4 ms·
As eloquent as this manifesto is, it fails to actually address some of the arguments against tau. In 2.1, it points out that d/dx sin(x) = cos(x) only holds if
by zbanks 16y ago
As eloquent as this manifesto is, it fails to actually address some of the arguments against tau.
In 2.1, it points out that d/dx sin(x) = cos(x) only holds if x is in radians.
This is key
Once you switch to expressing x in diameterians or tau-radians (or whatever you'll call them), this identity falls apart:
d/dx sin(x) = cos(x) / 2
d^2/dx^2 sin(x) = -sin(x) / 4
...
And so on. The trig functions lose their cyclical nature.
(More explanation on wiki: http://en.wikipedia.org/wiki/Trigonometric_functions#The_significance_of_radians http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig... )
I hate to be a Debbie Downer, but you can't ignore these things.
- jacobolus 16y agoWe went over this a few days ago (also it’s described in the article, in case you missed it). You are mistaken. sin(pi) = sin(3.14...) = sin(tau/2) cos(tau) = cos(6.28...) = cos(2 pi) etc. The sin and cos functions are functions of radians, and the arclength of a radian does not change when you start expressing a circle as 1 tau instead of 2 pi.