Tau Day, 2011

Happy Tau Day! Today is June 28, or 6/28 in the US date format, and τ = 6.283185307179586…

There’s a movement of sorts to use τ (which is equal to 2π), instead of the more familiar π. π is the ratio of the circumference, C, of a circle to its diameter, D.

π = C / D

τ proponents say that since a circle is defined as the set of points a fixed distance (the radius, r) from a given point, a more natural definition for the circle constant would use r:

τ = C / r

This of course makes τ equal exactly to 2π. One might well ask, “What’s the big difference?” τ advocates say simply, “π is wrong.” By this, they don’t mean that it’s wrong to say:

C / D = 3.14

That equation is wrong mathematically, just as any calculating device is wrong because it has to approximate π. Neither π, nor τ can be expressed as a simple fraction (or as a terminating or repeating decimal). But the argument here is not about approximations. It’s that π is wrong pedagogically: π is a confusing and unnatural choice for the circle constant. The confusions run through all sorts of statements about circles, angles, statistical and physical relationships.

The full reasons for using τ are explained in Bob Palais’s article P Is Wrong and in Michael Hartl’s The Tau Manifesto, which is

dedicated to one of the most important numbers in mathematics, perhaps the most important: the circle constant relating the circumference of a circle to its linear dimension. For millennia, the circle has been considered the most perfect of shapes, and the circle constant captures the geometry of the circle in a single number. Of course, the traditional choice of circle constant is π—but…π is wrong. It’s time to set things right.

Michael Blake has created a musical interpretation of τ up to 126 decimal places. It maps τ to musical notes, and sounds quite nice:

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