
Pi is Wrong - ssp
http://www.math.utah.edu/%7Epalais/pi.pdf
======
evanmoran
When I read this article a while back the part that impressed me was how in
intuitive radians become:

    
    
      2/3 * NewPi = (2/3's around the circle in radians).  
    

It is a much more intuitive way to think about angles. Ask a third grader, how
much cherry pie is missing. "About a two-thirds" they will say. They don't
mention PI, and right now no one does. This is the way people think about
angles naturally. NewPi makes this more intuitive by allowing you describe
angle as a number between 0 and 1 (which is usually the way to go, see
splines, animation, etc). 0.25NewPi just makes sense. It is a fourth of a
circle, and this way of thinking would help kids understand radians instantly.

Probably the only drawback is when doing wicked tricks on a snowboarding game
such as SSX. Doing a 1080 just sounds cooler then a 3, but which is more
intuitive?=)

~~~
amalcon
You can do this with regular pi; you only need to use diameter-ans instead of
radians. You can do it without a pi at all; there's an actual (used) unit
called the "cycle". 1 Hertz is defined as 1 cycle/second.

The only problem with these units is that, like with degrees, d/dx sin(x) !=
cos(x). It messes with calculus.

~~~
aston
Not true. Calculus would be the same (a radian is a radian). sin(pi + x) !=
cos(x) in the new system, though.

~~~
zbanks
Chain rule: Let x be angle in radians, y be angle in diameter-ians (2pi) x =
2y d/dx sin(x) = cos(x)

d/dy sin(y) = d/dx sin(2 _x)_ d/dx (2x) = 2 cos(2x) = 2 cos(y)

It's the same reason why you use radians for angles in calculus: degrees mess
it up.

[http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig...](http://en.wikipedia.org/wiki/Trigonometric_functions#The_significance_of_radians)

~~~
jacobolus
What? sin(x) is still sin(x). Just because we have a different value for pi
doesn’t mean we have a different sin function. sin(6.28...) = sin(6.28...),
etc., etc.

Crucially, we still have exp(x + iy) = exp(x) * (cos(y) + i sin(y)), because
we haven’t changed the definitions of any of these functions. If we did change
the definitions of sin and cos, that’d really be a bummer, you’re right.

We still measure angles in radians. No diameter-ians in sight. Our old x or
new y (notice, those have the same value) is just a different fraction of
newpi than it is of oldpi, is all.

It amazes me that amalcon’s being voted up and aston is being voted down.
People clearly aren’t thinking it through for themselves.

~~~
amalcon
_Just because we have a different value for pi doesn’t mean we have a
different sin function._

Which is exactly what I just got done saying that I'm not saying. Reading
comprehension, much?

To be entirely clear: All I was saying is that the reason we use radians in
the first place (instead of, say, cycles) is that it fixes calculus. It has
little to do with 2pi. It only relates to the comment it was said in reply to.

~~~
jacobolus
> _Reading comprehension, much?_

Yes, I’ve re-read your original post 4 times, and your intended meaning is
quite confusing, because you’re talking about a different way of changing our
notation than the link is, but without clearly stating that, and your notation
change, which you criticize, is something of a non-sequitur in context of the
parent comment and the article, as far as I can tell.

Thus, you seemed to be implying† that the new definition of pi results in
messing up calculus. To clear things up: “We could measure angles in any
arbitrary units we want, but using radians makes calculus work, and if we’re
using radians, the circumference is 2 pi of them, which is why pi as a unit is
not ideal, and newpi = 2*pi would be better. If we wanted we could have an
angle of pi ‘diametrans’ in a complete circle instead, using our existing
definition of pi ~ 3.14, but that would be stupid, because it would break all
kinds of symmetries in calculus.”

†: This is apparently a misinterpretation though (mine and also aston’s, who
wrote “a radian is a radian”), and you don’t actually mean to be implying
that.

~~~
amalcon
Fair enough, I suppose.

------
Benjo
The pdf claims that for simplicity sake, the constant pi should have been a
factor of two larger.

Reminds me of electrical engineering "mistakes" such as the convention
establishing electrons as negatively charged; or the ohm being very small/amp
being very large compared to everyday usage.

~~~
tbrownaw
Whole amps and handfuls of ohms aren't _that_ rare, they actually match pretty
well to what comes out of the wall socket. And that 1.8v or 0.85v or whatever
it is these days space heater that runs your computer takes really quite a lot
of amps.

~~~
ori_b
On the other hand, Farads or Teslas...

~~~
amalcon
Coulombs are my favorite, because it's the fundamental amount of "something"
(as opposed to "something per time") that most of these can be traced back to:

Ampere = Coulomb/second

Farad = Coulomb/volt

------
benbeltran
Well, next monday we can celebrate 6/28 as 2pi day or proper pi day... Just in
time article.

~~~
pbhjpbhj
So you're going to celebrate refactoring a mathematical constant to give a
neater presentation on a day chosen based an apparently illogical ordering
scheme for dates.

That has to class as irony.

Out of curiosity: Does anyone here genuinely believe that Pi should be the
circumference÷radius and hold that dates should be written Month/Day/Year ?

I've heard one reasonable defence of American date ordering based on actual
priority of information (roughly: "you want the month first to broadly narrow
down the locus but the year will be assumed"). But I still go with English or
just [truncated] ISO dates.

