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On July 02 2011 12:48 Meta wrote:
I wholeheartedly agree that pi should be changed for the sake of mathematical clarity. Humanity got a lot of things wrong two millennia ago, and pi is one of them.
Edit: The people that disagree either haven't looked into it enough and are basing their opinion on their whims, or have never taken math higher than calculus. A = tau/2 * r^2 is mathematically elegant because the derivative is just dA/dr = C = tau * r, as opposed to C = 2*pi*r.
Edit 2: Think of how radians would be redefined! Pi = 180 degrees seems ridiculous. To go the full circle you need to go 2Pi radians. Seriously, who would possibly be against this shift? The only arguments I see are "fuck it, it's too hard." Well fuck that, mathematics should be as elegant as possible and if you disagree you clearly don't care for mathematics. Future students would see trigonometry more clearly with the redefinition and it would probably save them some grief. If clarity and elegance aren't enough reasons to merit the shift for their own sake, think of the future students.
Yet, at the same time, it would ruin such aspects in other things. For example, the integral from 0 to infinity of x^(2n)e^(-ax^2)dx = {[1*3*5*...*(2n-1)]/[2^(n+1)a^(n)]} {(pi/a)^(1/2)}. Too many formulas use both pi, and 2pi. Changing into tau just means a change in the way books are written and formulas expressed, it does nothing for the elegance of mathematics and science.
As a student training for this summer's IPhO, I can say with utmost certainty that pi is much more convenient than tau. Coulomb's law has the constant 1/(4piE) (note: the E is epsilon naught). The Maxwell distribution of speeds also has some very frustrating changes to it, specifically when integrating it to find the amount N of molecules moving between speeds v and v'.
Most of all, any problem dealing with angular quantities in physics will become infinitely more frustrating, considering that your angles will be in some multiple of tau, and the torque produced will also be denoted by tau...
Why don't we just denote the area of a circle to be pi*(d^2)/4? The controversy over this began because we use the radius instead. Pi is not to blame for being half of its counterpart, tau. We should be attacking the radius for being half of the diameter! That's sarcasm, in case it was too light. The idea is useless.
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On July 02 2011 13:44 Plexa wrote:
As a mathematician.
This is trivial.
So would you say, as easy as pi?
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Pi is God. You cant replace Pi with something else. Pi is Pi. Lol at americans thinking they are so clever. Thinking that something that has been in use for 2500 years is wrong. Please man, can we have USA get broke? We dont need the stupidity that comes from over there, spreading to all over the world.
And if you say tau = 2*pi then you still have pi. You dont get rid of pi.
One can easily think that the americans are only recognising the last 250 years of history to be important, and the rest can be discarded as monkey business.
http://library.thinkquest.org/C0110195/history/history.html
User was banned for this post.
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I think the problem is 2pi is a lot easier than doing 1/2 tau.
Multiplying is simply easier than division which is why multiplication is taught before division in schools.
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Surely this is an odd OP. From the perspective of "pure mathematics", what would it matter?
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On July 02 2011 14:28 exeexe wrote:Pi is God. You cant replace Pi with something else. Pi is Pi. Lol at americans thinking they are so clever. Thinking that something that has been in use for 2500 years is wrong. Please man, can we have USA get broke? We dont need the stupidity that comes from over there, spreading to all over the world. And if you say tau = 2*pi then you still have pi. You dont get rid of pi. One can easily think that the americans are only recognising the last 250 years of history to be important, and the rest can be discarded as monkey business. http://library.thinkquest.org/C0110195/history/history.html
Dude calm down. There are a few things you need to know.
1- This is not an american thing. It's a mathematics thing.
2- Nobody is saying that pi is wrong, they're saying that using tau may be more elegant or more handy. It's a small thing. A tiny detail, really.
3- "Thinking that something that has been in use for 2500 years is wrong." as if it was impossible is an absurdly stupid thing to say. It's not the case here because math's kind of a beautiful thing, but concepts that have been in use for 2500 years CAN be wrong. Very wrong in fact.
Don't jump the gun like that, it makes you look bad.
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On July 02 2011 14:28 exeexe wrote:Pi is God. You cant replace Pi with something else. Pi is Pi. Lol at americans thinking they are so clever. Thinking that something that has been in use for 2500 years is wrong. Please man, can we have USA get broke? We dont need the stupidity that comes from over there, spreading to all over the world. And if you say tau = 2*pi then you still have pi. You dont get rid of pi. One can easily think that the americans are only recognising the last 250 years of history to be important, and the rest can be discarded as monkey business. http://library.thinkquest.org/C0110195/history/history.html
If you'd take a moment to look through the literature on tau, most, even the most vehement zealots, aren't dismissing pi is wrong or incorrect. Their titles might be inflammatory and sensationalist, but the content doesn't quite match up. See my earlier post for a very superficial treatment on the topic and a few other posts that also deal with it. Better yet, read the original literature.
