For Math Fans, Nothing Can Spoil Pi Day—Except Maybe Tau Day

Tomorrow, March 14, is a national holiday. Some number nerds think people should be celebrating Tau Day instead; ‘geekier version of pi’

By Robert McMillan

March 13, 2020 / Wall Street Journal

From its humble beginnings more than 2,000 years ago, pi—that never-ending number that starts with 3.14—has become the superstar of mathematical constants.

Schoolchildren celebrate Pi Day on March 14. Math geeks make it their wedding day. In 2009, Congress declared Pi Day—which is tomorrow—a national holiday. Some venues have canceled Pi Day events that draw crowds because of coronavirus.

But the real rain on Pi Day’s parade: the taus.

For Michael Hartl, tomorrow’s holiday just doesn’t add up. In some circles, math fans think people should be celebrating Tau Day instead.

Ask Dr. Hartl about it, and he will unleash a litany of equations, all of which would be simplified by using a different never-ending constant—equal to two times pi, and beginning with 6.28. Dr. Hartl, a 46-year-old physics Ph.D. and author of programming tutorials, calls this constant “tau.”

The idea caught on with other math rebels who would like to see the world celebrate Tau Day on June 28. But Dr. Hartl admits the numbers are against him. “Those who stubbornly cling to pi will always find a way to rationalize their error,” he says.

There have been some tau victories. In 2013, the calculator used by Google’s search engine started recognizing tau. Microsoft’s Bing has yet to join the tau party, although a spokeswoman says the company’s Math Solver app is tau-enabled.

At the Massachusetts Institute of Technology, they’ve struck a compromise. While MIT does inform high-school students of its admission decisions on Pi Day it now publishes the decisions at 6:28 p.m. on weekdays, a nod to tau.

“We love all our ratios equally, and while to some people tau makes more sense mathematically, to everyone pi is more delicious,” said Stuart Schmill, dean of Admissions and Student Financial Services.

Archimedes took the first shot at calculating pi, the number, but he didn’t name his constant. Pi was popularized in the 1700s by Swiss mathematician Leonhard Euler, considered one of the greatest of his day. Starting in the late 1980s, pi became a geek juggernaut.

That’s when staff at the Exploratorium, a museum in San Francisco, decided to host their first Pi Day, or as Dr. Hartl calls it, half-Tau Day.

Pi Day is the math world’s annual bacchanal. The Exploratorium typically hands out thousands of pieces of pie—lemon meringue, pecan, apple and chocolate cream—on March 14. At 1:59 p.m.—159 being the three digits that follow 3.14 in pi—there’s a parade to a pi shrine, where people walk around it 3.14 times while singing “Happy Birthday” to Albert Einstein, who was born on March 14. This week, the museum said it is closing until the end of March because of coronavirus precautions; instead, it will have a virtual Pi Day, with kitchen calculation tips on how to use pi to bake a better pie.

“We just like pi,” says Ron Hipschman, a science educator at the Exploratorium. “Pi has a history.” He isn’t opposed to Tau Day. He just prefers to call June 28 “2pi Day.”

Tauists say history is on their side too. Euler, the Swiss math whiz, himself was unsteady in his use of the constant—sometimes referring to pi as 3.14, at other times doubling that. “He was flip-flopping all over the place,” says Bob Palais, a math professor at Utah Valley University, who some consider to be the godfather of tau.

Twenty years ago, Prof. Palais realized his students were having an easier time learning trigonometry when they used tau instead of pi.

To get pi, you divide the circumference of a circle by its diameter. For tau, you divide by the radius. So, to describe 3/4 of a circle in trigonometry, you would say 3/4 tau radians. But in the pi world, that’s 3/2 pi radians.

“Blegh!” says Prof. Palais. “People are just so ingrained that they don’t even see how stupid it is.”

Prof. Palais is a bit of a math maverick. He also takes exception to the term X-axis. “I call the X-axis, the Y=0-axis,” he says. “There’s nothing X about it.”

In 2001, Prof. Palais wrote a paper titled “Pi is Wrong.” It was the rallying cry for Dr. Hartl, who followed nearly a decade later with his own publication and a website titled “The Tau Manifesto,” a 9,000-word call-to-arms that lays out the arguments for tau in excruciating detail.

Tau quickly blew up in the internet savvy tech community, talked about on coder sites. A video about tau went viral, with over two million views. Dr. Hartl says he started meeting people at parties who would make small talk by dissing pi in favor of tau.

“I knew that this would be the geekier version of pi,” he says.

Acceptance in the mainstream mathematical community, however, has been an uphill fight. Textbook publishers are largely pi-loyalists. “They are afraid of being mocked for doing something different,” Dr. Hartl says. “Nobody’s ever lost a contract for using pi in their math tests.”

Much of the math establishment remains unconvinced. Using tau would be akin to driving on the left-hand side of the road; you’d still get where you were going, but the driving would be different, says Scott Chapman, past editor of the American Mathematical Monthly. “It’s just a little wrong,” he says.

Prof. Chapman says that while the Tau Day vs. Pi Day debate can get heated, it’s all in good fun. “When you’re a mathematician you really have to have a little bit of a sense of humor,” he says. “I mean, how much do we have to celebrate?”

Moving the celebration would have practical challenges. “If we went to Tau Day, we’d go to June 28 and school would be out,” says William Dunham, a math historian and research associate in mathematics at Bryn Mawr College.

Prof. Dunham rejects the tauists argument that removing pi would restore elegant simplicity to many mathematical formulas. For example, the mathematical formula known as Euler’s equation is simpler with tau.

With pi, however, the formula contains what Prof. Dunham calls the “most famous constants in mathematics,”—e, i,pi,1 and 0. “If you were having a party and wanted to invite the greatest numbers in the universe, you’d invite these five,” he says.

So incensed are some of the pi faithful that they have resorted to the ultimate nerd weapon to battle tau: the palindromic slogan. “I prefer pi,” Prof. Dunham says, echoing what has become the 21st century’s battle cry for pi.

While a tau switch-over would simplify some mathematical equations, it wouldn’t be the seismic event that in the math world that happened, for example, when we switched from Roman to Hindu-Arabic numerals, said Terence Tao, a noted mathematician and a professor at the University of California, Los Angeles. “This may all be an instance of the Bike-Shed Effect, also known as the Law of Triviality: Important complex problems are difficult to solve and discuss, so often people focus on unimportant problems that are easier to argue over instead,” he said.

Google’s addition of tau to its search engine calculator was a big endorsement, but even Google isn’t squarely in tau’s court. The suggestion to add tau was made by Eve Andersson, a Google director of inclusive machine learning & accessibility engineering. A Google spokeswoman says Ms. Andersson describes herself as a “die-hard pi fan.”

Ms. Andersson made the suggestion to add tau because she “thought our calculator feature should be inclusive,” the spokeswoman said.