Using Pi Is a Gigantic Mistake
It's Pi (π) Day 2019, and across the world, math teachers, students, and number fanatics are no doubt celebrating with colorful circles and delicious pie. Any day in which science and mathematics are acknowledged is worthwhile, but it's also worth mentioning that π itself is "wrong."
Such a harsh indictment of the irrational number representing the ratio of a circle's circumference to its diameter might come as a shock to Lu Chao of China, who, in 2005, memorized and recited 67,890 digits of π. It also will definitely bum out consumers hoping to cash in on all of the punny Pi Day deals at pizzerias and bakeries. (Who doesn't love $3.14 pizzas?) But the criticism is definitely merited in the opinion of Bob Palais, Chair of the Mathematics Department at Utah Valley University.
"I am not questioning [Pi's] irrationality, transcendence, or numerical calculation," he wrote back in 2001," but the choice of the number on which we bestow a symbol conveying deep geometric significance. The proper value, which does deserve all of the reverence and adulation bestowed upon the current impostor, is the number now unfortunately known as 2π."
6.283185... It doesn't roll off the tongue as well as 3.1415926... But let's hear Professor Palais out.
Palais' critiques boil down to a couple of key points: First, 2π appears in a medley of important scientific theorems and formulas, including the Fourier series, Maxwell's equations, and the ubiquitous formula for the circumference of a circle (2πr). There's simply no need for the number two! Why not replace it with a single symbol?
Second, Palais contends that π creates unneeded work and confusion for young geometry and trigonometry students. Fractions of a circle are commonly described in radians, equal to roughly 57.3 degrees, making a complete turn of a circle equal to 2π radians, which is madness, he says.
"An enlightening analogy is to leave clocks the way they are but define an hour to be 30 minutes," he wrote. "In that case, 15 minutes or a quarter of a clock would indeed be called half an hour, just as a quarter of a circle is half of π in mathematics!"
Now look what happens if we ditch π in favor of another term, Tau (τ). Advocated by entrepreneur, programmer, and physicist Michael Hartl in a follow up to Palais' piece, τ is equal to 2π, or the circumference of a circle divided by its radius.
Suddenly, a quarter turn of a circle is equal to τ/4, a half equal to τ/2, and so on... Much neater!
Okay, so replacing π with τ seems like a great idea, one worthy of celebration! How about Tau Day on June 28th?
The reality, however, is that π is ingrained in textbooks and teaching. It will be extremely difficult to dislodge it. Hartl, however, is hopeful that at least discussing τ would be a perfect chance to introduce students to the inner workings of science.
"We can embrace the situation as a teaching opportunity: the idea that π might be wrong is interesting, and students can engage with the material by converting the equations in their textbooks from π to τ to see for themselves which choice is better."
Knowledge is forged through hammering out ideas. Once the intellectual pummeling is complete, we sometimes disregard the old in favor of the new. Could Pi be on its way out? Unlikely. But you never know!