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Happy Tau Day

tauday.com

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Re: Happy Tau Day

#111

Post by mithaler »

skrebbel wrote: post #30

If mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.

I have to disagree.

I'm a programmer, but I'm not good at math. I know this. And yet, the Tau Day Manifesto explained the geometry of the circle to me more clearly and understandably than any of the math classes I've ever taken. And it's not just because it's a well-written work; the concept is genuinely simpler to understand.

Pi really is a pedagogical disaster, and tau really does help.

Re: Happy Tau Day

#112

Post by Bromskloss »

thanatropism wrote: post #99
thanatropism wrote: post #88

What's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?

Ha. I've said a lot of continental-philosophy stuff that gets downvoted by the techie culture, but this is amazing.

Just checking: Do you mean that your comment amounts to continental philosophy?

Re: Happy Tau Day

#113

Post by senorerik »

squeaky-clean wrote: post #103
gravypod wrote: post #65

Earlier quoted context omitted.

Have you watched the linked video? If not I will not be able to explain what's going on as well as the presenter. He is able to show that many common physical calculations for volume or area all relate to the same generic form. He also is able to present many other cases where pie wins out. It is very much worth a watch.

Getting a "This video does not exist." error from your link.

There is a trailing character missing,

https://www.youtube.com/watch?v=H69YH5TnNXI

Re: Happy Tau Day

#114

Post by jessriedel »

lamontcg wrote: post #102
jessriedel wrote: post #77

Earlier quoted context omitted.

You're right about the bikeshedness, but that doesn't mean there isn't a clearly better bike shed design. I also find that these sorts of inefficiencies/inelegances compound. One or two are trivial, but when you have 30 of them, suddenly the mental tax becomes noticeable. Furthermore, the cost falls mostly on the students, while the experts have already paid it and don't see the need to worry about it anymore.

Yeah, but this bikeshed got decided hundreds of years ago. Its only appealing to internet hipsters who want to brag about their organically grown free range tau. Making the next generation of math students use "2 pi" in their formulas is going to be vastly easier than literally rewriting all the books.

As a practicing physicist, I found it illuminating and non-trivially useful to know this when it was first introduced to me years ago. This is true even though I will never use in a paper, and even if I only rarely write it in my notes. In my head, 2\pi is a single character, to the point that I often write \frac{1}{2} 2\pi.

Re: Happy Tau Day

#116

Post by e12e »

jeffwass wrote: post #27
adwf wrote: post #4

Earlier quoted context omitted.

To use your own argument, 2*pi is far, far more common to encounter in physics/maths ie. real world examples, therefore minimizing friction would be using Tau ;)

So to save confusion over a mere factor of two, you're proposing devoting an entire new Greek letter to just double a constant, and requiring students to understand pi anyway to make sense of hundreds of years of mathematical and scientific corpus? It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.

Look, it's more about saying that the area of a right triangle is naturally represented (and explained) as half that of a rectangle sharing the height and width - but being divided in two equal halves by the hypotenuse.

You can argue that you're so used to right triangles that it's the square and the rectangle that should be considered special, and "twice the area" - but I don't think that makes much sense.

Pi is a useful constant, but it's chief role is in cycles/frequencies and circles. Not half-circles. It is perfectly ok to disagree - but I'm one of those people to find the concepts behind pi start making much more sense when thinking of tau as the constant, and half-tau (pi) as the special case.

Maybe it's because I always hate having logic and math concepts waved away as "that's the way it is" when there obviously is some pattern or explanation that's being hidden or lost. I'm no good at rote calculation, and with tau a lot of things that just look odd and "special" unify quite nicely.

It may very well be that for higher dimensions than two (or three) tau doesn't make much more sense than pi - but I found the "tau manifesto" examples plenty convincing.

It was easier for me to grasp, and I believe it would be a lot easier to teach.

Re: Happy Tau Day

#117

Post by Bromskloss »

kazinator wrote: post #86

Angular frequency (ω = 2πf) is related to this: https://en.wikipedia.org/wiki/Angular_frequency Note how convenient ω is when squared, in the expression of angular acceleration, eliminating a ridiculous 4 factor.

This ties into "ħ" vs. "h" as well:

E = ħω

E = hf

I don't mean this as an argument for anything; I just felt like mentioning it.

Re: Happy Tau Day

#118

Post by thanatropism »

Bromskloss wrote: post #112
thanatropism wrote: post #99

Earlier quoted context omitted.

Ha. I've said a lot of continental-philosophy stuff that gets downvoted by the techie culture, but this is amazing.

Just checking: Do you mean that your comment amounts to continental philosophy?

I'm saying this comment should be far less contentious than my comments that somehow cite Heidegger or Deleuze.

Re: Happy Tau Day

#119

Post by kerkeslager »

I'm in favor of keeping pi because of one simple equation:

   e^{i\pi} + 1 = 0
This is, IMHO, the most beautiful equation I've come across. It's concise and it relates all the most basic constants in mathematics. It's also useful, for example, for operating on the logarithm of a negative number:

    e^{i\pi} + 1 = 0
    e^{i\pi} = -1
    i\pi = \ln{-1}
    \ln{x} + i\pi = \ln{x} + \ln{-1}
    \ln{x} + i\pi = \ln{-x}
For more see Euler's Identity[1].

[1] https://en.wikipedia.org/wiki/Euler%27s_identity

Re: Happy Tau Day

#120

Post by karmakaze »

kerkeslager wrote: post #119

I'm in favor of keeping pi because of one simple equation: e^{i\pi} + 1 = 0 This is, IMHO, the most beautiful equation I've come across. It's concise and it relates all the most basic constants in mathematics. It's also useful, for example, for operating on the logarithm of a negative number: e^{i\pi} + 1 = 0 e^{i\pi} = -1 i\pi = \ln{-1} \ln{x} + i\pi = \ln{x} + \ln{-1} \ln{x} + i\pi = \ln{-x} For more see Euler's Id…

This simultaneously illustrates how e^(180') is halfway round a unit. Tau (literally/numerically?) > Pi
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