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.
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: