Pi vs Tau, Which Should We Celebrate? Pi vs Tau, Which Should We Celebrate?
Related Pi vs Tau, Which Should We Celebrate?


March 14th (known by many as Pi Day) is upon us, and a fierce debate has been rekindled, as two of the greatest mathematical rivals of our time have reemerged: pi (π) and tau (τ). Both pi and tau are not simply values used to describe ratios of a circle (circumference to diameter and circumference to radius respectively)- they are the keys that unlock a variety of essential mathematical equations.  Controversy has emerged over the past years regarding which should be permanently adopted as the quintessential ratio of a circle, and two Lariat staffers are committed to getting to the root of it.

The Case for Pi (π)


When we were growing up, we were always taught that to find the area or circumference of a circle we had to use pi. It has been a staple of our education for decades and has been an integral part of the larger mathematical community, playing a major role in equations not just about finding the area of a circle but also encompassing more complex ideas, most notably in Albert Einstein’s equation for general relativity. Yet with a new generation of scholars, pi seems to be under attack, threatening  centuries-old equations that would require most likely a few decades to phase out.

Having its origins in ancient Babylon, the pi we know today truly began to emerge with the Greeks, with the famous Archimedes of Syracuse taking up the challenge of calculating the ratio of a circle’s circumference to its diameter, the value which we now know as pi. Although coming close, Archimedes was unable to calculate the value of pi and it would not be for the next hundreds of years, during the twentieth century, that we would find the value which pi stood for (approximate considering it’s an irrational number). Despite not knowing the exact value of pi, by having an approximation, we were able to create a multitude of equations that are common in today’s math textbooks. Pi became so important that we have a day to celebrate it. If that doesn’t speak to its larger than life presence in math, I don’t know what can.

However, lately, there’s been a surge of people calling for its replacement with the “better” tau, or 2π. Although it does have its merits, tau simply doesn’t cut it. After such a long time of using pi, it has become a staple of math lingo and to just replace it with tau would cause worldwide confusion. It would be as if someone were to replace the entire English vocabulary with a completely new set of words. And even if we were going to replace tau with pi, such a mass movement would take unprecedented coordination, something that would be simply impossible.

“I think that if you’re gonna prepare students for the real world we need to use pi instead of tau,” math teacher Mr. Schultz said. “I would be doing a disservice to my students if I taught them tau while everyone else is using pi. So I am in favor of pi.”

At the end of the day, the question becomes if we really want to throw away millenniums of using pi for a poor alternative

The Case for Tau (τ)


The war between pi and tau gained ground on Tau Day (June 28th), 2010, with Michael Hartl’s The Tau Manifesto, of which outlined the various benefits of using tau over pi, but the conflict existed even earlier; in Volume 23 of The Mathematical Intelligencer, Bob Palais devised the tau motif, “π is wrong.” Both The Tau Manifesto and π is wrong are essential artifacts in the years-long conflict that has shown no signs of stopping, and both address the many merits of tau over pi. But what makes these two values (values which are ultimately proportional and easy to relate) so divisive? And why is tau so infinitely superior?

Put simply, tau represents one full rotation of a circle- a singular full turn. Pi, on the other hand, represents one half of a rotation of a circle- thus making pi times two a singular full turn. In effect, this means that one-twelfth of a rotation would be represented by π/6 radians. Alternatively, through the use of tau, one-twelfth of a rotation could be represented by τ/12 radians, a sensible fraction that is far more accessible to learners and far more efficient for experts. On top of this, 2π (the value of τ) is utilized far more frequently than π throughout the many equations mathematicians traverse, meaning that in most cases, τ is far more applicable. It should be noted that those enthralled by the π school of thought can, with some validity, point to the circular area formula as a true enemy to the τ cause; if τ is such a useful, versatile value, why does it inconvenience an equation as vital as A = πr2?

However, as elaborately proofed by The Tau Manifesto, this would relate it more intimately with another invariable equation of math- triangular area. Through implementing τ, the circular area equation would be adjusted to A = 12τr2, which bears striking similarity to the triangular area equation of A = 12bh, if τ is assumed to be the base and r is assumed to be the height.

Historical precedent would have us use pi over tau simply because such is tradition, but should we really sacrifice accessibility and efficiency for the sake of tradition, especially in a field as essential and complicated as mathematics? The transition could pose serious challenges, but with such benefits, wouldn’t it be worth taking the chance on a value that could revolutionize the way we think and approach the subject?

“Implementation of tau should be a slow, careful transition so it isn’t screwed up,” math enthusiast Cole Frishman said. “But ultimately it would be beneficial going long into the future.”

For more information on Tau Day and a full-length version of The Tau Manifesto, visit http://tauday.com.