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## Trigonometry

### Course: Trigonometry>Unit 2

Lesson 11: Long live Tau

# Tau versus pi

Why Tau might be a better number to look at than Pi. Created by Sal Khan.

## Want to join the conversation?

• Tau is not very common... Pi is much more common, but why?
• Imagine you are living a few thousand years ago and people are just starting to think about maths. You pick up something round (maybe a pebble, a coin or a bread roll) and you wonder about the ratios involved. Unless the thing you picked up happened to be a wheel (with an axle and maybe spokes) you don't really have anything to encourage you think about the centre. Even if it was a wheel you probably wouldn't think the centre was the most important thing. The two things most accessible to you are the circumference and the diameter. So it makes sense that the first ratio people asked about would be pi, based on the diameter, not the radius. They didn't realise that the radius was going to turn out to be massively important. To them it probably just seemed like half the diameter.
• What numbers are e and i? Are they variables?
• Those letters are generally reserved to represent special values, in fact, two of the five most important constants in math (the others are 0, 1 and pi). The letter i is occasionally used for other purposes (as an index variable) but usually refers to the square root of -1. The letter e refers to an irrational constant (2.71828...) that is extremely important in calculus and elsewhere in math, although an explanation of where it comes from and why it's significant might be too long for a response here.
• Tau is already super over booked. Time constants, shear stress, torque, etc. How do you convert a time constant to a frequency in radians? tau=1/(tau*f)?
• Pi is even used as well for primes below a certain number. Incidentally, so are most other constants such as e (electron charge).
• poor Pi
#justiceforPi
• Exactly what I was thinking! 🥧
• Is half a circle Pi?
• Half of the circumference of a circle isn't pi, unless the radius is 1. (2pi*r = 1)
The angle formed by going halfway around the unit circle, however, is pi radians, or 180 degrees.
• My question is..How was pi made? and why is it 3.1415926534? How did someone find out this and was it computer generated or was it manually made by someone? And..Is Tau less or more than pi? Is it split in half?
• Is there any point of argument in support of this use of tau that goes beyond an appeal to aesthetics? Framing it as an either-or argument seems to be trying to shoe-horn mathematical expressions to fit our brains, instead of adapting our brains to our observations of mathematics. It's an interesting idea, to be sure, but I don't really see any deeper insights that come from it.
• You are absolutely correct. It does not matter if we use 𝜏 or 𝜋. A symbolic change is not going to change the underlying mathematics, and if anything, it would confuse a lot of people if the convention suddenly changed.
• We should also petition for June 28th to be declared Tau Day.