3 ms·

I think tau is really just motivated by people who like things to be "clean". You see them in all walks, wishing programming language syntax, math notation, spe

by B-Con 13y ago

I think tau is really just motivated by people who like things to be "clean". You see them in all walks, wishing programming language syntax, math notation, spelling, grammar, etc, had been chosen to be cleaner or make more sense from the beginning. I don't have a strong opinion, but from what I've seen I think tau makes the most sense. These things are fun to think about, because it requires that you think about how pi is used in mathematics and contemplate how we organize and use the concepts related to pi. It's a good brain exercise. But it's hardly worth getting into a fight over.

dajohnson89 13y ago
But how much cleaner is using tau, beyond grade-school geometry? Euler's equation is arguably the most beautiful relationship in mathematics: e^(ipi)= -1. I'm afraid tau would dirty it up. Edit: OK, e^(itau)=1, which is quite nice. :-/
- epidemian 13y ago
  Not only that. If you think about multiplying any number z by e^(ia), where a is a real number, as rotating z by a radians in the complex plane, then i think the tau version of the Euler's equation conveys a more fundamental meaning: rotating any complex number by a whole turn yields that same number, it's the same as multiplying it by the multiplicative identity (i.e. doing nothing). e^(iτ) = 1 And, as rotating something by one whole turn is the same as rotating it by any number of whole turns, you can get a nice intuitive series of equivalences that are not as pretty if you where to use pi: 1 = e^0 = e^(iτ) = e^(i2τ) = ...
  - gaze 13y ago
    Can people really not separate out a factor of 2? There's weirdness in every language. If I started SUDDENLY speaking English with a more uhh... orthogonal grammar, people would maybe get what I was thinking, but also deem me a self-righteous asshole. This is EXACTLY how mathematicians see tau. Math is no more flexible than any other widely spoken language.
    - epidemian 13y ago
      Yes, once you have learnt the basics, factoring out a 2 is trivial. But that doesn't make it right to make children that still haven't learnt that wonder "what's the angle of 3/4 turns?". One and half pi? Why? It's 3/4 tau. It should be trivial. There shouldn't need to be any conversion by a factor of 2, especially for people that are starting with that stuff (angles and trigonometry is where lots of kids get lost at maths).

by B-Con 13y ago

dajohnson89 13y ago

But how much cleaner is using tau, beyond grade-school geometry? Euler's equation is arguably the most beautiful relationship in mathematics: e^(ipi)= -1. I'm afraid tau would dirty it up. Edit: OK, e^(itau)=1, which is quite nice. :-/

epidemian 13y ago
Not only that. If you think about multiplying any number z by e^(ia), where a is a real number, as rotating z by a radians in the complex plane, then i think the tau version of the Euler's equation conveys a more fundamental meaning: rotating any complex number by a whole turn yields that same number, it's the same as multiplying it by the multiplicative identity (i.e. doing nothing). e^(iτ) = 1 And, as rotating something by one whole turn is the same as rotating it by any number of whole turns, you can get a nice intuitive series of equivalences that are not as pretty if you where to use pi: 1 = e^0 = e^(iτ) = e^(i2τ) = ...
- gaze 13y ago
  Can people really not separate out a factor of 2? There's weirdness in every language. If I started SUDDENLY speaking English with a more uhh... orthogonal grammar, people would maybe get what I was thinking, but also deem me a self-righteous asshole. This is EXACTLY how mathematicians see tau. Math is no more flexible than any other widely spoken language.
  - epidemian 13y ago
    Yes, once you have learnt the basics, factoring out a 2 is trivial. But that doesn't make it right to make children that still haven't learnt that wonder "what's the angle of 3/4 turns?". One and half pi? Why? It's 3/4 tau. It should be trivial. There shouldn't need to be any conversion by a factor of 2, especially for people that are starting with that stuff (angles and trigonometry is where lots of kids get lost at maths).