For many years we have used pi as a constant in mathematics and other math-heavy disciplines such as physics. There is a movement to create a new constant with a value ~= 6.28, or 2*pi. Read this article (from http://news.yahoo.com/mathematicians-want-goodbye-pi-154001699.html ):
"I know it will be called blasphemy by some, but I believe that pi is wrong." That's the opening line of a watershed essay written in 2001 by mathematician Bob Palais of the University of Utah. In "Pi is Wrong!" Palais argued that, for thousands of years, humans have been focusing their attention and adulation on the wrong mathematical constant. Two times pi, not pi itself, is the truly sacred number of the circle, Palais contended. We should be celebrating and symbolizing the value that is equal to approximately 6.28 — the ratio of a circle's circumference to its radius — and not to the 3.14'ish ratio of its circumference to its diameter (a largely irrelevant property in geometry). Last year, Palais' followers gave the new constant, 2pi, a name: tau. Since then, the tau movement has steadily grown, with its members hoping to replace pi as it appears in textbooks and calculators with tau, the true idol of math. Yesterday — 6/28 — they even celebrated Tau Day in math events worldwide. But is pi really "wrong"? And if it is, why is tau better? The mathematicians aren't saying that pi has been wrongly calculated. Its value is still approximately 3.14, as it always was. Rather they argue that 3.14 isn't the value that matters most when it comes to circles. Palais originally argued that pi should be changed to equal 6.28 while others prefer giving that number a new name altogether. Kevin Houston, a mathematician at the University of Leeds in the U.K. who has made a YouTube video to explain all the advantages of tau over pi, said the most compelling argument for tau is that it is a much more natural number to use in the fields of math involving circles, like geometry, trigonometry and even advanced calculus. "When measuring angles, mathematicians don't use degrees, they use radians," Houston enthusiastically told Life's Little Mysteries, a sister site to LiveScience. "There are 2pi radians in a circle. This means one quarter of a circle corresponds to half of pi. That is, one quarter corresponds to a half. That's crazy. Similarly, three quarters of a circle is three halves of pi. Three quarters corresponds to three halves!" [A Real Pie Chart: America's Favorite Pies] "Let's now use tau," he continued. "One quarter of a circle is one quarter of tau. One quarter corresponds to one quarter! Isn't that sensible and easy to remember? Similarly, three quarters of a circle is three quarters of tau." Making tau equal to the full angular turn through a circle, he said, is "so easy and would prevent math, physics and engineering students from making silly errors." A better teaching tool Aside from preventing errors, as Palais put it in his article, "The opportunity to impress students with a beautiful and natural simplification has turned into an absurd exercise in memorization and dogma." Indeed, other tau advocates have said they've noticed a significant improvement in the ability of students to learn math, especially geometry and trigonometry where factors of 2pi show up the most, when the students learn with tau rather than pi. Though 2pi appears much more often in calculations than does pi by itself (in fact, mathematicians often accidentally drop or ad that extra factor of 2 in their calculations), "there is no need for pi to be eradicated," Houston said. "You might say I'm not anti-pi, I'm pro-tau. Hence, anyone could use pi when they had a calculation involving half of tau." Tau, the 19th letter of the Greek alphabet, was chosen independently as the symbol for 2pi by Michael Hartl, physicist and mathematician and author of "The Tau Manifesto," and Peter Harremoës, a Danish information theorist. In an email, Houston explained their choice: "It looks a bit like pi and is the Greek 't,' so fits well with the idea of turn. (Since tau is used in angles you can talk about one quarter turn and so on.)" Pi is too ingrained in our culture and our math to succumb to tau overnight, but the movement pushes ever onward. "Change will be incremental," Houston said.
Apparently, the ratio of the circumference of a circle to its diameter is less useful, important, and elegant than the ratio of the circumference of a circle to its radius. I was hoping to have a discussion about the pros and cons both in terms of pure mathematics, and from a perspective of different disciplines that use pi.
To give a bit of perspective as a physics dude, 2*pi comes up way more than pi in most physics that I've studied. Having a new constant, such as tau, theoretically would simplify a lot of the mathematics done when using formulas.
Some math/physics arguments I've thought to include (both for and against):
Area of a circle, instead of being pi*r^2 would be (tau/2)*r^2
e^(i*pi)=..., euler's equation, would now be e^(i*tau/2)=... I guess
Circumference of a circle would be tau*r
Simple Harmonic Motion would have a coefficient of Tau instead of 2*pi
A circle would be tau radians instead of 2*pi radians
The speed of an object going in a circle would be tau*r/T instead of 2*pi*r/T
Etc... could go on and on
What is your take? Should we make a change? Should we leave well enough alone?
I really don't see any advantage of using tau over pi, especially since pi is already engrained in our culture. I don't think pi is confusing at all (half pi = quarter circle, it's not difficult if you envision pi as a half circle) There are far more 2pi's than normal pi's in physics but the first time you are exposed to pi is geometry, where the area of a circle is pi*r^2. Teaching it as (1/2)tau*r^2 is harder than teaching 2*pi*r for circumference imo
Just use tau when it makes sense to use it (e.g., for circumference of a circle) and keep using pi when it makes sense to use pi (e.g., for area of a circle). As the article said, you don't have to be anti-pi in order to be pro-tau. We don't have to get rid of pi in order to use tau.
Its a lot simpler in most cases but I don't think it'll catch on. I mean all it really does is simplify stuff and doesn't really warrant an overhaul of mathematics.
Mathematical conventions seem unlikely to change, especially on something as arbitrary as this. I say just introduce tau's definition in early-ish mathematics and allow individuals to use it when appropriate.
In elementary geometry, when learning areas/circumference of circles and such; pi seems to have simpler formulas.
bleh, i dont see what the big deal is with tau. Yeah sure things might make "more sense" that way, but ppl have been using pi since...ever, kind of hard to change it now.
Yeah I used tau today in an RC circuit problem so that woulda messed with me if pi/tau somehow came into the problem lol... kinda like when voltage and velocity are in the same problem (railgun problems).... my v and V is hard to distinguish with my handwriting XD
As has already been pointed out, the issue is not the correctness of pi (it is correct), but the elegance of tau over pi in many cases. Adding tau to our repertoire - as has, frankly, already been done; much new literature over the past couple of decades uses tau and increasingly so - does not invalidate the use of pi where it would be more elegant and if there is anything pure mathematicians get really excited about, it's elegance.
The fact that every one of us has been raised and trained with pi makes it much more natural and easy for us to use: as a general rule, humans aren't fond of changes like that; remember the outcry over Pluto (another topic for another place)? But from an educational point of view the ease with which tau works with geometry just as described in the article in the OP is, well, elegant and intuitive. I was not one of the natural mathematicians in my group; I had to slog pretty darn hard at it to get to where I am and tau would have been more intuitive for me.
Thus, in response to the question that ends the OP, I think that making tau the norm for most of the places we now use and teach pi is absolutely a good idea. In response to the topic title, though, we will never get rid of pi. It is an important and useful tool. We still use Newtonian mechanics, don't we?
Edited out an inelegant example. Sincere thanks, JeeJee. Good catch. Dumb on my part.
On July 02 2011 11:41 Muirhead wrote: :X As a mathematician, I can say "who cares?" :D
As a mathematician-in-training, I agree. It's just a number. Who cares what constants appear in equations, they're just constants... The only reason pi is neat is because it shows up in many contexts and there's a lot of history behind it. Sure, 2pi shows up in many contexts too, but so does pi/2, and so does 1/(2pi), and so does any number of things that nobody bothers to give a special name to. Who are these mathematicians who think it's "crazy" that we say 2pi for the angle 6.283... radians? Apparently not ones who have better things to do with their time, say for example, doing actual mathematics...
On July 02 2011 11:44 GGTeMpLaR wrote: I feel like the US should make a full switch to the metric system before we consider changing pi.
lol this is probably far more important. seriously come on united states make an effort to convert! the metric system makes total sense and won't lead you to embarrassing NASA mistakes
I saw a dude's website about tau a few months ago, imho if its only for the sake of elegance and things looking pretty, then it's kind of silly to think that we would change our comfort with the symbol to change a silly 2pi to tau. If you wanna use it in your paper and be cool and original, by all means state tau=2pi. I feel like it's trying to make tau a new style, much like how hipster mathematicians will try to use it and be like "lol I was using tau way before it got popular". It's just a little dumb to me =P
edit: I hate the name of that yahoo story "mathematicians" as if half of them are aware of this so called style sweep. At my uni I have never once seen people trying to replace tau with pi, even in the courses that use it often. I still think it's the hipster mathematicians trying to make this happen.
In my opinion this comes out to be kinda like the metric system--the metric system may be better but in the US we're pretty stuck on the english system so changing now would cause a huge headache.
Also pi is the only pi, there are a couple of taus: torque, shear, or time constant.
My handwriting is bad enough and my subjects already use enough cross over symbols so please just keep pi pi.
The only reason to hold onto pi is from purely sentimental. First guy to reply said that the US still uses the imperial, but the fact that it's still used doesn't make it any less stupid, in my very correct opinion (vide http://en.wikipedia.org/wiki/Mars_Climate_Orbiter).
Tau just seems to be a better way to do things from a practical point of view.
Also, as stated in the video, e^(iTau)=1. better than e^(iPi)=-1, I'd say.
Edit: Ninja'd, gg Bactrian. but eh. still relevant.
