e^(τi/2) = -1 Didn't think so.
Yes, which means "a half turn around the unit circle in the complex plane is -1". Try explaining that in words without saying "half" or something equivalent to it.
The Tau Manifesto
21–30 of 37 posts
Re: The Tau Manifesto
#22This is probably the most pointless math argument. Apparently, some people consider it too cumbersome or confusing to write two glyphs instead of one, and would prefer to replace the whole thing with a single glyph. The chosen glyph happens to be one of the worst possible options, because it conflicts with torque (an angular force, which frequently appears in the same calculations as pi). This despite there being doz…
I think most of your arguments are valid, especially about the choice of glyph, tau is already used a ton. However, I think there is something to be said for the fact that, by virtue of being the ratio of C/R, there are exactly tau radians in a circle. This really does simplify the math, and gives more meaning to the constants on tau vs. pi. There's more meaning from '3 * tau / 4' vs. '3 * pi / 2' because the constan…
> which leaves you with '3 / 2 of a half a circle', which isn't obvious how much that actually is
I like pi. I think it's quite obvious too, but maybe you need to stop thinking about circles and start thinking about planes or lines instead. Pi is simple, straight line, or equivalently the whole half-plane above the x axis. Pi/2 is half the turning needed to get back to the straight line, i.e. right square. And so on...
Re: The Tau Manifesto
#23e^(τi/2) = -1 Didn't think so.
Yes, which means "a half turn around the unit circle in the complex plane is -1". Try explaining that in words without saying "half" or something equivalent to it.
Opposite of 1 on the unit circle in the complex plane is -1. Pi just means "enough of a turn to get back to the straight line".
Re: The Tau Manifesto
#24I think this whole argument is silly. I really do not think one is fundamentally better than the other. Factor of 2 constants will exist no matter which one you choose. Might as well go with pau http://xkcd.com/1292/
I don't like to think about it this way. I think it's silly to go all out and insist one is always objectively "better" than the other (it's a tradeoff), but to have this discussion is illuminating. Look through the comments at how many people gained a better understanding of geometry as a whole by reading.
Re: The Tau Manifesto
#25Both 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…
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?
Re: The Tau Manifesto
#26Both 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…
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.
Re: The Tau Manifesto
#27Both 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…
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 (…
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
Re: The Tau Manifesto
#28Earlier quoted context omitted.
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 (…
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.
Re: The Tau Manifesto
#29Both 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…
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 (…
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.
Re: The Tau Manifesto
#30e^(τi/2) = -1 Didn't think so.
...
e^(τi) = 1
so still better.