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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 "
the saying that you can't step into the same river twice? :-)
Great one!
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.
I minored in math and I'm not sure just what is meant by Pi in the fourth dimension. By definition a circle is a two dimensional object. By definition Pi = C/r where C is the circumference of the circle, and r is the radius of the same circle. Therefore Pi by definition is the ratio of two properties of a two dimensional object.
Which leaves me (or us) with the question of what does the fourth dimension have to do with the value of Pi?
Just showing my ignorance...
"Oh drat these computers, they're so naughty and so complex, I could pinch them." --Marvin the Martian
If you did more cycles you would see that all the pi's are about equal and closer to the real pi. It just uses a brute force method so you need more cycles to see that they are more equal.
I wish I had mod points to mod this down, as it is offtopic, please mod the parent of my comment down and also mine as there are both offtopic.
Submit a story and/or create your own discussion area.
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))
I WILL KICK YOU'RE FUCKEN ASS!!!!
You are obviously a paki. I suggest reporting yourself to the authorities immediately.
"Why did they cancel my favorite Sci-Fi show? I downloaded ALL the episodes!"
It seems that the Slashdot editors agree with my anti-islamic stance. They are keeping my posts marked high.
Who's going to a barbecue tonight? I am! Hopefully we'll be able to roast a small muslim child alive.
"Why did they cancel my favorite Sci-Fi show? I downloaded ALL the episodes!"
Math nerds can calculate the percentage error.
Why the percentage error is exactly 3.14157429...%
Pi is defined to be the ratio of the circumference of a circle to its diameter. pi = c/d. Okay, we all know that.
Using calculus, you can determine the area of a circle in terms of pi.
Using calculus, you can determine the volume and surface area of a sphere in terms of pi.
And so on, and so on. Therefore, why would anyone think pi would be any different for higher dimensions? Are they also speculating that calculus is a load of poppycock?
OOOOOAAAAHHHHH (drool) N-Dimensional Pi......
"I would rather have your time than your money" --Henry Rollins Jan 14 2003 on the topic on internet file trading
You fuckhole, that's not Pi, Pi is 3.141592654. What the fuck are you slashdot losers smoking? It doesn't matter a rat fuck "how many dimensions" it is... Pi == Pi.
pi == 3
God told me so
I have been pwned because my
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.
I'm impressed!
Thats the real aim of the program. The C code wcich you ran is the actual verion. The Php one is for idiots without compilers who cancot download and compile the simple bit of code. I advice all the sceptics here to please download the original code and give it a try with BIG numbers.
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.
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As far as I know pi is just a number: it exists and it has his own value, like 666, sqrt(2), e, i, etc.
I suppose that the main reason why it has a name is that lots of geometrical constant happen to belong to Q(pi) (i.e. the minimal subfield of the complex field that contains all rational numbers and pi); since Q(pi) is also an (infinite dimensional) vector space on Q, and most of the useful constant belongs to the subspace generated by 1 and pi, we can just write them as a*1+b*pi and we're able to work with them in an easier way.
The "definition of pi" is just like the definition of any other real number, as a Dedekin section (not sure it's the name you use in english), and it happens not to say much about its value. Then when you have real numbers you can say whether two of them are the same or not, so you can demostrate that, e.g. the ratio between circonference and diameter of a circle is the same number as the limit of a few series, but calculating an aproximation of the first or some term of the second won't help much in this demonstration.
The main point of the project seem to dabble with different algorithms to calculate the decimal development of pi. While this is interesting, they are in fact very low level since the current record is in the millions (billions ?) of number. There are whole books dedicated to this sole topic.
Xavier
Do I make sense? Please report if not.
So, someone got fed up running endlessly in circles, and decided that he wanted another slice of pi. Got four dimensions, and did a new number.
I just what type of pi. Personally, I go for chocolate cream.
Have you read my journal today?
from http://www.joyofpi.com/pifacts.htm
Pi.
1.The Greek letter P or p, corresponding to the roman p.
2.A number, represented by said letter, expressing the ratio of the circumference of a perfect circle to its diameter. The value of pi has been calculated to many millions of decimal places, to no readily apparent purpose: no perfect circles or spheres exist in nature, since matter is composed of atoms and therefore lumpy, not smooth. Nature
herself sometimes takes to rounding off the more extreme decimals of numbers when they get sufficiently small, as Prof. Heisenberg has pointed out. However, the continued extension of pi provides a harmless exercise of computer power which would otherwise be misused playing Quake or surfing pointless web sites.
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."