Either way, I'm in favor of the tau movement. I mean, just for the sake of convention, call tau = 2pi and that's it. Everyone uses which one they thing it is right.
The reason I'm in favor of it is radians. I HATE radians. Tau would just make them easy to understand.
I think pi is a lot more useful. while we would have to write out 2*pi*r on some occasions, area formula, etc...(pretty much anything that doesnt involve 2*pi) pi would be better. besides, the pi symbol is freakin' awesome, and it sounds like a delicious foodstuff
I feel 2pi a million times is a lot better than tau/2 any time. The less fractions the better. Also tau is used for tons of other things, I don't see any of my dinosaur professors changing that anythime soon
As long as my ti89 can update its pi value to the one suggested, I'd care less. Otherwise, multiplying by two every single time would be really inconvenient, in addition to the fact that I might forget to do so.
Tough luck for grade school students if this change does make its way.
I wouldn't mind a new convention for 2pi so we dont have to write 2pi, but its not really a big deal especially since i finished my last college math course and should hopefully not need it in the fieldwork. :D
I don't see any large benefit in changing it. Seems like a lot of headache involved just to be able to take out the multiplication by 2 a few times. And then you'll probably be in the situation where both pi and tau will be used by different people, and some things could potentially get confused or changed in communication. If we could go back in time and have everyone start with tau instead of pi, then yeah sure I'd be all for it. But with humanity using pi for centuries, changing it is soo unnecessary.
I'm not going to consider teaching myself to forget pi. Trigonometry is already embedded into my mind in terms of pi. Plus, it's easier to write "2pi" than it is to write "tau/2" (in the cases where you would need a full rotation or half a rotation in a circle, respectively).
Pi is how many diameters needed to equal the circumference of a circle. It's awkward if we just say "tau is twice the number of diameters needed", because it's more arbitrary (and one wouldn't get why we used two circumferences instead of one until they learned "2pi" vs "1tau").
On July 02 2011 11:44 iamho wrote: Fuck no, tau has too many meanings already.
I'm also questioning why they want to use Tau. I remember using it in physics for things, which I want to say rotational acceleration or something close to that, but memory was never my strongest element. Personally I think they should just stack two pis on top of each other and call it something new. This "tau" is merely two pi so it makes more sense anyways. Then again I hate Greek letters with a passion so any opportunity to avoid them is a win.
Having learned the 20 first decimals of Pi, I'd be pretty sad to see it vanish, put I agree so much on the fact that it would make radians so much simple, and that it is way more logical. But still... I would be sad.
On July 02 2011 11:44 iamho wrote: Fuck no, tau has too many meanings already.
I'm also questioning why they want to use Tau. I remember using it in physics for things, which I want to say rotational acceleration or something close to that, but memory was never my strongest element. Personally I think they should just stack two pis on top of each other and call it something new. This "tau" is merely two pi so it makes more sense anyways. Then again I hate Greek letters with a passion so any opportunity to avoid them is a win.
The article pretty much explains it. A circle has a total measure of 2 pi radians, so proportions become complex and weird. Having 1 Tau radian instead is much more easier. Like a quarter of a circle becomes a quarter of a pau radian.
i dont know enough about mathemathics to judge if this is a good change or not
however, i think in general it would be much better to get rid of stupid stuff that people got used to
eg: non-metric system, timezones, writing dates the american way (like they did with 6/28 even in this text), qwertz keyboards, umlauts (öäü) and ß in german, similar letters in skandinavian languages and most accents in spanish italian and french, backward compatibility in computer systems, etc etc etc
also there is a lot of stuff that could easily be improved if you dont give a shit about tradition: rules for plenty of really popular sports could need improvement (football comes into mind), same for board games (chess)
simplify and optimize with no regard to tradition, if we didnt have people do that in the past (thank you napoleon) we would still be stuck with even more old baggage than we are
On July 02 2011 11:44 iamho wrote: Fuck no, tau has too many meanings already.
I'm also questioning why they want to use Tau. I remember using it in physics for things, which I want to say rotational acceleration or something close to that, but memory was never my strongest element. Personally I think they should just stack two pis on top of each other and call it something new. This "tau" is merely two pi so it makes more sense anyways. Then again I hate Greek letters with a passion so any opportunity to avoid them is a win.
The article pretty much explains it. A circle has a total measure of 2 pi radians, so proportions become complex and weird. Having 1 Tau radian instead is much more easier. Like a quarter of a circle becomes a quarter of a pau radian.
Did you even read past the first sentence? I'm questioning the word choice not the reasoning behind it.
Really good explanation of why tau is better than pi.
The greek letter looks like a T, it would confuse me like hell in my works for school :/ Else I think Tau is better.
It only looks like a T if you don't make the hat thing squiggly like a ~ lol.
BTW as far as other tau uses go, We used the symbol a lot in my abstract algebra class when studying homomorphisms, isomorphisms, galios groups, etc. Although that was be the use of our professor because he seeming to like tau and lower case sigma the most for those types of things. Oh, and I've seen it used for the golden ratio like twice ever, because phi is so popular for it instead.
On July 02 2011 11:44 iamho wrote: Fuck no, tau has too many meanings already.
I'm also questioning why they want to use Tau. I remember using it in physics for things, which I want to say rotational acceleration or something close to that, but memory was never my strongest element. Personally I think they should just stack two pis on top of each other and call it something new. This "tau" is merely two pi so it makes more sense anyways. Then again I hate Greek letters with a passion so any opportunity to avoid them is a win.
The article pretty much explains it. A circle has a total measure of 2 pi radians, so proportions become complex and weird. Having 1 Tau radian instead is much more easier. Like a quarter of a circle becomes a quarter of a pau radian.
Did you even read past the first sentence? I'm questioning the word choice not the reasoning behind it.
A factor of 2 is not a good enough reason to change an entire fucking institution. Keep pi and multiply by 2 when necessary. It's not exactly difficult to do that.
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.
Actually no, I dont. This whole debate is so utterly pointless.. if there really is such a debate people should stop immediatly. Switching from being "forced" to do Pi*2 sometimes to instead using Tau/2 seems like an extremly unimportant thing for a mathematician to consider. I mean really... is it really worth the trouble of changing a buttload of formulas in every mathbook ever realesed? I mean, who cares... really?
I personally prefer pi. I study electrical engineering, and tau comes up quiet a bit. I am sure we could use other symbols instead of tau for stuff, but I'd rather leave the confusion of changing variables to mean different things, just for the sake of convenience of 2*pi. I'm sure people who do rotational dynamics would dislike the use of tau for a "new" pi too. I always liked pi because regardless of what mathematical subject I had studied, the symbol for pi always meant pi and nothing else. You may think that isn't a big deal, just wait until you look at a semiconductors book, every 2 chapters half the symbols mean a totally different thing.
As some one who has to use trig way too much not having to type 2pi every time would make it a lil nicer. However not many people actually care about the circles so it would only really help people in grade school learning trig. Honestly though, I would love this change.
Edit: ya don't call it tau though, use that shit in elec. >.<
who cares? you can use tau if you want you could call it bob for all i care just start off all your shit by declaring that bob = 2pi As long as it make sense it makes sense w.e is easier for you to visualize that's fine all this is is a constant so if it's 2pi or tau or bob i'm treating it like a constant. This is just nit picking something imo.
I've had this thought a long time ago when taking quantum mechanics because I got annoyed at having to constantly carry around 2*\pi all the time. I think it's a fairly good idea, but I don't think it's worth all the hassle of trying to everyone to convert. Also doing it by way of introducing a new variable, e.g. \tau, is a terrible idea. I already have a hard time coming up with a variable in physics, I don't think they need to add the confusion of removing another possible variable. Especially \tau, it comes up way too often as some sort of time related variable.
My main concern would be with Euler's identity, but I generally do feel that 2pi may be more fundamental than pi. Overall, I don't really feel too strongly either way.
These are reasonable arguments for why tau is better, if you had to wipe the slate clean and choose new conventions for everything. But in this case pi has historical value and it would be detrimental to try to change it and have a mess of notation/conflicts with past books, papers, etc.
On July 02 2011 13:15 Maliris wrote: If they want to change this, they should use a different letter/symbol instead of Tau which isn't already being used by other things
Might I propose the symbol, "donut", which is a small circle within a bigger circle?
On July 02 2011 13:15 Maliris wrote: If they want to change this, they should use a different letter/symbol instead of Tau which isn't already being used by other things
Might I propose the symbol, "donut", which is a small circle within a bigger circle?
We could call it the Torus! Even though doughnut is far more delicious. But I think its still more trouble than its worth. A more useful thing would be to add more symbols to mathematics, the Greeks just didn't make enough.
What is this? Does we need to discuss something superficial like that? for me it's just looks like a change for the sake of change, i think this guy should go work in fashion model if he likes making pointless changes.
Like other people said it, why he doesn't talk about real needed changes like metric system in US?
BASE 8 before TAU!!!!! AND METRIC!!! haha, I doubt people will ever change, just like we will probably never have a universal language, people do not like to switch what they already love.
It's really a debate over which is easier, multiplying by 2 or dividing by 2. If we keep using pi, area = pi(r)^2 and circumference will be 2pi(r). If we use tau, area is (tau/2)r^2 and circumference is tau(r). Which is the prettier set?
On July 02 2011 12:57 RezChi wrote: Keep pi as it is... it's going to be a huge hassle re-writing textbooks and changing peoples knowledge of pi to "tau" ~_~
I'm sorry, but this is an awful reason to not change to tau as the standard. I'm not intentionally singling you out as many people have made this exact same statement, it's just that under sheer weight of volume yours was the one that tipped me into actually bothering to respond.
