Happy Tau Day!
Every time I saw a 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 from a center point, where is the radius, so the radius is what defines a circle—not the diameter. 1
Now, the value of 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 : The proper circle constant should be the ratio of a circle’s circumference to its radius, or (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: .
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