Pi is wrong. And the answer is not cake. It’s tau.
We don’t mean to say that a circle’s circumference divided by its diameter is not 3.14159 and so on and so forth, just that the concept of pi as the circle constant is wrong.
The circle constant may seem like an arbitrary number and to many the importance of pi may never become immediately apparent, but it is, in fact, one of the most important numbers in the world. Airplanes, radios, navigation, statistical calculation, and many more all depend on the circle constant.
Currently, the circle constant is defined by the diameter of a circle. Pi denotes the ratio of a circle’s circumference to its diameter. However, a circle is defined as a set of points equidistant from a central point. This distance is the circle’s radius, not its diameter. It is this confusing convention that causes one-quarter turn of a circle to be one-half pi. Many students resort to rote memorization of the unit circle in lieu of understanding the concepts and relationships it represents. All of this could be averted if the radius of a circle, instead of the diameter, defined the circle constant.
This is the concept that Professor Bob Palais from the University of Utah wrote about in his article “Pi is wrong!” nearly a decade ago. In doing so Palais drew attention to the need to replace the constant that turns “the opportunity to impress students with a beautiful and natural simplification…into an absurd exercise in memorization and dogma.” Since then Palais’ idea has gained a moderate number of supporters. Physicist and educator Michael Hartl has published “The Tau Manifesto,” a declaration that officially called forth the Tau Revolution. Vi Hart, a YouTube Mathemusician, created a video titled “Pi Is (still) Wrong” and Kevin Houston, a professor from the University of Leeds in U.K. also created a YouTube video “Pi is wrong! Here comes Tau Day.” These are just a few examples of the attention the idea is receiving.
However, pi is a powerful foe. Ever since the Egyptians and Babylonians first estimated its value the deadly grip of this devilish constant has only strengthened. Pi is honoured every year on March 14. There are contests devoted to the recitation of pi’s digits. Entire books are devoted to praising pi. And of course pi brings to mind a particularly delicious pastry. It’s hard to see how tau could compete with this but that isn’t stopping people from trying.
Tau’s proponents are proposing the circle constant become 6.2831… or twice as large as pi. This number would be denoted by the symbol tau and there are many profound mathematical benefits that accompany this change, all of which are catalogued in a detailed list by Peter Harremoes.
Although it clear that tau would make many operations and formulae much simpler there remains a reluctance to change. One McGill professor did agree that while pi can be a pain, but it’s one that “we have to live with.”
The notion of keeping something that is an admitted inconvenience often stems from the appeal to antiquity. It is a common logical fallacy to think that older ideas are better, simply by virtue of being old. The appeal of antiquity does not restrict itself to discourse on mathematical constants but also extends itself to the hesitation that most new ideas meet.
It is understandable that mathematicians, scientists, engineers, and other professionals would not want to switch from pi to tau when they have been using pi their entire lives and have grown accustomed to its fickle ways. However, the most important consequence of retiring pi in favour of tau would be the pedagogical benefits. For students who are just learning these concepts the confusion pi causes can be a major deterrent. Making the more natural definition of the circle constant with regards to the radius would make not just math, but other related subjects, slightly more accessible to people.
Ultimately, most people show complete apathy, as this would change very little, if anything, of their day-to-day lives. Even with tau, calculus would probably be just as hard, statistics just as convoluted, and math and related subjects, just as confusing.
Judging from the current state of affairs it is unlikely that tau will be able to usurp pi in the near future. Perhaps if tau had a name as delicious as pi, it would be a different story.