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Poll: The π is a lie!
Switching to τ --- 6 (18.75%)
Sticking to π --- 26 (81.25%)

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Author: Subject: The π is a lie!
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[*] posted on 13-4-2014 at 10:07
The π is a lie!


I wasn't sure where to post this, but I saw a few math-related things here, so I'll try my hand at this.

π is wrong. (Not as a number, but as a concept.)

The ratio of circumference to radius, defined as τ=2π, is much more fundamental.

Seriously, if you haven't read the Tau Manifesto by Michael Hartl, read it now. Someone also wrote the Pi Manifesto - read this too.

So many things become simpler with tau:

There are τ radians in a circle:



EVERY trig function is periodic with respect to τ.




The Euler identity: some have decried it, saying that e1/2τi = -1 is less beautiful than eπi = -1.

I'll give you this: eτi = 1. This means that a rotation by τ brings you back to unity.



The nth roots of unity derive from this identity as well, and it can be easily shown that eπi = -1 is simply the second root of unity. And nothing more.

Then there's the area of a circle: 1/2τr2. This seems like it's a better case for π, but it's actually supposed to have the factor of one half. It can be shown that the area of a circle is equivalent to that of a triangle with a base corresponding to the radius r and an altitude corresponding to the circumference C. This relation doesn't exist with the diameter, which raises the question:

WHAT ARE YOU DOING WITH A CIRCLE CONSTANT DEFINED BY THE DIAMETER WHEN THE CIRCLE AND ALL OF ITS MEASUREMENTS ARE DEFINED BY THE RADIUS?!

I told some friends about this. Their reactions ranged from "who cares?" to "Oh my god, I've been lied to my entire life!"




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[*] posted on 13-4-2014 at 10:14


I like them both. Is there some reason we can't have both?

EDIT: Your poll is not sufficient for my purposes. :(

[Edited on 4-13-2014 by Etaoin Shrdlu]
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[*] posted on 13-4-2014 at 16:19


I can think about Tau more easily. Pi trips me up if I am doing too much mental math.

I'm not in the camp that says "who cares", but I'm also not in the "I've been lied too" camp either. Both constants work.

Edit: one plus side to pi is it doesn't look like a lower-case t, or a + sign if I am writing too fast. I could see myself looking at a parametric equation and getting very lost as to what was a t, +, or τ.

[Edited on 14-4-2014 by smaerd]




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[*] posted on 13-4-2014 at 17:03


I respect your tau-loving conclusion and I am happy it works (and makes sense) for you... BUT... Honestly, we are all chemists... higher order math is not very useful and Algebra 2 is as far as most chemists really need to go (except for those few that can use a bit of calc). Therefore, I like it simple and I will stick to the way I was taught since 3rd grade. ;)



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[*] posted on 13-4-2014 at 18:46


If you want to do anything semi-serious with kinetics expect to use calculus and differential equations. Or anything in physical chemistry. Honestly, I've found a good deal of the 'higher math' helped make sense of a lot of the gobbldy guck I've learned as an undergraduate chemistry major. For example rather then looking up zero, first and second order rate equations I can come up with them pretty easily with some mental math. From there the respective half-life equations too.

Sure, when you're mapping out a synthesis you're not solving ODE's or anything but being fluent in math can give you a good idea as to whether an SN1 or SN2 will be favored on a reactant. Even things in biochemistry such as structure solving require some rudimentary level of calculus (electrostatics, etc). Yes computers and soft-ware handle a lot of this now, but it's not all inclusive, and someone has to tell the computer what to do. Sure most of quantum mechanics after pchem can be forgotten for a lot of people, but in spectroscopy knowing the basic principles of simple harmonic oscillators can say tell you where if a dueterium atom was substituted from a hydrogen atom on a molecule where the peak 'should' be in an FT-IR spectra. Come to think of it, FT-IR, Raman spec, and NMR are all expressions of higher mathematics.

I wouldn't be so quick to chuck 'higher level undergraduate' math out the window if you're interested in 'graduate level' chemistry, is what I'm trying to say I guess.

Edit- jeese come to think of it I even had to use calculus on a bomb calorimetry experiment I did the other semester. Not sure how I would have done it accurately without it and polynomial curve fitting.

Edit again - even the most simple reactor models definitely requires the understanding of differential equations and chemical thermodynamics.

[Edited on 14-4-2014 by smaerd]




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[*] posted on 13-4-2014 at 19:00


The rationale for tau is that it doesn't needlessly confuse children learning about circles. Other than that, I don't really care. Let people confuse themselves.:D

In all seriousness, I only use tau in any calculations I do.




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[*] posted on 13-4-2014 at 20:16


If you find a factor of 2 confusing, then maths is not for you.

One rationale for pi is that if you are holding a circular object, measuring the diameter is easier than measuring the radius (if the center isn't marked). (Imagine yourself 2000 years ago trying to work out the relationships in a circle.)