Textbooks are rewritten and updated relatively frequently to reflect the fact that new things are discovered and old things are being changed. Additionally, priorities for what is or is not critical to be taught at different levels also changes over time and is frequently being reviewed. It isn't being suggested that the mathematics education change *right now*, but that it should be a standard that is phased in as a replacement for pi *as a standard*.
Pi isn't going away; see my and other earlier posts as well as the some others not on this site. Also look to some of the popular articles on it, let alone some of the less-mainstream literature.
Rather, introducing tau into mainstream education could make a lot of geometry and complex more intuitive. There are certainly instances in which pi works better; no one is denying that, and it could be a mistake to try and make tau a standard for many of the functions of pi. I don't think it is, but I have no issue with being proved wrong.
The tau-proponents have, in many instances, done an awful job of arguing their case. Or at least, the awful jobs are getting a lot of attention. The "No, really, pi is wrong" article (which is responded to more frequently than the article it references) relies on a sensationalist title and a some important looking functions (okay, they are really important, just not really for the purposes of the article!) to drive home the point that... there's really nothing wrong with pi, tau is just more elegant in many geometric functions, which is where pi originated. The weakness of their arguments doesn't mean their conclusion is wrong, any more than the weakness of your argument means that your conclusion is wrong.
But your argument given above has the frightening corollary: if it isn't earth-shattering, and might take just a bit of work, why bother teaching it? I sincerely hope I, and in fact most others, have brought better to the table for ours students than that. I sincerely hope that most people have a desire to learn and adapt that goes beyond this.
Since I learned the way how the number Pi was found in the first place in school, I think it is a good number because there is a logical way how it was created. If pupils learn that, they'll understand it much better than Tau.
And I think that pupils will always have to know pi. Introducing just another symbol replacing 2pi is just even more confusing!
The use of tau simplifies a lot of other things that use 2pi. So because of this one example you've found, you want to just stick with that? edit - that equation is part of the Gaussian distribution, which uses 2pi, so there you go.
You could argue it's pretty trivial like plexa did just above, but I guess it really depends on what you find important in mathematics. If you're one for elegance and funadementality (if that's a word) then you'd probably want to go with tau.
If you're one for the imperial system because you think your car drives farther when it uses gallons of petrol rather than litres, then you'd be one for pi I'd assume.
I was kidding as it's the one thing I can think of, don't hurt me please.
On July 02 2011 13:44 Plexa wrote: As a mathematician. This is trivial.
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?
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.
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.
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.
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.
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.
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?
On July 02 2011 13:44 Plexa wrote: As a mathematician. This is trivial.
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...
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.
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
I'm gonna go out on a limb and guess that those mathematicians who are for this change tend to be applied mathematicians >_>.
Really though, I can't see this actually happening, only because mathematicians have a tendency to use notation they're comfortable with and not give a shit. For example, you'll see sup and lub both used to denote the least upper bound of a set, or perhaps one professor will use dy/dx to denote a derivative as opposed to f'. Yes, some groups of mathematicians have a tendency to prefer one symbol over another (the two real analysis texts I've used have utilized f' and one went so far as to call the leibnizian notation barbaric), but it's really just preference.
Anyway, that's my beer-induced opinion on the matter.
On July 02 2011 11:41 Muirhead wrote: :X As a mathematician, I can say "who cares?" :D
Don't most mathematicians value mathematical elegance? Isnt tau more elegant than 2pi?
Mathematical elegance isn't quite "hey, this equation looks pretty!" The quality of mathematical elegance has more to do with proofs. For example, Cantor's diagonal method is a very elegant way to prove that the set of reals is uncountable (as opposed to the other methods he published).
Changing this detail wouldn't matter to me, but I think you're reacting to this in a very childish and sad way.
I think the americans are reacting to this in a very childish and sad way.
Our understanding of mathematics, today, is better and superior to what it was a thousand years ago. Not sure what your question implies, this is obvious.
And "the Americans" aren't reacting in a very childish way. It was brought up and it's being considered while some brilliant folks from Denmark (well, just you) are just throwing it out without giving it thought!
On July 02 2011 15:00 MrBludgeon wrote: I'm gonna go out on a limb and guess that those mathematicians who are for this change tend to be applied mathematicians >_>.
Really though, I can't see this actually happening, only because mathematicians have a tendency to use notation they're comfortable with and not give a shit. For example, you'll see sup and lub both used to denote the least upper bound of a set, or perhaps one professor will use dy/dx to denote a derivative as opposed to f'. Yes, some groups of mathematicians have a tendency to prefer one symbol over another (the two real analysis texts I've used have utilized f' and one went so far as to call the leibnizian notation barbaric), but it's really just preference.
Anyway, that's my beer-induced opinion on the matter.
Heheheh.
Recently, a colleague declared a grant proposal of mine to be "fit only for Philistines and swine!".
You may be on to something. As much as I might wish otherwise, I'm ultimately an applied mathematician. Incidentally, your description of mathematical elegance further down is, well, elegant.
On July 02 2011 15:09 Boblion wrote: I think it is quite funny that an American mathematician want to get rid of pi when they are still using their own customary units system.
Taus and inches are the future !
haha yeah and Guam may capsize
Its very bad, and we need to have more gallons of water on the lightweighted end of the island!
It's ridiculous imo, would be one thing if it was squared or such. 2pi is just about as easy to write down as tau. Seems to me like a mathematician has nothing of worth to put out so he's campainging for pointless crap like this.
Not to mention changing the value of pi in scientific papers world wide is only going to be a pain. And the use of tau is a complication in itself in every kind of engineering field since it's usually reserved for circuit constants and so on.
On July 02 2011 11:41 Muirhead wrote: :X As a mathematician, I can say "who cares?" :D
Don't most mathematicians value mathematical elegance? Isnt tau more elegant than 2pi?
No. elegance is not important. What is important is that the left side equals to the right side
1+1=2 2=2 x=x
etc
Wether it is written on a discarded candy wrapper or on an advanced computer with 2ghz of processing power, doesnt change the value of elegance.
No tau and pi is equal elegant, but it really doesnt matter anything.
Actually, elegance is quite important. An elegant solution is valued far more highly than an inelegant one. See MrBludgeon's post for a nice description.
Whether tau is more elegant than pi can be debated (or not, depending on your point of view and level of vehemence), but that isn't what you are saying.
Besides a pure aesthetic beauty to it, there are practical reasons to value elegance in mathematics. Elegant proofs and solutions are almost always simple and easy to check and understand. This same [relative] simplicity means that they can [more] easily be used elsewhere or corollaries [more] readily seen and extrapolated. And that's just the beginning of it.
Atheist Math Teachers Will Force Your Children to Learn “Irrational” Numbers
Cool Tom Kimbo
God is great. His reasoning is beyond that of yours or mine, and all of His creation is without flaw. Everything He makes, He makes for a reason, and nothing He makes is lacking in order or clarity.
But we are living in dark days. Heathen scientists have invented their own language to talk to each other and work to dismantle our Christian nation. They speak in hushed tones of numbers that go on forever, ever-twisting and changing like so many serpents. Atheist math teachers call these “irrational numbers,” a perfect name for a foolish sinful concept that denies God and reason. Atheists will tell you these numbers are “everywhere.” They are nowhere but in sinful heathen scientist’s minds.
Public schools are dens of sin where gothemo girls will try to rub their milk sacs all over your son. But advances from titful harlots are not the only dangers–even the teachers in public schools try to force sin on the young. The fabricated devil science of “evolution” has long been recognized by Christians as Satanic, but irrational numbers are equally as unholy, and children have been forced to learn them as “fact” for years.
The most popular “irrational number” is pi, or the circumference of a circle divided by its diameter. Atheists claim that pi is equal to 3.14159265… and on and on and never stopping even though your good Christian mind knows that it must stop at some point. But is this really the correct value for pi? Let’s consult the Bible, looking at a passage where Huram constructs a circular pool for King Solomon:
He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it. –1 Kings 7:23 Any child with a calculator or simple math skills can tell you that 30 cubits divided by 10 cubits–circumference divided by diameter–is 3. Pi is equal to 3. And yet atheist sin scientists continue to believe their made-up lies about devil-worshipping forever-numbers!
PI IS EQUAL TO THREE YOU HOMOPROMOTING DEVIL EVOLUTION SCIENTISTS!!!
To support their “theories,” math sinners have even come up with a host of other completely made-up irrational numbers, such as e and i, which are not numbers, they are letters. Moreover, they are two of the letters in the word “devil,” which is certainly not a coincidence. Neither is it a coincidence that the two letters in “pi,” “p” and “i,” are the two most important letters in “penis.” Homo math teachers want to touch your child’s penis and they are barely even being subtle about it.
The only solution to all of this math and science sin is to pull your child out of evil government school and teach him at home. Public school will teach your baby evolution lies and it will also teach them that God is not rational. Pi equals three and there is no argument to be made against it. Home school your children, and write your Senator to demand we stop funding the Chinese lies that are taught in our classrooms.
Hehe, joke reason to get rid of pi.
Edit: rereading the article I can't tell if he's joking or really actually that stupid.
Anyway, I always did pi*d instead of 2pi*r. And calculating radians would be much easier.
choosing tau is probably not a good idea, it is already taken up by other concepts. eg. tau pathologies in Alzheimer's disease.
