The Math Thread

dVanDaHorns
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Re: The Math Thread

Post by dVanDaHorns »

Basically, from what I've heard anyways, some professors want to replace pi with tau, where tau = 2*pi. I'm not the most researched in it, but from what I've heard, they argue that using Tau will make radial math much easier to learn, as the sine of tau is symmetric, and 2*pi pops up a lot more frequently than pi.
That, and there are mathematicians who like to flame war each other by posting various equations where using either pi or tau makes the equation simpler.
It's more of a convention thing than anything else.

And heh, wave equation for the win! >: D
Is this logical or just frivolous, ridiculous and silly?
In some cases, it is more logical, and in others, it is just ridiculous. Since it's so divided, I kinda think it isn't worth the effort to change the convention. They didn't re-define current when they discovered that electrons flowed in the opposite direction for that same reason.
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Re: The Math Thread

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How about just using tau instead of 2*pi and pi everywhere else? That would seem like the logical thing to do to me.
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Anteroinen
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Re: The Math Thread

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azareus wrote:How about just using tau instead of 2*pi and pi everywhere else? That would seem like the logical thing to do to me.
In a way, however, such a practice would invite a usage of a different symbol for each common fraction or multiple of pi. For example eta has been offered for half pi, since it can be useful whilst converting cosine to sine and visa versa.
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dVanDaHorns
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Re: The Math Thread

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azareus wrote:How about just using tau instead of 2*pi and pi everywhere else? That would seem like the logical thing to do to me.
Meh, that would make things a lot more complicated. It would be essentially like mixing our decimal numbers with roman numerals.

There was one professor I heard talking about it who had a pretty good idea, where you just use tau to teach the basic concepts, but let the students know that it equals 2*pi, and then you essentially get the best of both worlds.
Yet due to the fact that we haven't even changed current direction to match the flow of electrons out of convention, I highly doubt we're going to change around something less meaningful, like pi vs tau.
In a way, however, such a practice would invite a usage of a different symbol for each common fraction or multiple of pi. For example eta has been offered for half pi, since it can be useful whilst converting cosine to sine and visa versa.
That is an idea I am in agreement with; however, problems will arise when it comes to memorization, and more notably, when you get some fraction of pi within the same equation as another variable which happens to be represented by that same letter. (For example, the reason Engineers use j for imaginary numbers rather than i, because to them, i denotes current. Thus, one had to be changed to avoid confusion, which causes more confusion in the end.)
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Anteroinen
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Re: The Math Thread

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dVanDaHorns wrote:
azareus wrote:How about just using tau instead of 2*pi and pi everywhere else? That would seem like the logical thing to do to me.
Meh, that would make things a lot more complicated. It would be essentially like mixing our decimal numbers with roman numerals.

There was one professor I heard talking about it who had a pretty good idea, where you just use tau to teach the basic concepts, but let the students know that it equals 2*pi, and then you essentially get the best of both worlds.
Yet due to the fact that we haven't even changed current direction to match the flow of electrons out of convention, I highly doubt we're going to change around something less meaningful, like pi vs tau.
I think that is a pretty good idea, although if it is but mentioned most people will just ignore pi in that case, like most people just forget things they don't really use. They are like the rarer punctuation rules in grammar, which most people to a large degree forget. So if pi and tau are both used but either is more prevalent, people would soon forget the other and wonder what on Earth it is when they see it. Of course there are conversion tables and booklets for this stuff, so this is not such a big issue.