Yes, its a weak rationale, but if you have to pick some basis for a definition you want a simple one.
e.g 24 hour day because 12 (and 24) has lots of factors, making it easy to divide up time using fractions.

[Edited on 14-4-2014 by Twospoons]




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[*] posted on 13-4-2014 at 21:55


I forgot to include something: η (eta). τ = 4η

η appears to be the n-sphere constant. It's shown to be an integral part of the surface area and volume formulae for an n-sphere. It's mentioned in the Tau Manifesto, and there's a good video on it. Though η likely will not catch on because it's not really common in basic mathematics, unlike τ.

I'm surprised that so many people want to keep using π! When I learned about τ I stopped using π completely. It's almost foreign now.

There's also a video on the matter by ViHart and Michael Hartl. I'm also going to try to promote it at Spaceweather.com (they had a thing for π Day).




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[*] posted on 13-4-2014 at 22:08


Also τ is used in electronics to denote the time constant of a circuit, and pi is used in various other places (relating to frequency), so using τ to replace 2*pi would cause a lot of confusion. I'll be sticking with pi thanks.



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[*] posted on 15-4-2014 at 00:07


Quote: Originally posted by Twospoons  
Also τ is used in electronics to denote the time constant of a circuit, and pi is used in various other places (relating to frequency), so using τ to replace 2*pi would cause a lot of confusion. I'll be sticking with pi thanks.


What, you think
tau = R*C
and
F = 1 / (tau * tau)
is confusing?! Bah! :D




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[*] posted on 15-4-2014 at 12:25


Well, if the notation doesn't work, change the notation. Why not χ for the time constant (from Greek χρόνος;)? Or N for torque (another common complaint)?

Remember, physicists have to deal with the formula ψ(r) = Ne-me2r/ħ2. And the expression for N has an e in it (the exact e intended is left to the reader as an exercise). Notational conflicts can easily be resolved.

π is used somewhere else in chemistry, I forgot exactly what it's used for...

[Edited on 15.4.2014 by Brain&Force]




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[*] posted on 16-4-2014 at 13:22


Tau is a fun concept, but it shouldn't change pi or normal math.



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[*] posted on 1-5-2014 at 03:28


But... wait... the area of a circle would be an equally valid statement! In fact, the perimeter of the circle is the derivative of the area!


LONG LIVE PI




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[*] posted on 1-5-2014 at 09:37


Quote: Originally posted by Eddygp  
But... wait... the area of a circle would be an equally valid statement! In fact, the perimeter of the circle is the derivative of the area!


LONG LIVE PI

My second wonderful contribution to this form:
LONG LIVE PI!




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[*] posted on 1-5-2014 at 13:08


Not really.

A circle is defined by the set of all points a fixed distance (the radius) away from the center. These points form an arc which is τ times the length of the radius. The area is not constructed: it is a DERIVED definition. The area relationships have a natural factor of 1/2 that arises from integrating the proportionality τr with respect to r.

The area is also defined by breaking the circle into an infinite number of skinny triangles of area 1/2 × r × dC and summing them up through integration to get 1/2 × r × C. C = τr, so A= 1/2 × τ × r2.

tl;dr: Τau is the τruth; π is for eating. :cool:

[Edited on 1.5.2014 by Brain&Force]

[Edited on 1.5.2014 by Brain&Force]




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[*] posted on 1-5-2014 at 22:07


Actualy who cares.
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[*] posted on 10-5-2014 at 10:46


I care!

The reason being that π, being ill-defined, makes math harder for students. I'm not saying we should rewrite our scientific papers and replace every instance of π with τ - that's unnecessary and pointless. Scientists are fine with 2π. It's the kids that are affected by this.

I would be OK with using both π and τ, but there's a problem with π that extends into the geometry of n-spheres (this is explained in the Tau Manifesto; I can't really explain it myself). I am OK with using η in the context of n-spheres because it is the fundamental unifying constant of their geometries.




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[*] posted on 10-5-2014 at 11:14


Its only constant, you dont need 2 constants. Only problem with pi ts transcendental nummber.
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[*] posted on 10-5-2014 at 13:16


Sorry, couldn't resist!

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[*] posted on 28-6-2014 at 08:41


Happy Tau Day! (Well, today is 6/28 for us in the US - but it doesn't matter for those of you in Europe, either. 6 and 28 are perfect numbers, so today is a PERFECT DAY!)



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[*] posted on 25-10-2014 at 17:10


Just wanted to say this: When I first read this thread back when it was started, it didn't really mean much to me at all and I thought "who cares?"
Now, I've been in Precal for a few months, and ever since we started getting into trig functions using the unit circle and stuff, I've realized how much easier it would be to use τ than π. It seems to me like using τ/2 where π is needed would be simpler and more efficient than using 2π in the multitude of situations where τ fits. No disrespect is meant to π, since it has had such a great and productive history, however history alone is not reason enough to continue using it.

I vote for τ.




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