And it would be interesting for mathematicians to actually have to relearn stuff like every other profession once in a while.
As a mathematician I don't care which one gets used, they both have advantages and disadvantages.
But I take offense to the use of both Tau and Pi as put forward by some people in-thread and briefly in that article. No, we don't need two Greek letters used up for two constants which are multiples of 2 from each other. h and h-bar in physics is bad enough!
I already write 2*pi*hbar instead of just writing h most of the time....
If people want to introduce tau as a standard constant with the value of 2*pi I see nothing wrong with that. I very highly doubt that pi will disappear. But like Planck's constant I see no harm in having two different "versions" of pi available for when one makes notation simpler than the other.
If the new Pi is more accurate then we should definitely be migrating to it in the long run would it not be better to have a more accurate representation?
On July 02 2011 15:41 Drium wrote: Why does it matter? The number is the same if you write it as tau or 2pi.
in fact it doesn't matter at all, but if i was a bad mouth i would call this guy an attention *biiiip* who have nothing important to say in mathematics because he is an average guy in his field. To sum up, it is as important as the wise statement "which seat can i take" from rebecca black, our modern philosopher.
On July 02 2011 15:49 Nazarid wrote: If the new Pi is more accurate then we should definitely be migrating to it in the long run would it not be better to have a more accurate representation?
It's not more accurate in any way. It just changes the way things are expressed, but ultimately they mean the exact same thing
On July 02 2011 15:00 MrBludgeon wrote: I'm gonna go out on a limb and guess that those mathematicians who are for this change tend to be applied mathematicians >_>.
Really though, I can't see this actually happening, only because mathematicians have a tendency to use notation they're comfortable with and not give a shit. For example, you'll see sup and lub both used to denote the least upper bound of a set, or perhaps one professor will use dy/dx to denote a derivative as opposed to f'. Yes, some groups of mathematicians have a tendency to prefer one symbol over another (the two real analysis texts I've used have utilized f' and one went so far as to call the leibnizian notation barbaric), but it's really just preference.
Anyway, that's my beer-induced opinion on the matter.
Heheheh.
Recently, a colleague declared a grant proposal of mine to be "fit only for Philistines and swine!".
You may be on to something. As much as I might wish otherwise, I'm ultimately an applied mathematician. Incidentally, your description of mathematical elegance further down is, well, elegant.
Cheers. (I still stand by my opinion, though )
Wow, that actually makes math sound a bit like art. Really interesting.
The move to tau should be seen as a stylistic proposition, not a questioning of efficiency. How has this thread lasted 8 pages? That is more a interesting discussion, I think...
On July 02 2011 15:41 Drium wrote: Why does it matter? The number is the same if you write it as tau or 2pi.
in fact it doesn't matter at all, but if i was a bad mouth i would call this guy an attention *biiiip* who have nothing important to say in mathematics because he is an average guy in his field. To sum up, it is as important as the wise statement "which seat can i take" from rebecca black, our modern philosopher.
All right, so this has come up twice now so I'm going to address it. Let's be fair: Palais actually has pretty decent publications under his belt and has made some pretty decent contributions to the field of computational medicine and biochemistry.
Sure, a lot of his pure mathematics work has to do with small tweaks on the way we look at some fairly established things but we can't all be Erdos or Euler and a large body of global published work will fall into this category.
On July 02 2011 15:41 Drium wrote: Why does it matter? The number is the same if you write it as tau or 2pi.
in fact it doesn't matter at all, but if i was a bad mouth i would call this guy an attention *biiiip* who have nothing important to say in mathematics because he is an average guy in his field. To sum up, it is as important as the wise statement "which seat can i take" from rebecca black, our modern philosopher.
All right, so this has come up twice now so I'm going to address it. Let's be fair: Palais actually has pretty decent publications under his belt and has made some pretty decent contributions to the field of computational medicine and biochemistry.
Sure, a lot of his pure mathematics work has to do with small tweaks on the way we look at some fairly established things but we can't all be Erdos or Euler and a large body of global published work will fall into this category.
Yeah that's what i'm saying, he is average. I didn't say he is bad, i just think he is gathering too much attention with such a pointless subject. If he doesn't like pi, he can use tau in his work and don't brag about it because seriously all the real mathematicians don't care at all about his tau, they have more important things to do.
You won't see Perelman (lol) or Tao speak about something pointless like that.
Do not want! Tau is already used for period of oscillation, torque, proper time, a certain lepton, and "temperature" in statistical mechanics. Pi is used for... a pion?
This is unnecessary. Physicians already replace stuff like 2*pi or much more complex stuff with just 1. Introduces more fractions which generally are uglier than products.
But most importantly: 6(.28...) is such a huge number, wtf.
I'm not just being a smartass. I dunno about you guys, but I literally just think about everything in terms of 2pi's already, because... duh? Give it a special name if you want.
Also, don't fuck up euler's identity, seriously man.
On July 02 2011 11:41 Muirhead wrote: :X As a mathematician, I can say "who cares?" :D
Don't most mathematicians value mathematical elegance? Isnt tau more elegant than 2pi?
That's like saying 2 is more elegant than 4, they are both more than elegant enough. Pi is a number, 2pi is a number. If you use 2pi a lot in one of your mathematical texts and you are too lazy to write the 2 (which isn't that rare ), just define tau = 2pi at the start and use tau if you like to.
I'm not just being a smartass. I dunno about you guys, but I literally just think about everything in terms of 2pi's already, because... duh? Give it a special name if you want.
Also, don't fuck up euler's identity, seriously man.
Euler's identity is better when you use tau.
e^(i*tau) = 1
no, you couldn't conclude e^(i pi) = -1 from this one, it could be e^(i pi) = 1.
I agree with most others that there is no need to use Tau instead of Pi. That said, I dislike the argument "we should use Pi because that's what we've been doing all along". In my opinion people should be able to use either one. I can understand that in several ways, using Tau is more 'natural' than using Pi.
It will be inconvenient to have standard angles of Tau/12 and Tau/8 though...
I think that it is more natural to learn pi since it is raiser to deal with diameter when learning about circumference. However, it is possible to change, as Planck's constant has shown us.
Use tau when tau is necessary, use pi when pi is necessary. Seems like the best idea to me. Besides, they have a point. 2pi comes up far more often... Hbar for example. Much easier to call it h/tau instead of h/2pi
I'm not just being a smartass. I dunno about you guys, but I literally just think about everything in terms of 2pi's already, because... duh? Give it a special name if you want.
Also, don't fuck up euler's identity, seriously man.
Euler's identity is better when you use tau.
e^(i*tau) = 1
no, you couldn't conclude e^(i pi) = -1 from this one, it could be e^(i pi) = 1.
Nobody is trying to redefine pi in this thread, they're trying to say that 2pi is more elegant/natural/fundamental/whatever than pi; so much so that this new constant deserves it's own name, tau.
I mean that the elegance of e^(i pi) = -1 is a bit lost in e^(i tau) = 1, of course it's still true but it isn't as obvious, while e^(i pi) = -1 instantly implies e^(i tau) = 1 (by squaring)
I read a german article about this "revolution" and hoped it is an idea of a german busybody, and now I hear it's a worldwide movement?
Seriously, who cares? If a factor of 2 troubles you, maybe you shouldn't dabble in mathematics. This change in nomenclature would produce misunderstandings for years to come, it's just not worth it for some insignificant advantages.
On July 02 2011 13:12 dangots0ul wrote: Why must it be one of the other. Pi may be more tradition but Tau may be more practical. It doesn't hurt to have both, no?
It hurts a lot to have both actually, much more than a factor of 2 ever could.
On July 02 2011 11:44 GGTeMpLaR wrote: I feel like the US should make a full switch to the metric system before we consider changing pi.
I don't get what the big deal about the metric system is. Because everyone else uses it? If so then how about people stop speaking any language other than Chinese, Spanish and English, because those are the top 3 languages spoken in the world (in terms of native speakers.)
And the fields that matter (science/military) use international units anyways.
If there could be both the Planck constant (h) and Dirac constant (h/2pi), there could be a constant that means 2pi along pi, I don't have anything against it. That said, I'd never use it.
I think the thread title is a bit misleading because you don't really get rid of pi as the number stays the same. You just replace the general definitions with tau to make it more intuitive.
How would having tau and pi hurt anything? Surely they could co-exist peacefully?
On July 02 2011 18:24 Schnake wrote: I think the thread title is a bit misleading because you don't really get rid of pi as the number stays the same. You just replace the general definitions with tau to make it more intuitive.
How would having tau and pi hurt anything? Surely they could co-exist peacefully?
Making 2 constants out of one is incredibly inefficient.
The thread title is indeed misleading. The introduction of a tau constant doesn't need to entail getting rid of the definition of pi. People who are used to pi use pi and tau could be used to teach younger generations. I doubt converting tau to pi would be so difficult to those who have learned to use pi.
Palais' idea of changing the definition of pi itself would be terrible though. =P
This will never catch on, pi is fine the way it is.
As an engineer I use pi divided and multiplied by a lot of numbers. To be honest i'd rather use pi/4 and 4pi than pi/8 en 2pi. If you wanna 'balance' pi you should prepare for gathering a lot of statistics.
Changing all the notebooks, people will get irritated, not worth it.
On July 02 2011 19:51 theSkareqro wrote: I study chemical engineering and tau represents something already in a formula. Its gonna be confusing as hell if it catches on.
