"I know it will be called blasphemy by some, but I believe that π is wrong." With this bold opening statement in a 2001 Mathematical Intelligencer article, mathematician Robert Palais launched a debate that continues to this day.
For many, an attack on pi is tantamount to an attack on all of mathematics! Hardly any other symbol is so strongly associated with the subject. Songs, poems, books and films have been dedicated to pi. The date of the International Day of Mathematics, March 14, is based on the first digits of pi. It is all the more astonishing, then, that Palais has won over quite a few supporters.
Anyone who thinks this is a circle of people who despise mathematics is completely wrong. On the contrary, their passion for the subject drives them to such disruption.
To make one thing clear from the outset: no one in this debate doubts the correct calculation of pi. But Palais argues that it was wrong to choose the value 3.14159... as the fundamental constant of a circle. He believes it would be much more appropriate to use twice that value, a value now known as tau (τ).
Nine years after Palais's article was published, physicist Michael Hartl posted "The Tau Manifesto" online. In it, he elaborated on and expanded upon Palais's arguments. "π is a confusing and unnatural choice for the circle constant," Hartl wrote. The manifesto lists several reasons why a constant tau is more suitable than pi.
"What really worries me is that the first thing we broadcast to the cosmos to demonstrate our 'intelligence,' is 3.14...," Palais wrote in his 2001 article. "I am a bit concerned about what the lifeforms who receive it will do after they stop laughing at creatures who must rarely question orthodoxy."
In the years following the publication of Palais's article and Hartl's manifesto, the topic attracted increasing media attention. Internet forums saw heated debates about which constant was superior, and in classrooms, some teachers and students began using tau instead of pi. Programmers, too, increasingly defined the constant tau as 2π in their code. "I hope that one day we will all be tauists," Hartl said in a 2011 interview with Spektrum der Wissenschaft, a German-language science magazine.
The arguments of the "Tau Manifesto" do not convince everyone, however. Quite a few experts remain convinced that pi is the right constant. Shortly after Hartl's proposal, "The Pi Manifesto" appeared (as you might expect). According to this manifesto, written by mathematician Michael Cavers, Hartl's arguments were "full of selective bias in order to convince readers of the benefits of τ over π." In many cases, tau would bring more disadvantages than advantages, Cavers claimed. The Pi Manifesto lists several reasons why replacing pi makes no sense.
The mathematics itself does not change one way or the other, of course. You might therefore ask why the experts are making such a fuss. After all, it's just about notation.
This may not seem particularly important — but notation doesn't just determine whether a result can be represented simply or in a complicated way. Notation is also crucial for intuitive understanding.
For example, the tau camp has made the case that angles can be expressed more intuitively using tau than pi. A full turn around a circle is simply τ rather than 2π, and a quarter turn is τ/4 rather than π/2.
But consider the contrast in notation when we look at the area of a circle: with pi, it is the familiar πr², while with tau, it becomes ½τr².
Whether pi or tau is more suitable here is not so easy to say. Both tauists and pi supporters concede that the opposing side has an edge in certain contexts and makes some valid arguments. The fact is that pi has been deeply rooted in not only mathematics but also popular culture for centuries. Letting go of this constant and introducing a new one would be anything but simple. And dealing with two different circle numbers would simply create confusion.
Some parties are, therefore, advocating for a compromise. "The Proper Pi Manifesto" (not to be confused with The Pi Manifesto) proposes keeping pi but introducing a completely new unit, "darians," instead of radians to measure angles.
Or even better, perhaps, is the idea mentioned in the web comic xkcd: a constant called "pau" that has a value of 1.5π. Then everyone would be equally confused.