cool stuff for about 4,000 years. But despite this illustrious history, pi is finding itself under attack by people who think it is only half as awesome as it ought to be. These folks are pushing to have pi replaced by the Greek letter tau, which has a value of 2Π.
As Victoria Hart explains in the video above, the thing that determines the circumference of a circle is its radius, not its diameter. Accordingly, she asks, “Why would we define the circle constant as a ratio of the diameter to the circumference?”
For Hart (a musician and math enthusiast who has made videos for Khan Academy), this problem is an offense to math itself. “Mathematics should be as elegant and beautiful as possible,” she says. “There’s a boatload of important equations and identities where 2Π shows up, which could and should be simplified to tau.”
In Hart’s view, pi is simply an unfortunate anachronism that has outlived its usefulness:
“Pi, as a concept, is a terrible mistake that has gone uncorrected for thousands of years. The problem with pi and Pi Day is the same as the problem with Christopher Columbus and Columbus Day. Sure, Christopher Columbus was a real person who did some stuff, but everything you learn about him in school is warped and overemphasized. He didn’t discover America. He didn’t discover the world was round. And he was a bit of a jerk. So why do we celebrate Columbus Day? Same with pi.”
Hart is not alone in her enthusiasm for tau. In this video, you can watch Steve Mould and Matt Parker (two-thirds of the trio behind the Festival of the Spoken Nerd and maybe rough British equivalents to America’s Bill Nye) go toe-to-toe in a tau-versus-pi smackdown.
Mould, who conducts science experiments for the BBC, sums up many of his objections to pi by saying, “There’s always this factor of two that you’ve got to keep in your mind when you’re doing calculations.”
Parker, who holds the title of London Mathematical Society Popular Lecturer, counters that “pi works just as well [as tau] in all cases. ... The fact that it’s got a bit of heritage doesn’t mean we should keep it around necessarily. But it’s worked for a very long time, it’s there for very good reasons,” and if you switch from pi to tau, “you gain as much as you lose.”
The final score is 23-27, but you’ll have to watch the video to see which constant comes out on top.
If you’re ready for a deep dive on the subject, check out the Tau Manifesto by Michael Hartl, or watch him give a lecture at Caltech. (It was delivered on June 28 — a.k.a. Tau Day — in 2011.)
Even if you’re open to the idea that tau is superior to pi, you can still celebrate Pi Day. Or as Hart puts it: “You can have your pi and eat it.”
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