Pi is used as symbols in formulas as well. As a physicist I think this change makes a lot of sense. If nothing else, then just because plancks constant/reduced would be a lot easier to remember. If it helps people understand the basic math better for some then by all means. The biggest effect for anyone with an understanding beyond basic geometry/trigonometry, would be having to write less on blackboards, on computers and so on.
On July 02 2011 11:45 micronesia wrote: Yeah I used tau today in an RC circuit problem so that woulda messed with me if pi/tau somehow came into the problem lol... kinda like when voltage and velocity are in the same problem (railgun problems).... my v and V is hard to distinguish with my handwriting XD
Hm, pi is used with permutations and chemical bonds, but the other pi probably isn't very common in the same context. As to your second problem, just use U, like we do :O
But I think that switching to Tyler's 120-min hours should be higher in priority that this.
If we switched over from Pi to Tau, it would mess up everyone in school who already had learned formulas with Pi and would make their lives a whole lot harder having to rememorize said formulas
On July 02 2011 20:24 hifriend wrote: lmao my math professor used to go on and on about tau and how it's superior to pi
is there any reason we can't use both?
Do you remember the Mars Climate Orbiter? Using different conventions can lead to misunderstandings, I think many people here don't even realize what the consequences of such a decision could be. And all of that over something so trivial?
On July 02 2011 20:24 hifriend wrote: lmao my math professor used to go on and on about tau and how it's superior to pi
is there any reason we can't use both?
Well it essentially becomes redundant, to force kids to learn about two irrational numbers and many new formulas when one number is just double the other... since many formulas don't just become 2* the other formula anymore.
I'm a math education guy, and I'm fine with sticking with pi. I've read the arguments for tau. Some are pretty cool, but not enough to make me a proponent for the change.
I personally think it's a dumb idea. If anyone is convinced about its profits, so be it, but I really doubt the benefits of the change will compensate for the sheer effort behind a possible change.
On July 02 2011 20:37 Klipsys wrote: Why not just use both? Really that hard to have 1 more important formula?
I believe quite recently we had a mars rover landing crash because some people did the math in feet but then programed the landing in meters.
Well that's just absurd, and if that's a NASA blunder I'm ashamed for my country lol. Seriously thought, getting rid of pi just feels wrong. I can understand the importance of accepting new information and implementing it correctly, but to disregard something as massive as pi seems foolish.
On July 02 2011 20:50 hns wrote: I personally think it's a dumb idea. If anyone is convinced about its profits, so be it, but I really doubt the benefits of the change will compensate for the sheer effort behind a possible change.
This is think is the wrong approach, there's no real way to determine how a change could effect anything.
This feels incredibly unnecessary. The value is just 2pi instead of pi so the change wouldn't mean something huge like using degrees or radians. Seems to me like the mathematicians are doing this for publicity or something.
On July 02 2011 21:14 Casta wrote: Keep pi as it is because of the history behind it.
If you really are annoyed just define 2pi as tau, do the calculations and then go back to 2pi in the result.
Btw im a math guy.
Couldn't you make that argument for the SI system as well? (Or any changes to conventions in math, really). It seems like a really conservative approach.
360 degrees equaling 1 tau radians makes a lot more sense, but its way too much work to try and change the system that the whole world uses and, as many have said, it could be put to more use by getting the whole world to use metric.
On July 02 2011 20:50 hns wrote: I personally think it's a dumb idea. If anyone is convinced about its profits, so be it, but I really doubt the benefits of the change will compensate for the sheer effort behind a possible change.
This is think is the wrong approach, there's no real way to determine how a change could effect anything.
Well, the change in fact does not change anything fundamentally. It's not like this will make us able to obtain new theorems or proofs or whatever which we couldn't find before. This is simply a more or less cosmetic change aimed at better understandability or intuition.
On July 02 2011 21:38 Eufouria wrote: 360 degrees equaling 1 tau radians makes a lot more sense, but its way too much work to try and change the system that the whole world uses and, as many have said, it could be put to more use by getting the whole world to use metric.
360° corresponding to 1 tau has a certain appeal I must admit, yet the area of the unit circle being tau/2 instead of pi just gives me the creeps.. :o
On July 02 2011 20:24 hifriend wrote: lmao my math professor used to go on and on about tau and how it's superior to pi
is there any reason we can't use both?
Well it essentially becomes redundant, to force kids to learn about two irrational numbers and many new formulas when one number is just double the other... since many formulas don't just become 2* the other formula anymore.
I'm a math education guy, and I'm fine with sticking with pi. I've read the arguments for tau. Some are pretty cool, but not enough to make me a proponent for the change.
He's right Tau > Pi because tau=2pi and 2pi>Pi .
Pi and Tau are dumb anyway. I'm a Sigma guy myself (S=3pi).
1) There aren't enough variables, with all of the greek and english alphabet we still have an ungodly amount of overlap taking away another one is not good. For the record lowercase pi is reserved for the most part, I don't think I've ever seen anyone use it as a variable, same with lowercase e.
2) Yes this simplifies radians but to say that it simplifies geometry is dumb. It may simplify some equations but certainly not all. circumference = tau*r, circumference = 2*pi*r yep that one becomes slightly easier area=tau/2*r^2, area = pi*r^2 and that one becomes more cumbersome
i think most of u miss the point that this is not to make some equations more simple because u dont have to divide by two, but to make a lot more sense when teaching it to kids, which i'd appreciate since i always hated the fact that 99% of people hate math and think it's some super complicated non-understandable magical thing ;P to those who understand it anyways it wont matter what constants they use
On July 02 2011 19:51 theSkareqro wrote: I study chemical engineering and tau represents something already in a formula. Its gonna be confusing as hell if it catches on.
Pi is used as symbols in formulas as well. As a physicist I think this change makes a lot of sense. If nothing else, then just because plancks constant/reduced would be a lot easier to remember. If it helps people understand the basic math better for some then by all means. The biggest effect for anyone with an understanding beyond basic geometry/trigonometry, would be having to write less on blackboards, on computers and so on.
Which ones? I've seen Pi before but never pi, that one is treated sacred as best I can tell.
On July 02 2011 19:51 theSkareqro wrote: I study chemical engineering and tau represents something already in a formula. Its gonna be confusing as hell if it catches on.
Pi is used as symbols in formulas as well. As a physicist I think this change makes a lot of sense. If nothing else, then just because plancks constant/reduced would be a lot easier to remember. If it helps people understand the basic math better for some then by all means. The biggest effect for anyone with an understanding beyond basic geometry/trigonometry, would be having to write less on blackboards, on computers and so on.
Which ones? I've seen Pi before but never pi, that one is treated sacred as best I can tell.
I'm positive I've encountered it somewhere, though the specific situation eludes me. But my point was that just because a greek symbol is used in a formula somewhere does not make it universally sacred. (And technically I did write Pi and not pi. =b )
Sadly, lesser educated people who read that some want to get "rid" of pi think they want actually get rid of pi or change the value of pi.
Using pi or a constant with a value of 2 times pi is virtually the same. No-one gets rid of pi if tau would be used. It's the same, just scaled by two.
I personally never liked that a full period is "2 pi" for example. Why two? With a constant of a value of 2 pi, it would be easier.
The OP should make a poll so we can get a general idea of what people think without surfing through these pages, though I'm pretty sure most of us share the same view.
I think that it's too late to do the change, and it's not that big of a deal anyway.
Euler's identity (e^(pi*i) = -1) and the area of a circle/sphere are really the best arguments against. And the fact is that area is a lot more useful in actual problems. Pi is fine.
The area of a circle for tau would be tau/2 * r^2 instead of pi * r^2. That's plenty ugly.
Additionally, any angle above pi is larger than 180 degrees, or improper angles which could be simplified down.
There is absolutely no reason is care enough to change. I don't see how it's any simpler to learn when you're younger.
I personally never liked that a full period is "2 pi" for example. Why two? With a constant of a value of 2 pi, it would be easier.
But if you actually look at a curve (which is how it is taught), it makes perfect sense. It goes up and comes down at pi, and then goes down and up at 2*pi. So right now the zeroes of a sine curve are at k*pi. Changing one part for simplicity will make other parts uglier.
Plain stupid. Edit: We should also change the time, because I don't think 24 hours is enough for one day. Instead we should have "zours" and the day would have 48 zours. Would be great.
I'm not a mathematical guru, but i had to endure quite a lot of mathematics in my studies and i think that everything in mathematics should be explained and proved as simple as possible. By that i mean that there should be a clear "meaning" of every part of formula. So i kinda like this. It really makes sense, if you look at the video post by someone in first page. I bet there can be found a lot of counter examples, though, where it would make more "sense" to use you Pi. So its a tough one. Interesting brain teaser though ^_^
Hey, i thought of it 5 years ago. i was solving some problems and then i thought "why do i have to write 2*pi*R? why isnt pi twice bigger, it would make so much sense". But then I had to find area of a circle and pi suddenly made sense.
On July 02 2011 22:40 DoubleReed wrote: Euler's identity (e^(pi*i) = -1) and the area of a circle/sphere are really the best arguments against. And the fact is that area is a lot more useful in actual problems. Pi is fine.
The area of a circle for tau would be tau/2 * r^2 instead of pi * r^2. That's plenty ugly.
Additionally, any angle above pi is larger than 180 degrees, or improper angles which could be simplified down.
There is absolutely no reason is care enough to change. I don't see how it's any simpler to learn when you're younger.
