Talk:Pi

Pi in science fiction literature

Every now and then I run into a science fiction novel that supposes the value for pi can vary according to a gravitational constant, or a local "curvature" in the universe. Um, I don't think so, but it is getting kind of predictable that this sort of thing keeps popping up in science fiction literature.

The main article could be improved if somebody put a link in there, connecting it to another Wiki article about Pi in science fiction literature. For instance, The Infinite Man by Daniel F. Galouye is one such novel that uses this as an essential part of its plot. His story proposes that computers using standard calculations, according to a standard formula, suddenly start spitting out a different sequence of decimal digits, because the whole universe starts changing its density levels, apparently in response to a supreme being deciding to change the amount of mass in the universe.

It isn't my purpose to argue against one plot in support of another, in terms of science fiction literature employing plausible plot lines, merely that this kind of thing apparently keeps happening, and among different writers around the world. Science fiction authors keep arguing that the formulas for calculating pi, as applied, produces results that are consistent with observable data. Dexter Nextnumber (talk) 07:50, 1 January 2010 (UTC)

2pi=(72/70)^-2

2Pi=(72/70)^-2 FERMAT SO GREAT YUUKI OKA GREAT

FERMAT'S LAST THEOREM isX=3,R Y=2,3,R Z=2,3,2X3,3X3,R X-n=2 Y-n=1 Z-n=3 MUST n>4 ,X^n+Y^n=Z^n X=3 Y=2 Z=2X3^3XR 3^3+2^3=(6^-3)^3 is only one X=3 Y=2 Z=6^-3 n=3 is FERMAT'S LAST THEOREM ANSWER 6^-3 IS ANSWER BUT not Natural Number so n=3 X^n+Y^n=Z^n is IMPISSIBLE in 4-TIME&SPACE DIMENSION 27+8 =35 FERMAT GREAT !!! 3.14159265 6^2=6^-3 35/36 : 3/3.14159263 S=R/2xT 2^3+3^3=6^2

2Pi=(72/70)^-2  —Preceding unsigned comment added by 220.208.50.26 (talk) 04:43, 13 February 2010 (UTC) 

Definition using the circle

While this is historically the correct way, and quite possibly the way the article should go, it is also dangerous, because it gives the layman the wrong impression. It is much more fruitful to consider pi an abstract constant (possibly defined through exp(i*pi)=-1), which happens to also give a certain relationship in a circle.

I would advice that, at a minimum, the introduction stresses that the "traditional" definition is a historical left-over and ultimately only a secondary characterization of pi. 188.100.196.8 (talk) 00:26, 7 January 2010 (UTC)

Polygons inscribed in a circle

A simplest way to calculate pi is to observe polygons (polygons from three sides, to polygons increasing by multiple of two) inscribed in a circle and watch the height and the base of the sides of the polygons and use the theorem of Pythagoras to find the degree of the angles. The more sides there are in the polygons and the less the degree of the angle of the triangles. Since the angles start with 60 degree and diminish by multiple of two and the sides increase by multiple of two we have an equation: Sin (60/2^x) * 2^x *3=pi

$\pi =(\sin(60/2^{x})(2^{x})(3))\,$

$\ (\sin A)/(\cos C)=1\,$

$\ (\sin 30)/(\cos 60)=1\,$

$\pi =(\sin(180/2^{x})(2^{x})\,$

Angles of triangles of polygons.

30+90+60,---------60/30=2

15+90+75,---------75/15=5

7.5+90+82.5,-------82.5/7.5=11

3.75+90+86.25,------86.25/3.75=23

1.875+90+88.125---- 88.125/1.875=47

From 2 to 5=3

From 5 to 11p=6

From 11 to 23 =12

From 23 to 47 =24

……Twentythreethousand (talk) 20:57, 11 January 2010 (UTC)

$\ (60/30=2)...(90/30=3)...(90/60=3/2)\,$

$\ (75/15=5)...(90/15=6)...(90/75=6/5)\,$

$\ (82.5/7.5=11)...(90/7.5=12)...(90/82.5=12/11)\,$

$\ (86.25/3.75=23)...(90/3.75=24)...(90/86.25=24/23)\,$

Twentythreethousand (talk) 00:25, 15 January 2010 (UTC)

you can check what it looks like on a graph with radians and degrees and the graph is a constant on pi and on 180. you can make a graph with this equation.Twentythreethousand (talk) 00:06, 22 January 2010 (UTC)

$\pi =(\sin(6/999999999......))*3\,$

$\pi =(\sin(60/x^{k})(x^{k})(3))\,$

Twentythreethousand (talk) 19:30, 31 January 2010 (UTC)

$\pi =(\sin(6/100000000......))*3\,$

$\ 0.6--90--89.4----90/0.6=150---89.4/0.6=149---90/89.4=150/149\,$

$\ 0.06--90--89.94----90/0.06=1500---89.94/0.06=1499---90/89.94=1500/1499\,$

$\ 0.006--90--89.994---90/0.006=15000---89.994/0.006=14999--90/89.994=15000/14999\,$

$\ 0.0006--90--89.9994--90/0006=150000---89.9994/0.0006=149999---90/89.9994=150000/1499999\,$

