TAU: THE NEW PI

By Paul Gabrielsen, senior science writer, University Marketing and Communications

Think back to March 14, when Facebook was full of pies of all varieties, made in celebration of that famous mathematical symbol – π (pi), or 3.14159265359. . .

That celebration may have been premature. Mark your calendar for June 28.

A former University of Utah math professor is the founder of a movement that has proposed τ (tau), or two times pi, as a simpler, more intuitive way to understand circles, triangles and other principles of geometry. Tau, or 6.2831853071 etc., makes math simpler and less scary, according to Robert Palais, who is now a professor at Utah Valley University, but remains an adjunct professor at the U. Pi, he says, is simply wrong.

The numerical value of pi is not in question, of course. Tau is the ratio of a circle’s circumference to its diameter, and is first known to have been approximated by Archimedes. In the 18th century, mathematician Leonhard Euler popularized the Greek letter π to represent the ratio, defined as “half the circumference of a circle of radius 1.”

Picture a circle. You can measure an amount of rotation around the circle in degrees. A quarter-turn is 90 degrees. Half a turn is 180, and a full turn is 360 degrees. You can also measure the rotation in radians, or fractions of pi. In this system, a full turn around the circle is 2π radians, a half turn is π radians, and so on.

Palais realized pi’s inelegance while administering a math test at the U. The test asked students to calculate sine of π/2, or the height of a point that has ascended a quarter-turn on a circle with radius 1. The answer is 1. But Palais saw students reaching for their calculators nevertheless. “Why is it so hard to see that sine of π/2 is 1?” Palais says, and holds his thumb and forefinger at a 90-degree angle to each other.

“I’m looking at this right angle,” he says, “and I’m thinking there’s something off here. π/2? I see a quarter in my mind. There’s something off when I see a quarter and it’s telling me over 2.”

It’s analogous, he says, to a system where a full turn of a clock’s minute hand yields two hours of 30 minutes rather than one hour of 60 minutes. Fifteen minutes, then, would be half an hour instead of a quarter hour, even though 15 minutes is one quarter of a circular clock face.

In 2001, Palais published his observations in an article titled “π is wrong” in The Mathematical Intelligencer. “I know it will be called blasphemy by some,” he begins, “But I believe that π is wrong.” Instead, he proposed using the value of around 6.28, or two times pi, to measure radians and replace pi in other formulas. The ratio of a circle’s circumference to its radius is 6.28, and Palais says that Euler, the mathematician who popularized pi, switched back and forth between values of 6.28 and 3.14 before the latter became the accepted definition. Palais proposed a symbol of a “three-legged π” to represent the new number.

A few years later Michael Hartl, an entrepreneur with a doctorate in theoretical physics, noticed Palais’ article “in the kind of places math nerds frequent on the internet,” he says. In 2010, to help the concept gain momentum, he wrote a new explanation of the need for 6.28 as a trigonometric constant and gave it a name – the Greek letter τ. In this system, a full turn around a circle is τ radians. One quarter turn, or 90 degrees, is τ/4. No memorization required.

With Hartl’s evangelism, tau took off. He created tau day each June 28 as a counterpart to pi day. To celebrate, Hartl says, “you eat twice as much pie. There are no desserts called τ.”

Today, you can type “tau=” into Google and see the answer pop up. A video on the subject by “recreational mathemusician” Vi Hart has been viewed 2.5 million times. Massachusetts Institute of Technology, which announces admissions decisions on pi day, now announces them at tau time (6:28 p.m.). Palais has heard that somewhere in the U.K. there is a car sporting a tau-themed license plate.

“It’s already achieved more than I expected,” says Hartl, who will celebrate this year’s tau day with a visit to Google’s Venice, California, offices. “I wanted it to be something that computer and math literate people were likely to know about. It did work as a social hack.”

Cultural impact aside, however, tau has gained traction as a pedagogical tool. An MIT undergraduate wrote to Hartl telling how he taught his 15-year-old sister trigonometry with tau. “Just as I was drawing the fractional segments of a circle labeled with τ, τ/2, τ/3, etc., her eyes lit up — she grokked it,” the undergraduate wrote, in what Hartl has posted as a “τ-stimonial.” Further, mathematics instructor Phil Smith at American River College in California has written a textbook for teaching trigonometry with tau and shared his experiences for other math teachers to help them acclimate to the new number.

Palais says the whole movement is about simplicity and elegance in mathematics. “We’re throwing people off the track with this pi thing,” he says, and adds that some of the conventions of math may contribute to students feeling like math is an impenetrably difficult game. “We don’t know who we’ve lost.”