"I know it will be called blasphemy by some, but I believe that pi is wrong."
That's the opening line of a watershed essay written in 2001 by mathematician Bob Palais of the University of Utah. In "Pi is Wrong!" Palais argued that, for thousands of years, humans have been focusing their attention and adulation on the wrong mathematical constant.
Two times pi, not pi itself, is the truly sacred number of the circle, Palais contended. We should be celebrating and symbolizing the value that is equal to approximately 6.28 — the ratio of a circle's circumference to its radius — and not to the 3.14'ish ratio of its circumference to its diameter (a largely irrelevant property in geometry).
Last year, Palais' followers gave the new constant, 2pi, a name: tau. Since then, the tau movement has steadily grown, with its members hoping to replace pi as it appears in textbooks and calculators with tau, the true idol of math. Yesterday — 6/28 — they even celebrated Tau Day in math events worldwide.
But is pi really "wrong"? And if it is, why is tau better?
The mathematicians aren't saying that pi has been wrongly calculated. Its value is still approximately 3.14, as it always was. Rather they argue that 3.14 isn't the value that matters most when it comes to circles. Palais originally argued that pi should be changed to equal 6.28 while others prefer giving that number a new name altogether.
Kevin Houston, a mathematician at the University of Leeds in the U.K. who has made a YouTube video to explain all the advantages of tau over pi, said the most compelling argument for tau is that it is a much more natural number to use in the fields of math involving circles, like geometry, trigonometry and even advanced calculus.
"When measuring angles, mathematicians don't use degrees, they use radians," Houston enthusiastically told Life's Little Mysteries, a sister site to LiveScience. "There are 2pi radians in a circle. This means one quarter of a circle corresponds to half of pi. That is, one quarter corresponds to a half. That's crazy. Similarly, three quarters of a circle is three halves of pi. Three quarters corresponds to three halves!" [A Real Pie Chart: America's Favorite Pies]
"Let's now use tau," he continued. "One quarter of a circle is one quarter of tau. One quarter corresponds to one quarter! Isn't that sensible and easy to remember? Similarly, three quarters of a circle is three quarters of tau." Making tau equal to the full angular turn through a circle, he said, is "so easy and would prevent math, physics and engineering students from making silly errors."
A better teaching tool
Aside from preventing errors, as Palais put it in his article, "The opportunity to impress students with a beautiful and natural simplification has turned into an absurd exercise in memorization and dogma."
Indeed, other tau advocates have said they've noticed a significant improvement in the ability of students to learn math, especially geometry and trigonometry where factors of 2pi show up the most, when the students learn with tau rather than pi.
Though 2pi appears much more often in calculations than does pi by itself (in fact, mathematicians often accidentally drop or ad that extra factor of 2 in their calculations), "there is no need for pi to be eradicated," Houston said. "You might say I'm not anti-pi, I'm pro-tau. Hence, anyone could use pi when they had a calculation involving half of tau."
Tau, the 19th letter of the Greek alphabet, was chosen independently as the symbol for 2pi by Michael Hartl, physicist and mathematician and author of "The Tau Manifesto," and Peter Harremoës, a Danish information theorist. In an email, Houston explained their choice: "It looks a bit like pi and is the Greek 't,' so fits well with the idea of turn. (Since tau is used in angles you can talk about one quarter turn and so on.)"
Pi is too ingrained in our culture and our math to succumb to tau overnight, but the movement pushes ever onward. "Change will be incremental," Houston said.
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Natalie Wolchover was a staff writer for Live Science from 2010 to 2012 and is currently a senior physics writer and editor for Quanta Magazine. She holds a bachelor's degree in physics from Tufts University and has studied physics at the University of California, Berkeley. Along with the staff of Quanta, Wolchover won the 2022 Pulitzer Prize for explanatory writing for her work on the building of the James Webb Space Telescope. Her work has also appeared in the The Best American Science and Nature Writing and The Best Writing on Mathematics, Nature, The New Yorker and Popular Science. She was the 2016 winner of the Evert Clark/Seth Payne Award, an annual prize for young science journalists, as well as the winner of the 2017 Science Communication Award for the American Institute of Physics.