Pi or Tau? Which should be recognized more?
Background: You may have heard about the number Pi (or approximately 3.14159....) and its importance in mathematics (its the ratio of a circle's circumference to its diameter.) It has such great mathematical importance that it even has it's own day in the U.S. (March 14th or 3/14.) However, there are people who argue that Tau, or twice Pi (or approximately 6.28...) is actually more important than Pi. There are some who celebrate Tau Day on June 28th (6/28.)
Why would some consider Tau more important? Let's look at some mathematical formulae:
Key:
r = radius
d = diameter
x*y = x multiplied by y
x^y = x raised to the power of y, or x multiplied by itself y times
e = 2.718....(Natural Exponential Function Base)
i = square root of -1
Circles:
Circumference = Pi*d = 2*pi*r = Tau*r
Area = Pi*r^2 = (Tau/2)*r^2
Spheres:
Surface Area = 4*Pi*r^2 = 2*Tau*r^2
Volume = (4/3)*Pi*r^3 = (2/3)*Tau*r^3
Common Angles:
30 degrees = Pi/6 radians = Tau/12 radians
45 degrees = Pi/4 radians = Tau/8 radians
60 degrees = Pi/3 radians = Tau/6 radians
90 degrees = Pi/2 radians = Tau/4 radians
180 degrees = Pi radians = Tau/2 radians
360 degrees = 2*Pi radians = Tau radians
Euler's Identity:
e^(i*pi) + 1 = 0
e^(i*Tau) - 1 = 0
Well, looking at the formulae, Tau appears in all of them and makes some calculations easier, especially the circumference of a circle and some of the common angles seem a little more intuitive. So I can see why some people would consider Tau more important. However, I still stick with Pi for traditional reasons I guess.