I don't think this will be changed either, convention is a menace.
In a way, however, such a practice would invite a usage of a different symbol for each common fraction or multiple of pi. For example eta has been offered for half pi, since it can be useful whilst converting cosine to sine and visa versa.
That is an idea I am in agreement with; however, problems will arise when it comes to memorization, and more notably, when you get some fraction of pi within the same equation as another variable which happens to be represented by that same letter. (For example, the reason Engineers use j for imaginary numbers rather than i, because to them, i denotes current. Thus, one had to be changed to avoid confusion, which causes more confusion in the end.)
That tradition is even more confusing since split-complex numbers (or perplex numbers) are of the form a+bj, where j^2=1, but j isn't equal to 1. On the other hand, due to the lack of available symbols (or rather the non-use of other than Greek and Latin ones) we have already come across that problem many times over, I mean just look at this list: http://en.wikipedia.org/wiki/E_(disambiguation) It is still a problem though, perhaps we should start accepting Cyrrilic symbols?
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dVanDaHorns
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Re: The Math Thread

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I think that is a pretty good idea, although if it is but mentioned most people will just ignore pi in that case, like most people just forget things they don't really use. They are like the rarer punctuation rules in grammar, which most people to a large degree forget. So if pi and tau are both used but either is more prevalent, people would soon forget the other and wonder what on Earth it is when they see it. Of course there are conversion tables and booklets for this stuff, so this is not such a big issue.

I don't think this will be changed either, convention is a menace.
I'm still fine with that. If they were to go about the whole change process, it would have to be like that. Have a mix of both, and then see which one holds out in the end. That way, the entire world isn't forced to stop and re-program their brains to accept tau, since I can guarantee that I would botch up and end up writing something akin to sin(tau/2)=1.
Since, in my opinion, if they want to go about making this change, might as well change the whole number system to make it more conventional, as I mentioned previously. :P
That tradition is even more confusing since split-complex numbers (or perplex numbers) are of the form a+bj, where j^2=1, but j isn't equal to 1. On the other hand, due to the lack of available symbols (or rather the non-use of other than Greek and Latin ones) we have already come across that problem many times over, I mean just look at this list: http://en.wikipedia.org/wiki/E_(disambiguation) It is still a problem though, perhaps we should start accepting Cyrrilic symbols?
Indeed, I am aware of this. And not being in electrical engineering, the entire process is confusing as heck. (Although, not as confusing as, say, biochemistry, and their half a dozen various unrelated usages of alphas and betas...it's as if they didn't even try and just got lazy. xD No offense to any biochemists out there...) Indeed, I believe we should be doing more symbol alterations similar to h vs ℏ, as well as other alphabets. Or heck, just make up a symbol.
But alas, this convoluted melting pot of all mathematics and sciences will never get itself straightened out, no matter how hard people try. :P
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Re: The Math Thread

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We might as well use some han characters (the simple ones, of course :P), or just inventing some good diagrammatic notation. For example I use Penrose's diagrammatic notation for tensors, sometimes an hybrid with letters instead of shapes, it turns out to be very useful. After all, maths isn't about the notation, but about what it represents. We could derive all of maths using stones, like the Romans with their calculi XD.
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Re: The Math Thread

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Yes! All that matters is what it represents, and how you convey its meaning in a way so that others can understand and expand upon your work.

And as that conversation draws to the close, what levels of math are you guys all at, out of curiosity?
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Re: The Math Thread

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What do you mean by levels of math? Is it anything country-based?
Anyways, since I'm interested in these topics I looked most of it by myself, rather than following the courses. My maths teacher when I was in high school told me that I knew things from the equivalent to 4th year of mathematics degree, so either I'm some sort of genius or Spanish education is crap XD
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Re: The Math Thread

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OnyxIonVortex wrote:What do you mean by levels of math? Is it anything country-based?
Anyways, since I'm interested in these topics I looked most of it by myself, rather than following the courses. My maths teacher when I was in high school told me that I knew things from the equivalent to 4th year of mathematics degree, so either I'm some sort of genius or Spanish education is crap XD
Ah. I wasn't really meaning country-based, given that there are people from all over the world here. More like, what are you guys currently studying, math-wise?

Actually, scrap that. I have no clue how accurately describe that. xD
Hmm. I guess I'll leave it up to someone else to find another math topic...
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