Happy Tau Day!

Every time I saw a Pi ($\pi$) symbol in mathematics that represented the value 3.141592653…, there was usually a “2” in front of it. This is no coincidence: a circle is the set of points that are the same distance $r$ from a center point, where $r$ is the radius, so the radius is what defines a circle—not the diameter. 1

Now, the value of $\pi$ represents the ratio of a circle’s circumference to its diameter…     wat?     No wonder there’s always a persistent factor of 2 in almost every equation involving $\pi$: The proper circle constant should be the ratio of a circle’s circumference to its radius, or $2\pi \approx 6.283185307\ldots = \tau$ (see the figure below). This has a profound connection with radians and the trigonometric functions sine, cosine, tangent, etc. Even the Euler Formula looks better: $\mathrm{e}^{i \, \tau} = 1$.

This is not just me being non-conformist2, this is actually part of a world-wide movement to correct the circle constant to what it should have been.

1. In fact, what is the diameter but $2r$ anyway? ↩︎