No one is getting rid of pi; this has little to do with Americans. Mathematicians are well aware of the weight of history and the importance of pi.
To dismiss an idea because it might not be the same as one that has been around for a very long time is also ignorance.
Especially when the idea really isn't different at all. Plexa is not wrong in saying that this is mathematically trivial. 
I also don't think it invalidates the question of whether tau should be taught in place of pi for general geometry.
I take it, then, that you would also declare Kant to be dismissing history as monkey business? And Schrodinger, Galileo, Copernicus and Wittgenstein?
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On July 02 2011 14:05 taldarimAltar wrote: I agree, simply multiplying pi by 2 or dividing tau to get pi is no problem, i don't think it has hardly any benefits other than simplifying some things. I grew learning w pi, and i don't think i'll use tau even if it became standard and i didn't have a pressing need to ie. job. If it ain't broken why fix it?
I agree with this, if it's confusing for you to have 2pi to you... define 2pi as tau and in your work use tau and then at the end just replace it with 2pi...
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On July 02 2011 14:08 zer0das wrote:So would you say, as easy as pi?
Hehe, that was clever.
I'm not really qualified to say anything regarding this sort of math, but I'm utterly confused after reading through the op. Good job!
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On July 02 2011 14:34 Djzapz wrote:Show nested quote +On July 02 2011 14:28 exeexe wrote:Pi is God. You cant replace Pi with something else. Pi is Pi. Lol at americans thinking they are so clever. Thinking that something that has been in use for 2500 years is wrong. Please man, can we have USA get broke? We dont need the stupidity that comes from over there, spreading to all over the world. And if you say tau = 2*pi then you still have pi. You dont get rid of pi. One can easily think that the americans are only recognising the last 250 years of history to be important, and the rest can be discarded as monkey business. http://library.thinkquest.org/C0110195/history/history.html Dude calm down. There are a few things you need to know. 1- This is not an american thing. It's a mathematics thing. 2- Nobody is saying that pi is wrong, they're saying that using tau may be more elegant or more handy. It's a small thing. A tiny detail, really. 3- " Thinking that something that has been in use for 2500 years is wrong." as if it was impossible is an absurdly stupid thing to say. It's not the case here because math's kind of a beautiful thing, but things that have been in use for 2500 years CAN be wrong. Very wrong in fact. Don't jump the gun like that, it makes you look bad.
1:
Yes it is an american thing.
OP is american and
That's the opening line of a watershed essay written in 2001 by mathematician Bob Palais of the University of Utah.
And Utah is american last time i checked.
2:
But using tau isnt more elegant or more handy. Like if you multiply something with 2 then all your problems go away? lawl, come on give me a break.
Why not use Omega which i invent here and now, and is 4*pi? That would be even better than tau i assume.. jeez
3:
No its not a bad argument. Pi was invented independently in many places on earth. Did you not read my link? Pls man, think before you speak.
The creation and acceptance of Pi is not because someone was stupid and like a politician could fool everyone. But because it has stand to the test of scientific critical analysis for 2500 years. Years with medival thinking and years with computers to really crack down on the tiniest detail of fault. Yet with all these methods it has stand the test of time.
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e^(i*tau) =1 instead of e^(i*pi) = -1. More graceful, actually
Came here to post Vi Harts video, but someone was all over that already apparently
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Thanks for the information.
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On July 02 2011 14:48 susySquark wrote:
e^(i*tau) =1 instead of e^(i*pi) = -1. More graceful, actually
Came here to post Vi Harts video, but someone was all over that already apparently
Indeed.
I already acknowledged my oversight, but I acknowledge it again as this is actually quite beautiful.
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Considering that in order to not invalidate every textbook ever made that contains a pi, students will have to be taught what pi is, if we introduce tau it'll just be used alongside of pi.
If you REALLY want to do it, say tau = 2*pi and be done with it. Use both. The beauty of algebra is that you can make symbols mean whatever the fuck you want them to mean and it still works. So as long as people know you're letting tau = 2*3.1415926... then it's cool.
As a Mathematician also, I'm with Plexa on this: it's trivial.
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I agree it's be a little more efficient, but to be honest, it's not really something worth changing. An extra or lack of a 2 every so often isn't really worth changing something that's used so often.
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On July 02 2011 14:46 exeexe wrote:Show nested quote +On July 02 2011 14:34 Djzapz wrote:On July 02 2011 14:28 exeexe wrote:Pi is God. You cant replace Pi with something else. Pi is Pi. Lol at americans thinking they are so clever. Thinking that something that has been in use for 2500 years is wrong. Please man, can we have USA get broke? We dont need the stupidity that comes from over there, spreading to all over the world. And if you say tau = 2*pi then you still have pi. You dont get rid of pi. One can easily think that the americans are only recognising the last 250 years of history to be important, and the rest can be discarded as monkey business. http://library.thinkquest.org/C0110195/history/history.html Dude calm down. There are a few things you need to know. 1- This is not an american thing. It's a mathematics thing. 2- Nobody is saying that pi is wrong, they're saying that using tau may be more elegant or more handy. It's a small thing. A tiny detail, really. 3- " Thinking that something that has been in use for 2500 years is wrong." as if it was impossible is an absurdly stupid thing to say. It's not the case here because math's kind of a beautiful thing, but things that have been in use for 2500 years CAN be wrong. Very wrong in fact. Don't jump the gun like that, it makes you look bad. 1: Yes it is an american thing. OP is american and Show nested quote +
That's the opening line of a watershed essay written in 2001 by mathematician Bob Palais of the University of Utah.
