I don't understand when the chords come into play - I don't understand the rules.
But seems like you could generate nice, non-repeating elevator music by hooking something up to an RNG or PRNG, and never hear the same song in the elevator twice.
The earliest example I've seen of 2π is in a 1763 letter from Thomas Bayes (the paper that appeared in the Royal Society proceedings directly after the one that's famous). He used c for the circumference of a circle whose radius is unity.
If you've ever used Stirling's approximation, this is the paper that first points out that it's a divergent series.
The most compelling argument for me in using tau, (and I have started trying to think in tau when it comes up) is the radians argument: one quarter of a circle is tau/4, or pi / 8, you pick.
I am certain my kids will have an easier time remembering tau/4, as I do myself.
The other compelling thing for me came from remembering just how many integrals from 0 to 2pi I wrote over my freshman complex analysis class. A lot. Less notation is always nice; having tau represent the entire circle just makes a lot of sense!
I'm a Tauist myself, but it should be pointed out the first one is a legitimately good argument. (Local introduction of a constant is easy, though.)
I don't expect to wake up one day and everybody suddenly agrees "Yes, tau is the winner!" I expect that either things will peter out, or tau will just gradually start showing up in real papers and stuff. Unfortunately, since K-12 mathematical curricula seem to have gotten stuck in 1920, switching the "official curricula" to tau is well down on my list of things that needs to happen to K-12 math education and at the current rate even if formal mathematics did just wake up tomorrow and decide tau was the way to go, it would be at least 50 years before that penetrated back down.
I've dozens of subtle little reasons, but I think that one shows it off best and is easiest to understand.
I was going to add that zero crossings for sine waves (I am into sound synthesis) are at integer multiples of pi, but that's just a funny way of stating the above.
> The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we need to move to tau/2 and tau, only to get a pi-manifesto in a couple of decades.
The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we need to move to tau/2 and tau, only to get a pi-manifesto in a couple of decades.
I like the compromise of using Tau and its fractions when it makes sense and using a single Pi when it's not so intuitively-connected with a circle. e.g. \int_{-\infty}^{\infty} e^{−x^2} dx = \sqrt{\pi}.
If it's not broken, don't fix it. I don't see pi broken as it has been used for _centuries_. Why should we change it all of a sudden? To signify that we're into a new era? The Tau era?
Why did we move from Roman Numerals or other systems of writing down numbers, to the current numerals we use today? Simple - they make lots of things easier.
Now, no one is claiming that Tau vs. Pi is even close to the same level of importance. But it makes some things just that much easier.
The Greek letter tau is already used to refer to the period of an oscillation, the time constant of a decay interval (these are intimately related), plus plenty of other stuff. There really aren't any Greek letters left that aren't used for a million things already. tau-as-time-constant is the standard use for the thing, and the confusion with torque and natural temperature is bad enough as it is.
Yes, pi shows up as the prime counting function, but there it's a function, which clears up the otherwise ambiguous notation. Furthermore these abuses of notation are generally considered a bad thing, something we try to avoid.
As for the intuitiveness of such deep results as Stirling's formula and the even values of the Riemann zeta: this is to concern oneself with the upholstery on the Space Shuttle.
If you want a new pi symbol, might I suggest the variant pi described here: http://en.wikipedia.org/wiki/Pi_%28letter%29 -- though I'm afraid this is all a waste of time and energy.
[+] [-] imurray|14 years ago|reply
(Yes, we know that Tau doesn't really sound like anything, but this was fun and better than I expected.)
[+] [-] pavel_lishin|14 years ago|reply
But seems like you could generate nice, non-repeating elevator music by hooking something up to an RNG or PRNG, and never hear the same song in the elevator twice.
[+] [-] ignifero|14 years ago|reply
[+] [-] imurray|14 years ago|reply
If you've ever used Stirling's approximation, this is the paper that first points out that it's a divergent series.
