Pi’s not wrong: on the Tau Manifesto

A friend asked me via Twitter what I thought of this io9 article about why pi was wrong. That’s right, pi: the circumference of a circle divided by its diameter. In Euclidean geometry that’s equal to approximately 3.1415926535897… and is irrational. The person io9 interviewed for the article is a proponent for a new constant called tau (after the Greek letter) that is the circumference divided by the radius. In other words, a constant for twice pi.

There’s a website promoting the correctness of tau as the correct value, claiming pi to be wrong just as the article does. The website isn’t not talking about the mathematical incorrectness of pi, but the site and io9 are using headline trickery to pull readers in.

The Tau Manifesto is disappointing. All it shows is that the choice of pi vs. tau is arbitrary at best, and we as a society chose pi over history because pi was discovered first. Besides, writing 2*pi is nicer than tau/2. This tau movement isn’t going to catch on. It’s not even on Wikipedia!

23 replies on “Pi’s not wrong: on the Tau Manifesto”

I agree that tau will probably never catch on, and that’s somewhat unfortunate.

I think you are wrong to assert that “the choice of pi vs. tau is arbitrary at best”. Au contraire, the manifesto does succeed in pointing out that tau is a superior choice though not the one made by homo sapiens. I can even contribute my own (admittedly obscure) example:


A system of angle representation known as Binary Angular Representation used sometimes in computer programming can be defined algebraically as a scaled binary integer with an assumed radix point before the most significant digit and a scale factor of 2pi. (There goes the 2pi again.) Simply putting a tau would make things clearer and derives from what the paper correctly points out that 1 tau is a full turn. (When an arithmetic operation causes a BAM to “overflow”, the circle has been turned and the residue in the BAM represents the normalized angle.)


Also, saying that writing 2pi instead of tau/2 misses the point. The simple fact is 2pi (or simply tau) comes up all the time, pi by itself rarely does; and when it does it is usually in the context of a quadratic form which Harti makes a good case for tau being a better choice.

I also think that saying that “pi was discovered first” is a red herring. The significance of the discovery was figuring out that a circle constant existed at all, not the choice of constant made to represent it. By analogy, common logarithms were “discovered” before natural logarithms though they are both logarithms and share all there properties thereof. However the choice of the natural logarithm is not arbitrary. We would reasonably expect an extraterrestrial mathematician to be familiar with e but as a “natural” base, but not necessarily 10 as a “common” one.

And maybe there lies another suggestion. Borrow from the example of logarithms:

pi is the “common” circle constant.

tau is the “natural” circle constant.

Disappointing that you do not give ANY arguments why pi is not wrong, either. Truly disappointing. I think the idea of tau is a good one and it really is thought through. Just stating the opposite does not change anything.

Where are *your* arguments in *favour* of pi???

Radians are better for calculus. Simply because if we calibrated the trig functions for tau, then the derivative of sin(x) would be 2*cos(x) instead of cos(x).

This is the reasoning behind using radian instead of degrees when doing calculus. The derivative of the degree sine function is (pi/180)*cos(x)

Workit: The definition of a radian would not change if we used Tau as the fundamental constant rather than Pi. The derivative of sin(x) would still be cos(x). There would be Tau radians in one complete revolution. My interest in exploring Tau is to find out if it makes trig, and radians, easier to understand if the standard angles were in terms of Tau. For example, a right angle is one quarter of a revolution or Tau/4. Seems like it this is worth exploring.

I believe Tau (for teaching Math) can be argued as Phonics was argued in teaching reading. It makes it easier for the end user or student to understand, but fundamentally, we are still working with Pi and could ultimately cause confusion. But it is interesting to explore to see what patterns come up with a different series of numbers and may let us look at Pi with new eyes. As in a musician finding themselves in a melodic rut until they change instruments and their fingers can explore different patterns.

Bare Bear. 🙂 Tau Pi

Tau may be useful, but pi is definitely not “wrong”. I’ve never seen a bigger HOOK even in Hollywood, and this is being done by professional mathematicians? Arrogance at its best. And if they think “tau” is somehow more “right” than pi, stay tuned until the day “tau” is found to be incorrect. All scientific knowledge is subject to critical revision. But the way mathematicians are jumping up and down about tau, it’s clear they are interested in salesmanship, more than science or the science of rationality. Hollywood.

Wow, seriously, the article gave a comprehensive argument to show why tau is more natural, and you say “It’s wrong because I don’t like it.”

Real mature there.

Sorry to disagree with you guys, but pi IS more correct (or, if you prefer “more natural”) than tau.
All the reasoning to prove that tau is better are based on drawing circles in a 2d world.
But circles do not exist.
We do not live in flatlandia, but in a 3d world.
Circles do not exist: spheres do.
pi diameter squared.
nothing to add, really

And that “diameter” argument is exactly why pi is flawed, says the article.

You’re still missing the point. The article says that 2pi shows up all the time, not pi. And read the “coup de grace” part. It says that the factor of half is a NATURAL thing produced by integration. Same should follow for your example.

There must be something wrong with integrals 😉
The relationships are what matters. The prefered appearance or what you make it in terms of for aesthetic purposes doesn’t matter to me. Tau is as good as Pi as far as I’m concerned.
I find math people often neglect how easy it is to measure a rods diameter vs finding it’s radius. The drafter person in me prefers radius since compasses are nice.

This is bullsh!t, why don’t we just use pi where pi is more convenient, tau when tau is more convenient, and use either if either is convenient!

If pi is more convenient for a specific case, present that case. Don’t just dismiss the whole article as stupid for superficial reasons, like this blogpost did, because that kind of response itself looks stupid.

By that logic, 1/2pi, 1/3pi, 1/4pi, 1/5pi, etc. are special too. Then “special” loses all meaning.

Show me a specific argument from the pi manifesto and I’ll answer it, but otherwise that comment doesn’t show anything.

How about you actually read the site and the Wikipedia page (yes it’s there) before prematurely dismissing it like that. You’re missing the point.

Pi is the more natural ratio of C/D. Why? C and D are EMERGENT properties of the radius. C & D rarely pop up in analytic formulas themselves. The Gaussian Integral evaluates to the square root of Pi. And what about the most famous unification formula of all time?

e^(i)pi + 1 = 0

Tauist give e^i(tau) + 0 = 1, how degenerate! The real Euler’s formula gives more than aesthetics,it says something about the special relationship of the 5 constants!

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