4 ms·

It's bugged me as well. It feels like whenever you have a unit where all your measurements contain a multiplication by a constant factor, you should just pick a

by sunfish 12y ago

It's bugged me as well. It feels like whenever you have a unit where all your measurements contain a multiplication by a constant factor, you should just pick a more convenient unit. This applies to radian measure regardless of whether one uses Pi or Tau. It's odd that the unit of radian measure is a quantity which one almost never encounters, and that the quantities one most often encounters are all transcendental (except 0), even in the most basic of situations. But instead of picking an arbitrary number like 360 or 1337 or whatever, how about we pick 1? Let's give this unit a name, say "turn". One full rotation = 1 "turn" Half a rotation = 1/2 "turn" 1/10 of a rotation = 1/10 "turn" etc. What do you think?

alecrn 12y ago
I always liked this as well, and in this case, tau is basically that unit. In fact, maybe we could think of tau as being short for "turn". One full rotation = tau Half a rotation = 1/2 tau 1/10 a rotation = 1/10 tau
- harperlee 12y ago
  I especially like that this conversation went full circle and back into tau.
sunfish 12y ago
And as a bonus, this would make sin and cos library functions easier to implement on computers. Typically, to compute sin or cos, one has approximation functions like Taylor series which work for small values, and then one reduces the input down to that small range by doing a modulus, since sin and cos are periodic. This modulus is very complex to get right in practice, and can be very slow, especially for large values. But, if we switched from radians to turns, it would be as trivial and fast as just taking the fractional part of the input, and dividing by 4 if needed. And as a further bonus, working in turns would mean that many more common quantities can be represented exactly, rather than requiring rounding as most multiples of Pi or Tau do.
- Retra 12y ago
  Tau is turns. They're the same thing.

by sunfish 12y ago

alecrn 12y ago

I always liked this as well, and in this case, tau is basically that unit. In fact, maybe we could think of tau as being short for "turn". One full rotation = tau Half a rotation = 1/2 tau 1/10 a rotation = 1/10 tau

harperlee 12y ago
I especially like that this conversation went full circle and back into tau.

sunfish 12y ago

And as a bonus, this would make sin and cos library functions easier to implement on computers. Typically, to compute sin or cos, one has approximation functions like Taylor series which work for small values, and then one reduces the input down to that small range by doing a modulus, since sin and cos are periodic. This modulus is very complex to get right in practice, and can be very slow, especially for large values. But, if we switched from radians to turns, it would be as trivial and fast as just taking the fractional part of the input, and dividing by 4 if needed. And as a further bonus, working in turns would mean that many more common quantities can be represented exactly, rather than requiring rounding as most multiples of Pi or Tau do.

Retra 12y ago
Tau is turns. They're the same thing.