No. Euler's identity becomes even more elegant with Tau ( e^(i*Tau) = 1), which also neatly highlights the geometric interpretation of the formula (That one TURN in the complex plane takes you around in a circle and back to the same place).
Also, lets look at some common quadratic forms that pop up in physics:
*The distance a body falls in earth's gravitational field is (1/2)gt^2 *The energy stored in spring is (1/2)kx^2 *The kinetic energy of a body is (1/2)mv^2
On July 02 2011 21:14 Casta wrote: Keep pi as it is because of the history behind it.
If you really are annoyed just define 2pi as tau, do the calculations and then go back to 2pi in the result.
Btw im a math guy.
Couldn't you make that argument for the SI system as well? (Or any changes to conventions in math, really). It seems like a really conservative approach.
Well mathematics is very conservative.
If you want to change something already defined or proven in the world of mathematics you better have a very good reason backed up by solid logic and proof. This reason seems too small and only really comes down to the oppinion of the person doing the calculations. That said if you want to use tau instead nothing is stopping you, but I think it will never ever replace pi entirely, it will always just be known as 2pi.
While I agree with the "pro-tau" arguments in this thread, I would like to highlight to you all again the difficulties involved in switching. π has been used for centuries in every other mathematical/physical paper. You cannot simply change that because another constant is better suited for the task (which I also think it is).
Also, it would actually be harder to learn, because we would need to explain to future generations why π actually existed in the first place, and they would have to keep two different constants (just by a factor of 2) in their heads all the time.
On July 02 2011 23:29 KharadBanar wrote: While I agree with the "pro-tau" arguments in this thread, I would like to highlight to you all again the difficulties involved in switching. π has been used for centuries in every other mathematical/physical paper. You cannot simply change that because another constant is better suited for the task (which I also think it is).
Also, it would actually be harder to learn, because we would need to explain to future generations why π actually existed in the first place, and they would have to keep two different constants (just by a factor of 2) in their heads all the time.
I believe it is not worth the effort.
"While I agree with the "pro-SI" arguments in this thread, I would like to highlight to you all again the difficulties involved in switching. Pounds, feet and gallons has been used for centuries in every other mathematical/physical paper. You cannot simply change that because another constant is better suited for the task (which I also think it is).
Also, it would actually be harder to learn, because we would need to explain to future generations why pounds, feet and gallons actually existed in the first place, and they would have to keep two different constants in their heads all the time.
I believe it is not worth the effort."
Just teasing, but arguments like "people would need to keep two sets of constants in their heads" isn't really a valid argument, because that argument can be said about any advances that has ever happened in science. Effort is probably a decent argument, while this change would make it easier for some to initially understand the concept of pi/tau, it's really trivial later on. If you wanted to switch you'd just teach the new generation tau, be consistent and when they got to more advanced math it would be trivial anyway.
Switching to this would be like my mother switching from counting British money in crowns, shillings etc. into pounds and pence; I do all of my pi-related math with pi and all of the elegance that comes with it (along with having like 9 digits memorized by heart). It's too late for me (read: too lazy) to switch at this point, so it would be something for the next generation to take hold of if they wanted to. But, I really don't see any particular benefit to the switch. It's still the same old constant. The concept of pi is a lot more important than the digits themselves.
I'm curious as to why there's this need for it. I'm perfectly fine with having just Pi, and Tau is just another simplification (which isn't necessary anyway).
I'm not a mathematician but what's the problem with just using both?? If the formula is easier to understand using pi then use pi, if it is with tau then use tau! But maybe there's an issue I'm not seeing
On July 02 2011 22:40 DoubleReed wrote: Euler's identity (e^(pi*i) = -1) and the area of a circle/sphere are really the best arguments against. And the fact is that area is a lot more useful in actual problems. Pi is fine.
The area of a circle for tau would be tau/2 * r^2 instead of pi * r^2. That's plenty ugly.
Additionally, any angle above pi is larger than 180 degrees, or improper angles which could be simplified down.
There is absolutely no reason is care enough to change. I don't see how it's any simpler to learn when you're younger.
No. Euler's identity becomes even more elegant with Tau ( e^(i*Tau) = 1), which also neatly highlights the geometric interpretation of the formula (That one TURN in the complex plane takes you around in a circle and back to the same place).
Also, lets look at some common quadratic forms that pop up in physics:
*The distance a body falls in earth's gravitational field is (1/2)gt^2 *The energy stored in spring is (1/2)kx^2 *The kinetic energy of a body is (1/2)mv^2
Aaaand i guess you can see where this is going...
*The area of a circle is (1/2)Tau*r^2
BAM.
That's a coincidental and purely cosmetic similarity. There are lots of 1/2xy^2 things in physics because there are lots of linear relationships you integrate to get a quantity which is more meaningful. Lots of constant gradients.
The relation of the area of a trivial object in a plane to its defining characteristic (circle: radius) is just a function of how you construct the object and doesn't really have a deeper meaning. Unless you want to use it as an analogy. With tau, you want to define a circle by its diameter, which is not actually how you naturally construct a circle (in my opinion). It seems ugly to me. The reason we have pi is because the greeks used a compass to do geometry.
What if I wanted to arbitrarily choose a new defining characteristic for a square? I want to "name" a square by its diagonal, r, not its side, x. Usually we say A = x^2. In terms of the diagonal, it's A = 1/2 r^2. BAM rings hollow. Though I admit it's superficially attractive at first.
On July 03 2011 01:39 MementoMori wrote: I'm not a mathematician but what's the problem with just using both?? If the formula is easier to understand using pi then use pi, if it is with tau then use tau! But maybe there's an issue I'm not seeing
The point the Tauists are trying to get across is that its pretty much always easier or more intuitive to use tau instead of pi.
To the people saying it would just be more confusing for students: You dont have to make a big deal out of this. All you have to do is at some point say "for convinience sake let tau = 2*pi" and continue from there.
On July 02 2011 11:41 BlackJack wrote: I'd hate to think that people doing advanced mathematics would be helped out a lot by not having to multiply something by 2.
LOL but multiplying by 2 makes it sooooo confusing! :D
On July 02 2011 22:40 DoubleReed wrote: Euler's identity (e^(pi*i) = -1) and the area of a circle/sphere are really the best arguments against. And the fact is that area is a lot more useful in actual problems. Pi is fine.
The area of a circle for tau would be tau/2 * r^2 instead of pi * r^2. That's plenty ugly.
Additionally, any angle above pi is larger than 180 degrees, or improper angles which could be simplified down.
There is absolutely no reason is care enough to change. I don't see how it's any simpler to learn when you're younger.
No. Euler's identity becomes even more elegant with Tau ( e^(i*Tau) = 1), which also neatly highlights the geometric interpretation of the formula (That one TURN in the complex plane takes you around in a circle and back to the same place).
Also, lets look at some common quadratic forms that pop up in physics:
*The distance a body falls in earth's gravitational field is (1/2)gt^2 *The energy stored in spring is (1/2)kx^2 *The kinetic energy of a body is (1/2)mv^2
Aaaand i guess you can see where this is going...
*The area of a circle is (1/2)Tau*r^2
BAM.
That's a coincidental and purely cosmetic similarity. There are lots of 1/2xy^2 things in physics because there are lots of linear relationships you integrate to get a quantity which is more meaningful. Lots of constant gradients.
The relation of the area of a trivial object in a plane to its defining characteristic (circle: radius) is just a function of how you construct the object and doesn't really have a deeper meaning. Unless you want to use it as an analogy. With tau, you want to define a circle by its diameter, which is not actually how you naturally construct a circle (in my opinion). It seems ugly to me. The reason we have pi is because the greeks used a compass to do geometry.
What if I wanted to arbitrarily choose a new defining characteristic for a square? I want to "name" a square by its diagonal, r, not its side, x. Usually we say A = x^2. In terms of the diagonal, it's A = 1/2 r^2. BAM rings hollow. Though I admit it's superficially attractive at first.
But there is a linear relationship that you integrate to get the area. You integrate rdrdtheta, and theta would be integrated from 0 to Tau.
On July 03 2011 02:06 fabiano wrote: So no serious consequences from a possible change? If so, why not keep pi since its what everyone already knows...
lol I thought the same thing... It's bad when you relate words to starcraft. I knew the Caduceus was something related to the medical field because of the Caduceus reactor for medivacs...
On July 02 2011 22:40 DoubleReed wrote: Euler's identity (e^(pi*i) = -1) and the area of a circle/sphere are really the best arguments against. And the fact is that area is a lot more useful in actual problems. Pi is fine.
The area of a circle for tau would be tau/2 * r^2 instead of pi * r^2. That's plenty ugly.
Additionally, any angle above pi is larger than 180 degrees, or improper angles which could be simplified down.
There is absolutely no reason is care enough to change. I don't see how it's any simpler to learn when you're younger.
No. Euler's identity becomes even more elegant with Tau ( e^(i*Tau) = 1), which also neatly highlights the geometric interpretation of the formula (That one TURN in the complex plane takes you around in a circle and back to the same place).
Also, lets look at some common quadratic forms that pop up in physics:
*The distance a body falls in earth's gravitational field is (1/2)gt^2 *The energy stored in spring is (1/2)kx^2 *The kinetic energy of a body is (1/2)mv^2
Aaaand i guess you can see where this is going...
*The area of a circle is (1/2)Tau*r^2
BAM.
