
The Tau Manifesto - acjohnson55
http://www.tauday.com/
======
fdej
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.

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

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giech
I 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/](http://xkcd.com/1292/)

~~~
mfisher87
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.

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sunfish
I distinctly remember when I was learning geometry that there were some things
that never really made sense. Why was pi defined in terms of the diameter when
literally _everything_ else we learned about circles used the radius? Why did
radian angles feel off by a factor of 2? When I later stumbled upon the Tau
Manifesto, it felt like a lot of things fell into place. And by that time, I
had also studied calculus and had a familiarity with the kinds of things that
happen in formulas which relate lengths and areas, so the discussion of the
circle area formula resonated as well.

Despite all the cheap dismissals one sees, this feeling of "woah, that would
have actually made sense!" is a big part of what makes the Tau Manifesto
popular.

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hugs
I didn't really understand why tau was "better" than pi until I understood the
relationship to radians. Figure 8 [1] in the Tau Manifesto was the eye-opener
for me. With tau, instead of pi, I now have a more intuitive sense of how to
think in radians when doing trigonometry.

[1]: [http://www.tauday.com/tau-manifesto#fig-
tau_angles](http://www.tauday.com/tau-manifesto#fig-tau_angles)

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jackmaney
[http://www.thepimanifesto.com/](http://www.thepimanifesto.com/)

~~~
thomasahle
I like Terence's suggestion of using 2 _pi_ i as the fundamental constant.
Sqrt(pi) could also be useful given how often it appears.

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lkbm
Numberphile also has a really fun debate on Pi v. Tau:
[https://www.youtube.com/watch?v=ZPv1UV0rD8U](https://www.youtube.com/watch?v=ZPv1UV0rD8U)

~~~
thomasahle
But changing our number system to base 12 would destroy pi day!

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lkbm
Yeah, but as Vihart pointed out, Pi = a half rotation, so Pi day is in June.
:-)

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ebbv
Do we really need to do this every year? Come on.

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amalcon
This 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 dozens of completely unused
glyphs in the non-English non-Greek alphabets (Hebrew, Russian, etc).

It seems almost like a parody.

~~~
DSMan195276
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 constant
tells you that you have exactly '3 / 4' of a circle. With pi, this is less
obvious because there are '2 * pi' radians in a circle, but the 2 frequently
disappears (like in my example), which leaves you with '3 / 2 of a _half a
circle_ ', which isn't obvious how much that actually is. pi definitely _does_
have it's uses when you're talking about the diameter, but when you're talking
about something like _rad_ ians, it makes more sense to use the ratio of
circumference to _radius_ rather then circumference to diameter. If we were
using diameterians then it would make sense to use pi, since there would be
exactly pi diameterians in a circle. Having them mismatched like we do creates
a mess.

~~~
tomp
> 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...

~~~
DSMan195276
I get what you're saying, but you can say the _exact_ same thing using tau and
it's simpler:

Tau is a simple, straight line, and stretches the entire length of a circle,
starting from the x-axis in the positive x direction, and ending at the x-axis
from the negative x direction. So Tau / 2 is the amount of turning needed to
go half-way around the circle. Tau / 4 is the amount of turning needed to go a
forth of the way around the circle, IE. a right square.

Pi might seem easier or obvious to you because you've already been dealing
with it for years, but it still creates a situation that is more complex then
it needs to be. Tau creates a simpler unit-circle, because Tau uses the
_radius_ , and we're talking about _radians_. Using something that's
calculated using the diameter, when you're talking about a unit that's
measured in radius's is asking for a mess.

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cplease
e^(τi/2) = -1

Didn't think so.

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StefanKarpinski
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.

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tomp
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".

~~~
stouset
You mean a vector in the opposite direction. Clear as mud.

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bau5
Do not want.