~~~
elbrodeur
I use UNIX time. So there.

~~~
pbhjpbhj
I suggest you wait until Wed 8 Feb 2169 01:15:07 GMT+0000 (BST) to celebrate

------
carterschonwald
the idea may seem trite, but the pedagogical motivation for making certain
symmetries more apparent in mathematics is sound.

on an unrelated note, when will the scribd links switch to html5?

~~~
ascuttlefish
I think any pdf link says scribd, even if it's not. Not sure why.

~~~
jmillikin
The [scribd] isn't a comment, it's a separate link -- you can click on it to
view a broken version of the original document.

carterschonwald is commenting that the Scribd link uses Flash, rather than the
recently released HTML5 Scribd implementation.

~~~
ascuttlefish
Jebus, I never noticed that. Thanks!

------
jessriedel
Same thing happened with the gamma function. MathOverflow:

[http://mathoverflow.net/questions/20960/why-is-the-gamma-
fun...](http://mathoverflow.net/questions/20960/why-is-the-gamma-function-
shifted-from-the-factorial-by-1)

------
codeflo
Unfortunately the article is down at the moment, but there's a beautiful
identity that suggests that maybe pi/4 is a constant of nature, not pi:

pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ...

That's arguing from pure mathematics. Judging from the comments, I think the
article argues (from kind of an engineering point of view) that 2pi would be
more convenient.

~~~
est
e^(pi*j)=1

~~~
codeflo
It's -1 actually, and I might just as well write:

e^(i pi/2) = i

e^(i pi/4) = sqrt(i)

both of which are arguably even more expressive.

------
btilly
Old news. This ranks up there with the fact that it was a bad idea to use base
10 instead of base 12. Absolutely and utterly true, but completely not worth
the switching costs.

~~~
cwp
Can you provide a reference for this? I'd like to know the reasoning.

~~~
petewarden
A slight tangent, but I recently ran across a fascinating theory on the origin
of base-12 systems. If you use your thumb as a marker, you can touch four
finger joints on each hand for a total of 12 positions. I tried it and it's a
surprisingly natural way of keeping count. Here's the source paper:

[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...](http://www-
groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html)

~~~
caf
If you use the tip of each finger as well, you can count in hex to 0xff with
two hands ;)

~~~
what
You can count to 1023 in binary using both hands.

------
edanm
Very interesting article.

On a related not, check out the book "Negative Math":
[http://www.amazon.com/Negative-Math-Mathematical-Rules-
Posit...](http://www.amazon.com/Negative-Math-Mathematical-Rules-
Positively/dp/0691123098/ref=sr_1_1?ie=UTF8&s=books&qid=1277192051&sr=8-1)

This book builds up a mathematics in which multiplying two negative numbers
gives you a negative, not a positive. The results are very interesting,
particularly this: _There are no complex numbers_. The root of -1 is -1.

This is another example of something you never think to question, you always
assume is "just the natural way", but which was a somewhat arbitrary choice
and can be changed.

~~~
crazyjimbo
It's also inconsistent if you assume that multiplication is distributive over
addition:

(-1 + 1) * -1 = -1 * -1 + 1 * -1 = -1 + -1 = -2

or

(-1 + 1) * -1 = 0 * -1 = 0.

~~~
edanm
Your'e right, but you don't have to assume that multiplication is distributive
over addition. You can build math without that assumption. It gets weird, but
it's very interesting to see that so many things we take for granted about
mathematics are really just conventions.

~~~
crazyjimbo
Very true, but I like my numbers to behave like... well, numbers. You can
define consistent algebras but I'd argue with you if you tried to call them
numbers.

------
detcader
I seriously have always suspected this. If you're going to use a value to
represent the perfection of a circle, why not take the derivatives of its
properties (area, then perimeter, and once more) until you get a constant? 2pi
is that constant.

------
cgs1019
One of my math professors pointed out that to be consistent, "π, φ, χ, ψ, ξ,
and ι" should actually be pronounced "pee, fee, khee, psee, ksee and ee-ota,"
which I found kind of funny and fascinating. Of course, common convention
beats out pedantic propriety and rightly so, I think. This sort of thought-
provocation is quite valuable nonetheless, if for no other reason than to keep
us aware of that about which we do not readily think.

~~~
JBiserkov
That's exactly how we pronounce them in Bulgaria (neighbor of Greece).

------
JacobAldridge
When I saw the host and title I was concerned it may have been a rehashing of
this urban legend - <http://www.snopes.com/religion/pi.asp>

Relieved to see it was actually this article, which I've actually referenced a
number of times in discussions with engineers to make myself sound like I know
more than I actually do!

------
ptarjan
Posted to mathoverflow: [http://mathoverflow.net/questions/29070/is-defining-
a-consta...](http://mathoverflow.net/questions/29070/is-defining-a-
constant-2pi-more-elegant)

~~~
jonsen
I find your downvotes and the rejective spirit over there puzzling. (Perhaps
it's just to overflow ;)

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Dilpil
What about the fact that sin and cosine have such elegant Taylor series
expansions if you use radians?

In radians, sin = x - x^3/3! + x^5/5! - x^7/7!...

In 'Double radians', we have a 2^n factor in front of each term.

~~~
SamReidHughes
No they wouldn't. This article is not talking about redefining what 1 radian
means.

------
Daniel_Newby
Even worse, in physics h-bar = h / (2 * pi).