Scan of original (it's also on JSTOR): http://www.york.ac.uk/depts/maths/histstat/letter.pdf
With modern typesetting and an explanation: http://www.stat.ucla.edu/history/letter.pdf
(I don't seriously think we should change from pi to tau.)
[+] [-] vessenes|14 years ago|reply
I am certain my kids will have an easier time remembering tau/4, as I do myself.
The other compelling thing for me came from remembering just how many integrals from 0 to 2pi I wrote over my freshman complex analysis class. A lot. Less notation is always nice; having tau represent the entire circle just makes a lot of sense!
[+] [-] jcarreiro|14 years ago|reply
I am not particularly well versed in mathematics but isn't 1/4 of a circle pi/2 radians?
[+] [-] ianterrell|14 years ago|reply
[+] [-] jerf|14 years ago|reply
I don't expect to wake up one day and everybody suddenly agrees "Yes, tau is the winner!" I expect that either things will peter out, or tau will just gradually start showing up in real papers and stuff. Unfortunately, since K-12 mathematical curricula seem to have gotten stuck in 1920, switching the "official curricula" to tau is well down on my list of things that needs to happen to K-12 math education and at the current rate even if formal mathematics did just wake up tomorrow and decide tau was the way to go, it would be at least 50 years before that penetrated back down.
[+] [-] smosher|14 years ago|reply
With 'tau' you only get the positive half (consider the integer values of x; which are 2, 4, 6 for 'tau'): http://www.wolframalpha.com/input/?i=plot+e^%28pi+*+i+*+x%29
I've dozens of subtle little reasons, but I think that one shows it off best and is easiest to understand.
I was going to add that zero crossings for sine waves (I am into sound synthesis) are at integer multiples of pi, but that's just a funny way of stating the above.
[+] [-] pavel_lishin|14 years ago|reply
> The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we need to move to tau/2 and tau, only to get a pi-manifesto in a couple of decades.
[+] [-] speckledjim|14 years ago|reply
WTF is this? I'm eagerly awaiting an explanation of what you can do with X that you can't do with 2X.
It's a moot anal point. X or 2Y, using one over the other doesn't solve anything.
[+] [-] michael_dorfman|14 years ago|reply
[+] [-] cuponthefloor|14 years ago|reply
[+] [-] J3L2404|14 years ago|reply
[+] [-] Confusion|14 years ago|reply
Previous discussions:
http://news.ycombinator.com/item?id=1468341
http://news.ycombinator.com/item?id=2322666
[+] [-] Jach|14 years ago|reply
Plus Tau Day's a fun excuse to eat two pies.
[+] [-] ianterrell|14 years ago|reply
http://www.kickstarter.com/projects/ianterrell/say-no-to-pi
[+] [-] TheOnly92|14 years ago|reply
[+] [-] edanm|14 years ago|reply
Now, no one is claiming that Tau vs. Pi is even close to the same level of importance. But it makes some things just that much easier.
[+] [-] SeanLuke|14 years ago|reply
This statement is never supported (the fan part). Bad BBC, bad!
[+] [-] scythe|14 years ago|reply
Yes, pi shows up as the prime counting function, but there it's a function, which clears up the otherwise ambiguous notation. Furthermore these abuses of notation are generally considered a bad thing, something we try to avoid.
As for the intuitiveness of such deep results as Stirling's formula and the even values of the Riemann zeta: this is to concern oneself with the upholstery on the Space Shuttle.
If you want a new pi symbol, might I suggest the variant pi described here: http://en.wikipedia.org/wiki/Pi_%28letter%29 -- though I'm afraid this is all a waste of time and energy.
[+] [-] ignifero|14 years ago|reply
[+] [-] dkastner|14 years ago|reply
[+] [-] Brashman|14 years ago|reply
[+] [-] saraid216|14 years ago|reply
[+] [-] ignifero|14 years ago|reply
[+] [-] jerrya|14 years ago|reply
[+] [-] dlat|14 years ago|reply
http://capslockday.com/