That's a coincidental and purely cosmetic similarity. There are lots of 1/2xy^2 things in physics because there are lots of linear relationships you integrate to get a quantity which is more meaningful. Lots of constant gradients.
The relation of the area of a trivial object in a plane to its defining characteristic (circle: radius) is just a function of how you construct the object and doesn't really have a deeper meaning. Unless you want to use it as an analogy. With tau, you want to define a circle by its diameter, which is not actually how you naturally construct a circle (in my opinion). It seems ugly to me. The reason we have pi is because the greeks used a compass to do geometry.
What if I wanted to arbitrarily choose a new defining characteristic for a square? I want to "name" a square by its diagonal, r, not its side, x. Usually we say A = x^2. In terms of the diagonal, it's A = 1/2 r^2. BAM rings hollow. Though I admit it's superficially attractive at first.
Yes, they are all the result of a simple integration and it doesnt have any meaning beyond being similar. However, i think the formula looks better this way since it clearly hints at how it was derived.
And thats my argument, i suppose. Tau is just a more elegant and beautiful way of defining the circle constant. There's a measure of subjectivity there i guess, so i'm not going to go out of my way to prove you "wrong".
Also tau is defined by the radius; pi by the diameter. I think you got it mixed up.
The only argument I can really understand for tau are for people who are newer to mathematics and have a hard time understanding the unit circle. I do agree that this is easier to grasp when angles are defined relative to the whole circle, rather than half a circle. But in higher level mathematics, I really hope I don't see pi changed. It's special to me
On July 03 2011 01:58 Workforce wrote: All you have to do is at some point say "for convinience sake let tau = 2*pi" and continue from there.
I think you underestimate how easily some students get confused lol... they have enough trouble understanding the unit circle (some students)... using a substitution doesn't help. You have to either teach these students using pi or teach them using tau.... LATER maybe you can go back and relate them... but many students couldn't handle doing it at the beginning.
On July 02 2011 22:40 DoubleReed wrote: Euler's identity (e^(pi*i) = -1) and the area of a circle/sphere are really the best arguments against. And the fact is that area is a lot more useful in actual problems. Pi is fine.
The area of a circle for tau would be tau/2 * r^2 instead of pi * r^2. That's plenty ugly.
Additionally, any angle above pi is larger than 180 degrees, or improper angles which could be simplified down.
There is absolutely no reason is care enough to change. I don't see how it's any simpler to learn when you're younger.
No. Euler's identity becomes even more elegant with Tau ( e^(i*Tau) = 1), which also neatly highlights the geometric interpretation of the formula (That one TURN in the complex plane takes you around in a circle and back to the same place).
Also, lets look at some common quadratic forms that pop up in physics:
*The distance a body falls in earth's gravitational field is (1/2)gt^2 *The energy stored in spring is (1/2)kx^2 *The kinetic energy of a body is (1/2)mv^2
Aaaand i guess you can see where this is going...
*The area of a circle is (1/2)Tau*r^2
BAM.
That's a coincidental and purely cosmetic similarity. There are lots of 1/2xy^2 things in physics because there are lots of linear relationships you integrate to get a quantity which is more meaningful. Lots of constant gradients.
The relation of the area of a trivial object in a plane to its defining characteristic (circle: radius) is just a function of how you construct the object and doesn't really have a deeper meaning. Unless you want to use it as an analogy. With tau, you want to define a circle by its diameter, which is not actually how you naturally construct a circle (in my opinion). It seems ugly to me. The reason we have pi is because the greeks used a compass to do geometry.
What if I wanted to arbitrarily choose a new defining characteristic for a square? I want to "name" a square by its diagonal, r, not its side, x. Usually we say A = x^2. In terms of the diagonal, it's A = 1/2 r^2. BAM rings hollow. Though I admit it's superficially attractive at first.
Yes, they are all the result of a simple integration and it doesnt have any meaning beyond being similar. However, i think the formula looks better this way since it clearly hints at how it was derived.
And thats my argument, i suppose. Tau is just a more elegant and beautiful way of defining the circle constant. There's a measure of subjectivity there i guess, so i'm not going to go out of my way to prove you "wrong".
Also tau is defined by the radius; pi by the diameter. I think you got it mixed up.
A = pi r^2 = tau/2 r^2
pi = tau/2
radius = diameter / 2
edit* I guess we should say, associated with
I think you got it mixed up? hehe ^^
But ya at a certain point it's subjective. But I stand by what I said.
On July 03 2011 01:23 Veldril wrote: I don't really mind using a constant to denote 2pi. But using tau is not a good idea because it is already used for so many variables already.
Both letters find common use as standard notation. Ultimately it's a trivial matter as many other mathematicians pointed out. However, despite being trivial I think the advocates for change make a compelling case, though perhaps not one that demands urgency. Would it be nice to see tau in use? Sure. Would I mind if it never saw use? No.
Why can't we just use both? I mean... with E=mc^2 we could change all mass in every equation to energy/c^2. That would simplify some equations, but it would make others more complex. Same exact thing as this. We use both degrees and radians for different equations and they are interchangeable and any physics class in college is nitpicky and makes you answer in degrees or radians and deducts points if you just do radians.
In my opinion this is started by physics professors who want to make a name for themselves because they're too lazy to do actual work or they want to find a way to cause their students lots of confusion.
On July 02 2011 19:51 theSkareqro wrote: I study chemical engineering and tau represents something already in a formula. Its gonna be confusing as hell if it catches on.
Pi is used as symbols in formulas as well. As a physicist I think this change makes a lot of sense. If nothing else, then just because plancks constant/reduced would be a lot easier to remember. If it helps people understand the basic math better for some then by all means. The biggest effect for anyone with an understanding beyond basic geometry/trigonometry, would be having to write less on blackboards, on computers and so on.
Which ones? I've seen Pi before but never pi, that one is treated sacred as best I can tell.
I'm positive I've encountered it somewhere, though the specific situation eludes me. But my point was that just because a greek symbol is used in a formula somewhere does not make it universally sacred. (And technically I did write Pi and not pi. =b )
Well its used for the pion sub-atomic particle, but that makes sense because its the pi meson. I'm pretty sure its used for some other stuff, but probably not as much as tau. I mean its so well known that it would be even more confusing than all the other letters that mean 400 different constants or variables (fuck you letter E).
On July 03 2011 03:22 saltywet wrote: so, americans and the british want to change a universal constant because 6.28 is somehow a "more correct" form for pi.
in conclusion, white mathematicians have too much time on their hands
Maybe they wanted to give Asian mathematicians some time to make ground breaking discoveries too. ZING.
But i m more used to Electronics and Pi is very useful for a phase (as you usally measure it between -Pi and +Pi)
Same can be said with the Z transformation (where the function is usually written as a complex)
Moreover, in Mathematics as well as Physics, nothing prevents you from saying at the start: new_constant= 2Pi and then use new_constant for the rest of it.
My busnumbers from downtown to my home is 3, 14 and 15. I'll never be able to remember my busses if this changes!!! On a sidenote, all busses are changing numbers completely soon, but still... I mean, it's pi! Don't mess with the O.G.'s!
On July 03 2011 01:58 Workforce wrote: All you have to do is at some point say "for convinience sake let tau = 2*pi" and continue from there.
I think you underestimate how easily some students get confused lol... they have enough trouble understanding the unit circle (some students)... using a substitution doesn't help. You have to either teach these students using pi or teach them using tau.... LATER maybe you can go back and relate them... but many students couldn't handle doing it at the beginning.
I would have definitely preferred tau for all things trig
I graduated from uni not understanding where the cosine or sine curve came from -_^ it just never clicked, lol. I just remembered the pi/4, pi/2, etc because "that's the way it is". That Vihart video made me go O_O /facepalm
I'm probably in the minority though lol, doubt anyone else is actually that clueless
On July 02 2011 11:44 GGTeMpLaR wrote: I feel like the US should make a full switch to the metric system before we consider changing pi.
yeah that's perhaps more pertinent. The amount of trouble metric system cause...
lol, I am myself still trying to figure out how the metric system versus the US measurement system has anything to do with this thread at all.
Personally I like the idea of embracing both pi and tau. I remember having trouble with radians back in high school and using tau certainly would have made things easier.
On July 02 2011 11:54 theonemephisto wrote: It's much easier to double something than to half it.
As in, I would rather write 2pi ten times than have to write tau/2 once. The less fractions the better.
More often than not, when using tau, you wouldn't have messy fractions to deal with as shown in the video. 1/4 of a circle is 1/4 tau radians, but for 1/4 of circle would be 1/2 pi radians. Tau could be plugged into many equations without the 2. It may seem petty to get rid of but think about how many miscalculations could be prevented by having one less step. The more steps a problem takes, it is that much more likely you could potentially make a mistake, either through calculators or in your mind.
wow, I'm actually amazed at how nice everything works out with tau.
I was a little skeptical at first "won't change anything or wouldn't be worth the hassle of changing everything" the fact that tau radians are much more intuitive than pi radians (i.e. 1/3th of a circle = 1/3 tau radians as opposed to 1/6 pi radians) I think thats much more useful and natural (which is in my mind, what mathematics strives to be) and well worth the trouble of learning the area of a circle as 1/2(tau)r^2 instead of (pi)r^2
that and Euler's equation somehow got sexier e^(tau)(i) = 1 as opposed to e^(pi)(i) = -1 or e^(pi)(i) + 1 = 0.
On July 03 2011 04:55 annYeong(o11) wrote: wow, I'm actually amazed at how nice everything works out with tau.
