4 ms·
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 th
by 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 agoCan 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 agoYes, 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).