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Comment by fdej | Hacker News Reader

Both tau and pi are inconvenient because you often need fractional multiples like 1/6 or 3/4.

We should instead take the fundamental unit of angle measurement to be pi divided by a highly composite number, say 2 * 2 * 3 * 3 * 5 = 180. Most common angles will be then be integer multiples of this unit. Let's give this unit a name, say "degree".

One full rotation = 360 "degrees"

Half a rotation = 180 "degrees"

1/10 of a rotation = 36 "degrees"

etc.

I can't believe I'm the first person to think of this. It's so simple that even the ancient Greeks could have figured it out. I should write a full internet manifesto and try to convert the world.

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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?

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

I especially like that this conversation went full circle and back into tau.

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.

Tau is turns. They're the same thing.

Stuff like signal processing is horrible if you try and use degrees.

I'm not even sure if calculating the area of a circle is in anyway better using degrees.

Recently went through this a few times, found it here on HN:

http://jackschaedler.github.io/circles-sines-signals/

Made me realize how useless degrees are, why pi is used, etc.

What happens when you have 1/7 of a rotation? There's no one multiplier that will solve all cases.

In any case, personally I think that fractions are way better, because they tell you exactly what's what.

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