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: \( \mathrm{e}^{i , \tau} = 1 \).

<img src="http://upload.wikimedia.org/wikipedia/commons/2/28/Circle_radians_tau.gif" class="figure-img img-fluid rounded" alt="There are &amp;tau; radians in a circle">

<figcaption class="figure-caption">
  <cite><a href="http://commons.wikimedia.org/wiki/File%3ACircle_radians_tau.gif" target="_blank">Image from Wikimedia Commons</a></cite>

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.

Read more about why pi is wrong at tauday.com

  1. In fact, what is the diameter but \( 2r \) anyway? ↩︎

  2. I type on a Dvorak keyboard layout and I use the terminal more than I use a GUI… I’m not just a non-conformist; I like being more efficient. ↩︎