And Utah is american last time i checked. 2: But using tau isnt more elegant or more handy. Like if you multiply something with 2 then all your problems go away? lawl, come on give me a break. Why not use Omega which i invent here and now, and is 4*pi? That would be even better than tau i assume.. jeez 3: No its not a bad argument. Pi was invented independently in many places on earth. Did you not read my link? Pls man, think before you speak. The creation and acceptance of Pi is not because someone was stupid and like a politician could fool everyone. But because it has stand to the test of scientific critical analysis for 2500 years. Years with medival thinking and years with computers to really crack down on the tiniest detail of fault. Yet with all these methods it has stand the test of time.
This guy is not worth arguing with fellas (troll arguments or an idiot). This uninformed nonsense connecting a country to this or this idea of pi being a scientific discovery (vs. something purely mathematical, and obvious/necessary given our mathematical axioms).
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On July 02 2011 14:43 Picklesicle wrote:
I take it, then, that you would also declare Kant to be dismissing history as monkey business? And Schrodinger, Galileo, Copernicus and Wittgenstein?
No i mean that because americans say this and that (where this and that are stupid statements), we the europeans and people from other places could easily think that the americans have a different perspective on things. Like that only the last 250 years are important for the americans.
So if the americans would stop saying stupid things all the time, we will not think ill of the americans. Its just that.
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On July 02 2011 14:46 exeexe wrote:Show nested quote +On July 02 2011 14:34 Djzapz wrote:On July 02 2011 14:28 exeexe wrote:Pi is God. You cant replace Pi with something else. Pi is Pi. Lol at americans thinking they are so clever. Thinking that something that has been in use for 2500 years is wrong. Please man, can we have USA get broke? We dont need the stupidity that comes from over there, spreading to all over the world. And if you say tau = 2*pi then you still have pi. You dont get rid of pi. One can easily think that the americans are only recognising the last 250 years of history to be important, and the rest can be discarded as monkey business. http://library.thinkquest.org/C0110195/history/history.html Dude calm down. There are a few things you need to know. 1- This is not an american thing. It's a mathematics thing. 2- Nobody is saying that pi is wrong, they're saying that using tau may be more elegant or more handy. It's a small thing. A tiny detail, really. 3- " Thinking that something that has been in use for 2500 years is wrong." as if it was impossible is an absurdly stupid thing to say. It's not the case here because math's kind of a beautiful thing, but things that have been in use for 2500 years CAN be wrong. Very wrong in fact. Don't jump the gun like that, it makes you look bad. 1: Yes it is an american thing. OP is american and Show nested quote +
That's the opening line of a watershed essay written in 2001 by mathematician Bob Palais of the University of Utah.
And Utah is american last time i checked. 2: But using tau isnt more elegant or more handy. Like if you multiply something with 2 then all your problems go away? lawl, come on give me a break. Why not use Omega which i invent here and now, and is 4*pi? That would be even better than tau i assume.. jeez 3: No its not a bad argument. Pi was invented independently in many places on earth. Did you not read my link? Pls man, think before you speak. The creation and acceptance of Pi is not because someone was stupid and like a politician could fool everyone. But because it has stand to the test of scientific critical analysis for 2500 years. Years with medival thinking and years with computers to really crack down on the tiniest detail of fault. Yet with all these methods it has stand the test of time.
1- The idea emerges in the US. It doesn't make it an evil american thing, much less should you go on a rant about america.
2- Hence why I say it's a detail
3- You twisted a line like a bad argument. I'm sorry for pointing it out, but you made it sound like things that are 2500 year olds are obviously infallible, which isn't the case. Pi was "invented" (laughable use of the term "invented", btw) in multiple places on Earth, yes. Some early "estimates" were literally 3, and it progressively got more decimals, etc... -- but the point is, we've been getting a better understanding of mathematics.
Better. Really. Just superior.
Changing this detail wouldn't matter to me, but I think you're reacting to this in a very childish and sad way.
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I don't think it should be discarded, or else 3/14 will have no meaning for me..
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they better not change this stuff- i'm still in calculus and I dont want to have to think of converting tau/2 as actually just pi.
I mean to a degree this is "simpler" but in reality you have to teach kids tau as 2pi since all of their calculators are reading in pi. They should go to Texas Instruments if they want to really make a difference.
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EPT
