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Get rid of pi?

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micronesia
Profile Blog Joined July 2006
United States24670 Posts
July 02 2011 02:29 GMT
#1
[image loading]


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 ):

+ Show Spoiler [full text] +
Mathematicians Want to Say Goodbye to Pi

"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?
ModeratorThere are animal crackers for people and there are people crackers for animals.
flamekin
Profile Joined April 2010
United States72 Posts
Last Edited: 2011-07-02 02:35:54
July 02 2011 02:33 GMT
#2
cos tau/8 looks stupid i prefer cos pi/4
and america still uses the imperial system what makes you think we will change to tau lol
L3gendary
Profile Joined October 2010
Canada1470 Posts
July 02 2011 02:35 GMT
#3
I say no, just for the sake of Euler's identity.
Watching Jaedong play purifies my eyes. -Coach Ju Hoon
GhostKorean
Profile Blog Joined November 2008
United States2330 Posts
July 02 2011 02:36 GMT
#4
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
Cowpieguy
Profile Blog Joined February 2011
United States97 Posts
July 02 2011 02:37 GMT
#5
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.
Retgery
Profile Joined August 2010
Canada1229 Posts
July 02 2011 02:37 GMT
#6
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

Does anyone have the link to the video?
Fall down 7 times, stand up 8.
Livelovedie
Profile Blog Joined April 2011
United States492 Posts
July 02 2011 02:37 GMT
#7
I'm born on pi day, so I want it to stay pi.
GhostKorean
Profile Blog Joined November 2008
United States2330 Posts
July 02 2011 02:39 GMT
#8
On July 02 2011 11:37 Retgery wrote:
Show nested quote +
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

Does anyone have the link to the video?

I think it's this
prototype.
Profile Blog Joined July 2009
Canada4200 Posts
July 02 2011 02:39 GMT
#9
pi is fine the way it is.

No need for pi 2.0
( ・´ー・`)
GrapeD
Profile Blog Joined August 2010
Canada679 Posts
July 02 2011 02:39 GMT
#10
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.
Some people hurt people. I defenestrate those people.
jgoonld
Profile Joined November 2010
334 Posts
July 02 2011 02:40 GMT
#11
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.
Muirhead
Profile Blog Joined October 2007
United States556 Posts
July 02 2011 02:41 GMT
#12
:X
As a mathematician, I can say "who cares?" :D
starleague.mit.edu
BlackJack
Profile Blog Joined June 2003
United States10464 Posts
July 02 2011 02:41 GMT
#13
I'd hate to think that people doing advanced mathematics would be helped out a lot by not having to multiply something by 2.
Sufficiency
Profile Blog Joined October 2010
Canada23833 Posts
July 02 2011 02:41 GMT
#14
I've read this before. It had some very good arguments, to be honest.
https://twitter.com/SufficientStats
itachisan
Profile Blog Joined June 2011
Canada109 Posts
July 02 2011 02:42 GMT
#15
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.
coplice_
Profile Joined July 2010
Canada128 Posts
July 02 2011 02:42 GMT
#16
If it ain't broke, don't fix it.
"the CIA should start using TvT as a torture technique" - telcontar
iamho
Profile Joined June 2009
United States3347 Posts
July 02 2011 02:44 GMT
#17
Fuck no, tau has too many meanings already.
Zealotdriver
Profile Blog Joined December 2009
United States1557 Posts
July 02 2011 02:44 GMT
#18
Leave it as pi. We'd lose the use of the tau symbol in equations, which would be annoying.
Turn off the radio
Hibzy
Profile Joined November 2010
United Kingdom445 Posts
July 02 2011 02:44 GMT
#19
it was hard enough for me to learn physics as it is, i'd rather not have to learn a whole bunch of new things now
"Uhh, I just have an insanely good sense of fashion." -TLO
GGTeMpLaR
Profile Blog Joined June 2009
United States7226 Posts
July 02 2011 02:44 GMT
#20
I feel like the US should make a full switch to the metric system before we consider changing pi.
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