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π versus τ: A modest Proposal

Ahh! The great pi vs tau debate of 2010 lives on.

Given that this blog has covered such contentious and pressing issues as the “king” of the generalized fibonacci sequences, it seems only natural that I weigh in on the defining mathematical debate of the decade.

For the lost, this is a circle:

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Pi is circumference divided by diameter, and Tau is circumference divided by radius:

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Some people who apparently don’t have anything better to do1 like to argue about which is the better of the two circle constants.


I hope to resolve this dispute once and for all.

But before we do that, let’s introduce our competitors:

Prominent tauists Michael Hartl, argues for the irrationality of pi in his seminal piece “The Tau Manifesto.” His principal argument goes something like this:

“When measuring angles in radians, a full circle is an ugly 2π, while it could be a clean (one) τ. This fact percolates through mathematics, depositing a 2π into various equations, and defaces our normally-elegant subject. It also makes angle measures counter-intuitive, like a quarter of a circle actually being π/2 radians.”

Pi supporters, on the other hand, are “very comfortable with pi, and multiplication by two.”2


So what’s to do? How can we bridge this treacherous chasm?

Fortunately, there is a solution.

Notice how I started my 53 word summary of “The Tau Manifesto”

When measuring angles in radians...

That little bit is the key to understanding this whole dilemma. You see, we measure angles using the radius of a circle, while employing a constant defined in terms of its diameter. It’s no wonder we have a factor of two lying around everywhere: our tools of measurement themselves are off by a factor of two.

The problem, then, isn’t the usage of pi. Rather, it’s the mismatch between our unit of measurement and our choice of constant.

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This suggests a rather simple compromise: use diameters instead of radii to measure angles.

The benefits of this compromise are clear:

Pi-supporters get to keep using pi, and thus can claim a technical victory.

Tau-ists get to revel in their intuitive understanding of angles.

Everyone else? Ehh. They’ll just be confused for awhile.


1guilty

2Siddhartha Gadgil, seen in the pi manifesto