$\pi =(\sin(0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000.......18)*10^{n})\,$

$\pi =(\sin(0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000.......6)*3)*10^{n}\,$

Twentythreethousand (talk) 01:13, 2 February 2010 (UTC)

$\pi =(\sin(1/10^{n}*18)*10^{n})\,$

1degree,0.1degree,0.001degree,0.0001degree,$1/10^{n}degree\,$ Twentythreethousand (talk) 16:24, 12 February 2010 (UTC)

May I ask what this has to do with improving the article? We know

$\pi =180\lim _{x\to 0}{\frac {\sin x^{\circ }}{x}}.$

— Arthur Rubin (talk) 17:24, 12 February 2010 (UTC)

dear Arthur Rubin you said you know,but your equation is not even in the article and what I have stated in this discussion group is not hard trigonometry and not even hard integral calculus $\pi .$ If the calculator machine allowed an irrational number without any increase or a decrease of the number which is a straight line and a measure of a distance that require only two or three digits,what's the use of calculating pi to the billions of digits.Twentythreethousand (talk) 18:09, 13 February 2010 (UTC)

Perhaps it should be in the article, but it's a trivial consequence of:

$\lim _{x\to 0}{\frac {\sin x}{x}}=1$

and

180 degrees is π radians.

The latter probably should be somewhere in the article. (Actually, it is, in the infobox, and in a picture caption.) — Arthur Rubin (talk) 19:13, 13 February 2010 (UTC)

$\lim _{x\to 0}{\frac {\sin x}{x}}=1$ x can not equal to 180 in this case.It's 0.174.119.27.38 (talk) 19:55, 13 February 2010 (UTC)

New Interesting Formula

I suggest adding formulas 1.1 and 2.13 from http://iamned.com/math/infiniteseries.pdf to the main article They are interesting —Preceding unsigned comment added by 71.139.200.147 (talk) 06:14, 17 January 2010 (UTC)

$\pi 2^{10}{\sqrt {3}}=\sum _{k=1}^{\infty }{\frac {1}{9^{k}{\tbinom {8k}{4k}}}}\left({\frac {5717}{8k+1}}-{\frac {413}{8k+3}}-{\frac {45}{8k+5}}+{\frac {5}{8k+7}}\right)$

$\pi ={\frac {\sqrt {3}}{60}}\sum _{k=1}^{\infty }{\frac {(2k)!(130k+109)}{({\frac {7}{6}})_{k}({\frac {11}{6}})_{k}(-1296)^{k}}}$

Extremely Accurate Approximation

$\pi -7.66*10^{-63}\approx \ {\frac {4{\sqrt {3z(5+g)}}}{9}}\left({\frac {-{\sqrt {89}}}{g^{2}(5+g)}}\left({\frac {9(10-g)^{2}}{4z}}+{\frac {1}{5}}\right)+{\frac {827}{5}}\right)^{-1}$

${\begin{array}{lcl}z=9(5+g)^{3}-(10-g)^{3}\\g={\sqrt[{3}]{500+53{\sqrt {89}}}}\end{array}}$

—Preceding unsigned comment added by 67.161.40.148 (talk) 05:44, 19 January 2010 (UTC)

So, you managed to get 63 significant digits of pi by a complicated formula with 80 symbols. Well, guess what: I can do away with only 64 symbols in a much easier way. I leave it as a simple exercise to the reader. — Emil J. 11:06, 19 January 2010 (UTC)

For those like Finell who do not get it, the solution is "3.14159265358979323846264338327950288419716939937510582097494459". — Emil J. 11:51, 19 January 2010 (UTC)

The often quoted ramanujan approximation uses 13 digits to get 10 places: http://mathworld.wolfram.com/images/equations/PiApproximations/Inline49.gif

there's a bunch of them here: http://mathworld.wolfram.com/PiApproximations.html

The only really good one is http://mathworld.wolfram.com/images/equations/PiApproximations/Inline77.gif but it's a coincidence due to the continued fraction expansion of pi^4

To me the problem with the MathWorld's "Pi Approximations" page is that most of them seem to be mathematical coincidences. Even when there is a deeper mathematical reason for the approximation, it may still be a long way from a practical method for computation.--RDBury (talk) 13:57, 20 January 2010 (UTC)

@RDBury From the work I;ve done those approximations are either coincidences or in the case of Ramanujan derived using elliptic integrals. All expressions that don't involve logarithms are constructable, but obtaining the approximation probably done though trial and error via a computer without an underlying theory. As for computation, you wouldn't use a pi approximation, but a pi formula. —Preceding unsigned comment added by 67.161.40.148 (talk) 16:25, 20 January 2010 (UTC)

Einsten the first to explain river meandering?

The text currently says that Einstein was the first to suggest that rivers have a tendency towards an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend. He may well have been the first to discover the connection with pi but I cannot believe he was the first to explain the process, even though the cited source claims this. Martin Hogbin (talk) 18:44, 30 January 2010 (UTC)

Economics

Strangely enough π is also used in economics to represent profit. l santry (talk) 16:11, 4 February 2010 (UTC)