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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.

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T'Pau

https://static.wikia.nocookie.net/startrek/images/4/44/T%27Pau.jpg/revision/latest?cb=20081012031640

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What's that supposed to be? There's no image.

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It's a picture of T'Pau. Sorry Alien, I'm too tired right now to tackle your Pi Tau dilemma.

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It's fine.

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You know who's T'Pau, right? Spock's mother. 🤣

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Dammit, gotta watch more Star Trek!

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Well, I hope you got my pun. Tau x Pi = T'Pau

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