There has been increasing buzz about Pi and Pi Day lately, probably because July 22 — 22/7 — is approaching. And though any web search can find this buzz, I would like to add a comment about Tau Day (June 28), which is adding noise to the excitement.
“Ya! Do tip: Laud Tau, at dual Pi, today!” “I prefer Pi”
Tau, having been recently replaced by phi as the symbol of the Golden Ratio, is a proposed symbol for the value 2*Pi, lauded (to borrow from the palindrome above) by those who think 2*Pi is a better measure in all ways than Pi.
This claim, of course, has created a heated but sometimes hysterical discussion, and post and video “war”, between two extreme camps: the Pi’s and the Tau’s. Add to this a third camp, those who argue for Eta (Pi/2 or Tau/4) as the standard, and a fourth, who promote Pi/4 (Tau/8) instead, and we have a mathematical event to behold.
Of course, none of this really has serious implications, since we all know that Pi/3 or Tau/6 ¹, the sextant, with its relationship to the equilateral triangle, radian, Babylonian sexagesimal system, Earth year and rational cosine value, is the real fundamental unit of the circle.
It seems we are confused.
This of course is all in good fun. Yet tell that to Tau Beta Pi and Tau Alpha Pi, the Engineering and Engineering Technology Honor Societies, whose society names are at risk at both ends.
It’s happened before
Nor is this the first time a math convention has been questioned. In fact, it is not even the first time a circular measure has been questioned.
Before there was trigonometry (the study of measures of closed three-kneed figures or triangles), there was circle geometry (the study, which we still have — but lacking the now analytic trigonometric part, of regular closed no-kneed figures or circles). In circle geometry, the chord is king and emphasis is on the geometry and measurement of the circle, line segments and angles. Everything was working really well.
Then came sine!
Sine, of course, is half a chord, chord/2. It seems weird to us now, but at one time sine was the oddity trying to replace the convention. Yet, when it did become convention, a new field of math was born.
In a history shamefully oversimplified, circle geometry split into two fields and, for the sine portion, analysis, ratios, angles and triangles became the emphasis, so leading to the title of trigonometry. Circle geometry continues to deal with geometry and measurement. And the chord is the usurp outsider.
And history we witness
So we have Tau (whole), and Pi (half), and Eta (quadrant), and Pi/4 (octant), and Pi/3 (sextant). I wonder what history will come of this.
Importance: A rose in the classroom
Does it really matter what constant we use as the base unit for circle measurement? They are just names. Some formulae will work better in some situations than others, and this will change with situation.
How we choose to deliver the concepts to students is far more important than what we call them. Truth be told, all systems should be taught interconnectedly with no mention of which might be the opinionated best.
The key is engagement and problem solving. Students need to understand how to use the math, why it works, where it is used and how it is used. It would benefit them if they learn their own formulae, and we help them “conventionalize” these to fit what other mathematicians do and say.
Changing of the conventional Pi to Tau, or Eta, or either of the other measures, might change the nature of circle and trigonometric math in ways we can not predict at present, but that will come in the future. Today we have these five fundamental units, which are all arbitrary, math-founded and related. Who is to say which is best?
By any other name, is a rose not still a rose?
Want more? Visit Benjamin Vitale’s June 28th Pi is wrong! Here comes Tau Day, watch Vi Hart’s Pi is (still) wrong, and read Bob Palais’s original π is wrong! which started the Tau, then two-pi, movement.
Then read Mike’s response to The Pi Manifesto, from the creator of Spiked Math Comics, then the continued debate on On Pi Day we eat pie. On Tau Day we eat Taoists? and ‘Tau day’ marked by opponents of maths constant pi, including its comments.
Given that we are rather gossipy creatures, most of the posts, discussions and video have titles that attack poor Pi and its Day, or Days (March 14 or July 22). But a few out there attack Tau as well. The Eta’s, Quarter-Pi’s and Equilateral’s just cling where they might be heard. Sounds like a school yard, doesn’t it?
This post actually started as an update comment to my Math Challenge: Pi Day, but the comment morphed into a post of its own, so I decided to make it so. If you are interested, please visit my Pi Day math challenge post.
¹ Given its Babylonian pedigree, perhaps we should call Pi/3 Sedis, which is six in Assyrian.