In support of Tau

An enlightening discussion about pi and tau.

In support of Tau

by metric man » Wed Dec 21, 2011 11:47 pm

Hi everyone,

I am an adjunct faculty member, teaching introductory precalculus at Towson University.

When it comes to explaining radian measurement, students are somewhat mystified as to its purpose. I can't remember if anyone has ever raised the question in class, but I think that the general sense is, "Why do we need radians. Why can't we just use degrees?"

For the most part, you have to content yourself with saying that radians are used in higher mathematics, such as calculus, but you cannot go on to explain why, because the answer is beyond the scope of a precalculus course.

But one meaningful thing is to state that radians offer a more efficient system for measuring angles involving more than one rotation. "Quick, how many degrees does an angle have that spins around eight-and-a-half times?" This is an example that I use when introducing the subject. Using degrees, the answer involves a clumsy multiplication of 8½ times 360 degrees — 3060 degrees. Using [tex]\pi\[/tex], the answer is 17 [tex]\pi\[/tex]-radians — much simpler.

In the end, however, even that sounds a little strange, right? Things are immediate and direct when using [tex]\tau\[/tex]-radians. In that case, 8½ rotations equals 8½ [tex]\tau\[/tex]-radians. One-quarter of a rotation is [tex]\frac{\tau }{4}\[/tex]-radians. One full turn is [tex]\tau\[/tex]-radians -- and not the counterintuitive 2[tex]\pi\[/tex]-radians. And so on and so forth.

I don't want to go on too long, and I am having trouble using Tex. (I have not used it for years, relying instead on MathType.)

Tau is intuitive and direct, just the opposite of pi.

I think that at least one of you accomplished and talented mathematicians out there should write a trigonometry or precalculus textbook, and show radians only in tau, not pi.
metric man
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Re: In support of Tau

by josephlindenberg » Sun Dec 25, 2011 5:14 am

What's even worse is that you first have to stop and think, do I multiply by 2 or divide by 2 here? Then, you have to actually do the multiplication or division.

Using your example of :
  • If it's turns, you have to multiply by 2 to get 17π radians
  • If it's 8½ π radians, you have to divide by 2 to get turns
If we can remove mental speed bumps like these by switching to tau, wouldn't that help everyone (not just the millions of students who learn radians each year) concentrate on the actual mathematics? (And these definitely aren't the only mental speed bumps pi causes.)
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
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Re: In support of Tau

by metric man » Sun Dec 25, 2011 1:54 pm

Exactly so.
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Re: In support of Tau

by 1=0 » Sun Mar 19, 2017 2:18 pm

If you walk a distance d around a circle with circumference C, it's dτ/C radians! All of our units of time, such as the day and the year, are based on full turns, which are tau radians.

I have a true story to demonstrate the counterintuitiveness of pi.
In algebra class we were talking about radians, and some people were confused as to why 7π/6 and -5π/6 are the same angle. I had to explain that it was because if you go 7/12 around the circle one way and 5/12 around the circle in the other direction, you end up in the same place because 7/12+5/12 is a whole number. (I was basically stating the fact that two angles, α and β, are the same angle if α-β is a multiple of tau, except worded differently). Of course, the reason for the confusion in the first place was that 7π/6 is 7/12 of a circle, and this problem is nonexistent with tau. Since 0 and τ radians are the same angle, -θ and τ-θ are also the same angle. Tau removes a major speedbump by making it much easier to figure out what negative angle corresponds to a positive angle.
And to all the people who say pi is more fundamental because it's the smallest number for which θ and -θ are the same angle, the only reason π and -π are the same angle is because τ is the period of angle measure and -π+τ=π.
Last edited by 1=0 on Thu Mar 23, 2017 6:10 pm, edited 1 time in total.
τ>π
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