Today is Pi Day, perhaps the most popular of geek holidays. But I'm here to tell you that Pi Day is wrong, or rather, the whole idea of pi as a mathematical concept is wrong.
It's easy enough to see why people like Pi Day: it all starts with a mathematical word game (the date is written as 3/14 in American notation, Pi starts with digits 3.14). It's easy, fun ritual to see how many digits you can uselessly memorize the famous endless number and never repeated (although 39 digits are more than enough for almost any calculation you need). More pi sounds like cake, and who does not like the cake?
π as a number is bad, and therefore, that's the whole wrong day dedicated to its celebration
But here's the thing: π as a number is bad, and therefore, that's the whole wrong day dedicated to its celebration. It's a lot to assimilate, and I was also once like you: they taught me the virtues of Pi for years, going back to the Pi Day parties in high school. But instead of pi, we should hold tau, an alternative circle constant referred to by the Greek letter τ which equals 2π, or approximately 6.28.
Not only am I inventing this from scratch: Pi's terribleness as a constant was first proposed by the mathematician Bob Palais in his article "It's wrong!" And then exposed in The Tau Manifesto by Michael Hartl, who serves as the basis of modern tauism. (The famous Internet musician Vi Hart is also a great defender of tau on pi, if you prefer your mathematical arguments in a more entertaining video form).
But the arguments of Palais and Hartl are reduced to some basic mathematics. Go back in time to the first time you learned geometry and remember the simple origins: no matter which circle you are using, if you divide the circumference of the circle by the diameter, you will get the same answer: an infinite number, starting with the digits 3.14195265 .. . (aka pi).
And there is the fundamental flaw. The point is that we do not use the diameter to describe circles. We use the radius, or half the diameter. The equation of the circle uses the radius, the area of a circle uses the radius and the fundamental definition of a circle – "the set of all points in a plane that are at a given distance from a given point, the center" – based on the radius By connecting that to our constant equation of circle, we get a new circle constant equivalent to 2π, or 6.28318530717 …, colloquially referred to by the Greek letter τ (tau). Changing to τ is not making an arbitrary change for the sake of it. It brings one of the most important constants in mathematics according to the way we do mathematics.
π is not really something that we use in everyday math to start
Now, you may be thinking that this will cause fundamental seismic changes in mathematics. "How the hell could you replace something as important as pi!", You might ask. But if we are honest, π is not really something that we use in daily mathematics to begin with. Unless you are someone who does a lot of geometric calculations in your daily life, chances are you only find pi when it comes time to recite some digits for Pi Day. Sure, it's a good introduction to the idea of irrational numbers, but tau would work just as well for that. And if you work a lot with π, replacing it with τ is beneficial for a lot of reasons, mathematically speaking. Again, I will address you to the Tau Manifesto for the complete argument, but I will only point out some here.
A great thing that arranges Tau are the Radian angles. You can remember that as "those annoying pieces of a circle represented by odd fractions of high school math pi", but with tau, it's simple: everything fits where you should do it fractionally. Then half the circle (180 degrees) – τ / 2. 1/12? τ / 12. It is a small change, but it makes the angular notation, a frustratingly obtuse part of the geometry that by the use of pi requires an elitist notion of the memorization of angles and conversions, a more welcoming and intuitive perspective for the new ones students.
Image of Michael Hartl / The Tau Manifesto
It also makes circular functions like sine and cosine easier, since it causes a complete cycle of the function to coincide with a full circle turn (tau), instead of the seemingly arbitrary 2π you get using π as the function of the circle. As with radian angles, it makes the sine and cosine values a simple process by simply drawing the function, instead of requiring students to remember that 3π / 2 is for some reason the three-quarter point in the wavelength.
Looking back at the years of math and physics notes with the illuminated lens of tau, I cry for my former self
Similarly, it makes a set of other mathematics integrals higher in polar coordinates, the Fourier transform and the Cauchy integral formula are simpler, since they also work in 2π terms anyway. Using tau simply cuts the middleman. Looking back on the years of math and physics notes with the illuminated lens of tau, I cry for my former self and the cumulative hours of unnecessary conversions and complications presented by pi.
However, they are not just practical purposes. Replacing π with τ makes mathematics more elegant in general. And deep down, is not that what we aspire to do with mathematics? The universe is vast and almost impossible to understand forever, but by distilling it into a system of logical numbers and symbols, we can make some order out of chaos. So, why not embrace a constant circle that makes our equations and formulas more beautiful?
Unfortunately, pi is probably too well installed in traditional mathematics so that we can free ourselves from his tyrannical control. Mathematics textbooks still defend the virtues of pi, and instilling such a systemic change in the way we teach mathematics is an uphill battle. (On the other hand, Common Core somehow seems to have succeeded, despite its – for my eyes – incredibly obtuse nature, but imagine). And that's a shame, given how much more sense does tau make as a constant circle even for the most basic functions we use pi for. But the first step is to stop glorifying pi, so I will not celebrate Pi Day this year, and neither should you.
But all is not lost for those looking for a fun day to celebrate mathematics: after all, Tau Day (6/28 or June 28) is only a few months away.