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Pi In The 4th Dimension
Anonymous Coward writes "Hoy! There is some crazy guy who is all set to prove that the value of the mathematical constant Pi is same for all dimensions. He has calculated Pi for the 4th dimension - and it..it's almost equal - 3.1447817532635 wheras the calculated value of Pi in 2 dimensions (circle) is 3.1416999189943. Math nerds can calculate the percentage error. The project is on SourceForge.net and they even have an online version "
Pi isn't different for different geometries, its just the series converge slower for the higher dimentions.
The only way pi could be different was if space itself was not "flat" but curved.
So he's all set to prove they're the same. A simple web page shows they're different.
Doesn't sound like a very exciting story to me.
Pi is 3.1415926...., not either of the values claimed in the article. Approximations of pi could perhaps have the values claimed in the article. I could approximate pi as 3, but that wouldn't make pi = 3.
"Those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded."
i had to go through the source to figure out what they meant by pi in higher dimensions. at first i assumed it had to be something interesting, since they bothered to post it, but it's not. they're just useing simple calculations to find the volume of spheres and hyperspheres, and plugging that into the known, proven formulas to find pi.
for a circle, A=pi*r^2
for a sphere, V=4/3*pi*r^3
for a hypersphere, V=pi^2*r^4/2
by "proving" that pi is the same in multiple dimensions, they merely demonstrate these well-established identities. of course, since they're using a clumsy "brute force" method to initially calculate the volume, they're not actually proving anything, since they only get an approximate answer.
#define F(x) int main(){printf(#x,10,#x);}
F(#define F(x) int main(){printf(#x,10,#x);}%cF(%s))
Math nerds can calculate the percentage error.
Why the percentage error is exactly 3.14157429...%
Thats because they didn't run the calculation for any real length of time. Behold:
./2d3d4d_1
--[~]--
INPUT
Calculate the Pi for circle, sphere and hypersphere.
Let us start the verification for 2d, 3d and 4d, Give Cycles
Cycles = 100000000000
CIRCLE
Area of circle by brute force method = 78539815867
Radius = 158113.883008
Calculated value of Pi = 3.141593
SPHERE
Volume of sphere by brute force method = 52359877534
Radius = 2320.794417
Calculated value of Pi = 3.141593
HYPERSPHERE
Enclosure of Hypersphere by brute force method = 30842511725
Radius = 281.170663
Calculated value of Pi = 3.141593
The longer it runs for, the closer it gets. Whether or not this actually proves anything is, of course, up to debate.
Paranoid
Bwaahahahahaa.
Yeah, I figured. I was surprised a PHP version existed at all, because you wouldn't want to run such hefty calculations on the server side anyway - make the clients do it. In any case, there is a .exe version available for download, suitable for most compiler-deprived idiots.
The Pi it calculates doesn't seem to have many significant digits... is there any way the algorithm can be reworked to use a BigFloat library or something, for better precision? And perhaps fork off some children to do the actual work, so the load will spread across my MOSIX cluster and SMP boxes? Even if it just used one process per dimensional calculation (one each for 2d, 3d, 4d), the run would have finished in 20min rather than an hour... =)
Paranoid
Bwaahahahahaa.
pi in 2d is defined in terms of a ratio of the circumference of a circle to it's diameter.
pi in 3d is conventionally defined in terms of the ratio of the 2d circumference of a circle to it's 2d diameter. It's pi, damn it, it is a constant.
But you can also use 4piR^2 for the surface area of a sphere, and 4/3piR^3 for the volume, which has been mathematically proven for quite some time. The authors of this program appear to be defining 3D pi wrt these ratios... physics geeks will note that the units balance out nicely.
As for 4D pi... I can only assume the ratios are something like npiR^3 surface and mpiR^4 for volume, seeing as how the units must balance and hypergeometry wasn't an emphasis at my college.
Still, though. Writing programs to calculate pi is a fun little project that everyone seems to do at some point in their high school or college career. I did pi in HS. In college I did 4D Tic Tac Toe. These people appear to be doing both. More power to them.
This Sig is a mnemonic device designed to allow you to recognize this author in the future.
Um what? I don't think so. e ~= 2.718, so e^4.2 would be in the vicinity of 75 or 80. pi = (ln (-1))/i though.
He was referring to the difference between the values of pi for different dimensions. The question he was addressing was whether pi was the same for every dimension. He offered a value for 3D, a different value for 2D, and said you could calculate the margin of error.
"Those who have never entered upon scientific pursuits know not a tithe of the poetry by which they are surrounded."