I was a little skeptical at first "won't change anything or wouldn't be worth the hassle of changing everything" the fact that tau radians are much more intuitive than pi radians (i.e. 1/3th of a circle = 1/3 tau radians as opposed to 1/6 pi radians) I think thats much more useful and natural (which is in my mind, what mathematics strives to be) and well worth the trouble of learning the area of a circle as 1/2(tau)r^2 instead of (pi)r^2
that and Euler's equation somehow got sexier e^(tau)(i) = 1 as opposed to e^(pi)(i) = -1 or e^(pi)(i) + 1 = 0.
tau fighting!
1/3 of a full turn is 2/3 pi rad not 1/6 pi rad.
But why shouldn't we redefine the radians in terms of the diameter instead? Circumference of the circle is pi*d, now wouldn't that be easy all of a sudden ^_^
π is used in countless books, computer programs and minds, I just don't see a justification to introduce a "new" (redundant) constant for so little gain. It would have been worth discussing hundreds of years ago, but not now.
Everything would've been so much simpler if we grew up with pi=6.28 instead of 3.14. Sure it takes a little more space to write tau/2 than 2*pi, but tau/2 is far more intuitive when you're using it in equations.
That being said it's too late to fix it now and tau is a terrible symbol to use since it's the perfect letter when integrating over time intervals.
Pi is a constant.. I can't care less. I got used to it. Besides, using spherical and cylindrical coordinates with pi would be more easy with pi... at least for me
I feel like changing the constant now would be more counter-intuitive. The purpose of the constant is to simply replace some mathematical value with an identity that is easy to memorize. So does it honestly matter what value it's equal to? As long as the majority of people are able to correspond its value with its symbol. Sure, let's make a new constant named tau, this will be its symbol: + Show Spoiler +
Sure maybe it will make a crap ton of physics equations more pretty to look at, but it's going to make Euler's and a bunch of other equations just as equally less pleasing to look at.
On July 03 2011 10:54 sureshot_ wrote:Sure maybe it will make a crap ton of physics equations more pretty to look at, but it's going to make Euler's and a bunch of other equations just as equally less pleasing to look at.
Seems like a stupid idea to me. What's the big deal about having or not having 2 in front of a constant? Does it really makes life so much harder to people? It sure didn't to me.
And what about the countless articles written with symbol pi? If they change it to tau they will have to keep teaching everyone an extra equation: tau = 2*pi...
On July 03 2011 03:22 saltywet wrote: so, americans and the british want to change a universal constant because 6.28 is somehow a "more correct" form for pi.
in conclusion, white mathematicians have too much time on their hands
I don't think you understand. This is the Michael Jordan of mathematical constants.
On July 02 2011 11:35 L3gendary wrote: I say no, just for the sake of Euler's identity.
Agreed. I was all for the switch until I saw Euler's identity would be messed up
Are you kidding? e^(tau * i) = 1. Isn't that even nicer than with pi?
One of the big factors was the fact that e^(i.pi)+1=0. So it linked the 5 big mathematical constants in one equation. Now with tau, it would be e^(i.tau)-1=0, which is a lot tackier. But I mean maybe e^(i.pi)+1=0 was never meant to be, so ¯\_(ツ)_/¯
We all know "game time" is the sacred unit of measuring time. How much of us relate to a real minutes? Game time is way more useful, think about it: - It takes 17.14 "Game Time" Hours for the earth to rotate on its axis. - It takes 260.71 "Game Time" Hours for the earth to orbit the sun. - It takes 1.43 "Game Time" Pi's to get a Tau.
On July 05 2011 13:32 Highways wrote: Lets get rid of APM.
We all know "game time" is the sacred unit of measuring time. How much of us relate to a real minutes? Game time is way more useful, think about it: - It takes 17.14 "Game Time" Hours for the earth to rotate on its axis. - It takes 260.71 "Game Time" Hours for the earth to orbit the sun. - It takes 1.43 "Game Time" Pi's to get a Tau.
I think rewriting the textbooks could make it easier to learn from. Until you're a bit more advanced in math it's hard to just say let 2*pi=tau from the onset and just work with it like this professor wants people to.
I am all for tau, the sooner it becomes standard the better. Although it makes most formulas nicer i think the main advantage is how more intuitive it is, it would make children learning the radian system for the first time have a much easier ride. Also from degree level i can tell you its always nicer to have math simplified when you are using it with much more complex maths, basically any way we can make maths "nicer" is a good thing, it means we can learn faster and reach new discoveries faster as we don't have to walk through the metaphorical mud we have created ourselves in our notation before we can understand/solve a problem or concept. Notation should always display as much information as possilbe in the smallest and simplistic form, adoption of tau moves in this direction, therefore we should adopt it.
Personally i used pi too much inschool, kinda hard to change. People probably going to keep it, just like conventional current, it's in too many textbooks and stuff, kinda hard to change.
On July 02 2011 11:39 prototype. wrote: pi is fine the way it is.
No need for pi 2.0
Haha this gave me a great laugh!
But as for OP, replacing all pi wit tau/2 will just take out a 2 from half the mathematics it's used in and put it in the bottom of the other half. Just a dumb idea in general
There's a lot of formulas that include pi in mathematics and physics and there are several simplified formulas that have odd numbers of pi which would be annoying if 2pi was made tau and pi was eliminated. I can't think of specific formulas but I can assure you that from the several field integrals i studied in electromagnetism there were quite a few.
Pi has worked elegantly for a long time and so I don't feel there is a need to change the constant because we often see 2pi.
I disagree with the "its not broken don't fix it" philosphy, that really hampers progree. Look at the American use of the Imperialistic method of measure. It is extremely inefficent, change is sometimes good.
I belive that the only thing holding this back is the us of "tau". That is extremely counter productive, using an inefficent name for an efficent symbol cancels the progress entirely.
On July 06 2011 05:50 MERLIN. wrote: I disagree with the "its not broken don't fix it" philosphy, that really hampers progree. Look at the American use of the Imperialistic method of measure. It is extremely inefficent, change is sometimes good.
I belive that the only thing holding this back is the us of "tau". That is extremely counter productive, using an inefficent name for an efficent symbol cancels the progress entirely.
Radian measure is the dumbest and most unintuitive part of math. I cringe at the sight of questions involving trigonometry simply because of radian measure.. Changing this to Tau is so much more them just removing a 2 in equations, and anyone who has had to go through this uncomfortable learning period, where you learn that three quarters of a circle is equivalent to 3 halves of pi, would agree with me. Some of you don't understand how this change would make measuring angles so much more intuitive.
Can't rewrite history! Pi has been loved and people have grown up with pi. Nerds memorized it to 100 digits, then to 500 digits and further. We take 2*pi to be the ratio of a circle's circumference to radius, and it's just fine. We've memorized important equations with pi (For ex. Euler's and the normal distribution).
On July 06 2011 08:23 Chras wrote: Radian measure is the dumbest and most unintuitive part of math. I cringe at the sight of questions involving trigonometry simply because of radian measure.. Changing this to Tau is so much more them just removing a 2 in equations, and anyone who has had to go through this uncomfortable learning period, where you learn that three quarters of a circle is equivalent to 3 halves of pi, would agree with me. Some of you don't understand how this change would make measuring angles so much more intuitive.
I definitely support this change.
Why didn't you just memorize it as 2pi*3/4? This feels like a teaching plunder to me to be honest (you should be angry at your math teacher).
If someone really wants to create a new constant that is just twice as much as the previous one, then tau isn't really the best symbol for it in my opinion (it's rather widely used in many places for other things).
On July 06 2011 08:23 Chras wrote: Radian measure is the dumbest and most unintuitive part of math. I cringe at the sight of questions involving trigonometry simply because of radian measure.. Changing this to Tau is so much more them just removing a 2 in equations, and anyone who has had to go through this uncomfortable learning period, where you learn that three quarters of a circle is equivalent to 3 halves of pi, would agree with me. Some of you don't understand how this change would make measuring angles so much more intuitive.
I definitely support this change.
Did it ever occur to you that angles greater than 180 degrees are used considerably less often? So in terms of measuring angles, it's not so bad. How is that more intuitive anyway? Either way you have to understand the equation. Now it's just "tau radians" rather than "2pi radians" but it's still 6.28 radians or whatever. I don't see how this makes radian measure any better. If anything, I think it makes it uglier as pi/12 and pi/24 would be further broken down to tau/48, and it just makes these numbers way bigger and bulkier.
You try to make one thing pretty, it will make others ugly. There's no real point.
Forget Tau. 2pi should be called Ti. And it doesn't mean pi should be abandoned. There are already whole bunch of constants and whatnot widely used, that are just some other constants multiplied by even more constants. One such is Planck's constant and whatever h-bar is called:
I firmly believe that anyone having trouble in understanding how radians work due to the 'confusion' that using pi brings will find using tau any easier.
EDIT: And this is not even remotely similar to making the switch to the metric system.
On the subject I'd think both cause coexist and it would be up to the educational book writers to use what they want. I might be wrong tho as it could bring confusion and disparity in formulas used globally.
I don't think it would be worth the effort to swap a constant for itself times two... it seems like way more effort than its worth.
If the vast majority of scenarios in which Pi was used involved multiplying it by two then maybe but as is its just going to add division everywhere instead of multiplication which really isn't better.
The people who actually posted content impressed me with their knowhow of math... The people who are trying to crack jokes... You're in a math thread...
EPT
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