Tau Day: Should Pi Be Downgraded?

June 28. National Paul Bunyan Day, National Insurance Awareness Day, National …  Tau Day?

Today (June 28) is the unofficial holiday Tau Day, meant to celebrate the number tau, that works out to approximately 6.28, or the ratio of a circle's circumference to its radius.

While pi may be the most famous irrational number, or a number that can't be expressed as a ratio of two integers, a small but dedicated band of nerds and mathematicians has argued that pi should take a backseat to tau, a more perfect circle constant.

Tau should be the real headliner because it directly relates a circle's circumference to the shape's radius; its irrational little brother pi relates the circumference to the diameter, which is less important mathematically, said Michael Hartl, the author of "The Tau Manifesto" and the "Ruby on Rails Tutorial" (Google Books, 2012), and the founder of education website learnenough.com. [The Most Massive Numbers in Existence]

It's not clear why Archimedes, who first described the number pi, chose to go with the less intuitive irrational number. One possibility is that it was simply easier to measure a circle's diameter than the shape's radius using a rod or something similar, "but that doesn't make it good math," Hartl said.

Pi cemented its place in the math pantheon in the 1700s when Swiss mathematician Leonhard Euler, a prolific mathematician who significantly advanced the fields of trigonometry and calculus, enshrined the convention of using pi to describe certain angles, Hartl said.

Pi's dominance remained unquestioned for centuries. Then, in 2001, University of Utah mathematician Robert Palais wrote a paper subtly titled "Pi is wrong" for the 2001 issue of the journal Mathematical Intelligencer. In it, he itemized the shortcomings of the most famous irrational number. And he advocated for a new constant to take its place: tau.

Tau, which equals 2 times pi, is a more natural and direct way to grasp how a circle's radius relates to the shape's circumference, Palais argued. That makes tau a more powerful constant, he said.

For instance, there are an infinite number of shapes with a constant diameter (for instance, a Reuleaux triangle), but only one (the circle) with a constant radius, Hartl wrote in "The Tau Manifesto."

What's more, tau creates a more intuitive way to think about portions of the circle, he added.

"The biggest place this shows up is in trigonometry," Hartl told Live Science.

For instance, every high-school trig student learns that a right angle equals pi divided by 2 radians. But a right angle actually delineates a quarter of a circle, Hartl said. The math would be easier to remember and work with if the angle were represented by tau, because the angle would then be tau divided by 4 radians. 

"These special angles people had to memorize in high-school trigonometry don't have to be memorized at all," Hartl said.

What's more, tau makes a number of other calculations and equations more elegant, such as the equation used to calculate imaginary numbers (Euler's identity), Hartl said. Using tau instead of pi also creates a beautiful symmetry between the equation for a circle's area (1/2 * Tau * radius^2) and other iconic equations, such as those for kinetic and elastic energy (1/2*k*x^2), as well as the equations for how far an object under the influence of gravity will fall in a given time interval, Hartl argued.

Whatever the case, there's no doubt that tau has risen in popularity, especially amongst the mathematically inclined. For instance, if someone types the Greek letter tau into Google's calculator, the irrational number will appear, Hartl said.

The Massachusetts Institute of Technology has even changed its admissions routine, announcing acceptances at tau o'clock on pi day: 6:28 p.m.

There are, of course, unequivocal downsides to enshrining Tau Day instead of Pi Day, Hartl said.

"You don't have quite the same food-based pun potential," Hartl said, referring to the tradition of serving pie on Pi Day.

However, the biggest reason Pi Day may forever overshadow the Tau holiday is simply that the former falls during the school year, giving math teachers everywhere a built-in way to celebrate their beloved subject matter, Hartl said.

Original article on Live Science.