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This is a simulation which uses a cannon to calculate PI.

Given a circular pond in a square field where the pond and field have the same diameter, we fire a cannon into the field over and over, hitting randomly and count the number of times we hit the pond.

Because the area of a square is (W squared) where "W" is the width of the square and because the area of a circle is (PI times D squared) where "D" is the diameter of the circle, if a circle and square have the same width, the ratio of the area of the circle to the area of the square is PI / 4.

So we keep shooting cannonballs into the field and then we check the ratio of times we hit the pond divided by the times we fired in total. Take that ratio, multiply by 4 and we get our current guess at the value of PI. As the number of cannonballs fired increases, we should get closer and closer to PI.

Keep in mind that, while this is a valid method of calculating PI, it is also very inefficient as each additional digit of accuracy requires 10x as many shots as the previous digit.
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DovSherman Featured By Owner Feb 13, 2007  Professional Digital Artist
Close. A circle with a radius of R has an area of 2*Pi*(R squared). If the circle is the same width as a square, that square has a diameter of 2R and an area of (2R) squared.

So that's 2*Pi*R*R for a circle and 4*R*R for a square. If we factor out the R squared, we get a ratio of 2*Pi to 4.
BorosilicateArachnid Featured By Owner Dec 5, 2009
What are you talking about? A circle with radius r has an area of Pi(r^2). But the radius is only half the width of the square, so the sides are 2r and the area is 4r^2.
DovSherman Featured By Owner Mar 6, 2010  Professional Digital Artist
Yes, that's what I said. 4*R*R == 4r^2
peachlight Featured By Owner Dec 17, 2008
I thought the area of a circle was simply Pi r2, and the circumference formula was the one that required the coefficient of two (i.e. 2 Pi r). Then factoring out the r2 from your area equation you get a ratio of Pi: 4, which is what you have based your program on...
I'm sorry if I come across as... something. I'm just confused myself and trying to clarify =]
sevenofeleven Featured By Owner Jan 6, 2007
Cool idea.
Never have heard of such a thing but now I know, kudos to you.
EdwardNavu Featured By Owner Dec 24, 2006
I thought that if the cannon in thid deviation is alive cutely.
Piscatella Featured By Owner Dec 5, 2006
An artist and a nerd!!! ( and I really admire nerds and geeks) You are my hero!!!
CZGoldEdition Featured By Owner Feb 9, 2006
Awesome! I can only guess as to what possessed you to create this, but you did quite a good job at it. Fascinating. :D
ZebraHDH Featured By Owner Dec 2, 2005
I find this really interesting. It makes it seem very simple. I watched 2600 fires and got 3.10162....... Great job for whatever the reason of creating it. I enjoyed it very much.
pczelda Featured By Owner Nov 27, 2005   Digital Artist
How do you calculate the exact value of Pi to X? (Given that X's value is any position in or after 3.14). I've always wondered how you do it, but never knew how.
DovSherman Featured By Owner Nov 27, 2005  Professional Digital Artist
In simplest terms, Pi is the ratio of a circle's diameter to its circumference so you can get a crude estimate for Pi simply by measuring a dinner plate with a tape measure.

More accurate methods have been devised by various thinkers throughout history from Archimedes to Newton and more.

There's a good article on various methods for calculating Pi at [link]
sharkoftheday Featured By Owner Nov 26, 2005  Hobbyist Writer
It would be interesting if you actually graphed the results of certain number of random sessions with a certain limit. Even though this may not be truly random (and thus accurate) it would be interesting to just see what it comes up with as a result over time. At 1200 right now its hovering in the 3.10-3.11 range and randomly decreasing.
DovSherman Featured By Owner Nov 26, 2005  Professional Digital Artist
It would run more quickly without the graphics, of course, and, when the idea for this program was first suggested in Scientific American (1985), Joshua Simons of the Harvard Medical School ran the program for one week, calculating 4 billion cannonball shots and coming up with an estimate of 3.14157 which is very good up until that 7 which, in Pi, is a 9.

Joseph McKean, a statistician at Western Michigan University, theorized that each additional digit of accuracy would require that the number of cannonball shots be increased by a factor of 100 which mounts up very quickly. For the first fifty digits, you'd need to calculate for a full googol of cannonball shots which would require more time than the expected lifespan of the universe.
gadgetsguru Featured By Owner Nov 26, 2005  Professional Photographer
In theory, if this cannon fires enough times (for instance, infinity), it will get the exact number of Pi, right?
DovSherman Featured By Owner Nov 26, 2005  Professional Digital Artist
It would definitely take infinity to do it. Even allowing for the fact that we're limited to the number of digits a computer can handle and the fact that random number generation isn't truly random (so the distribution may not be even), there's no way that two integers (the number of shots and the number of hits) can ever exactly match Pi. Pi is an irrational number which means that it can't be expressed as a ratio of two integers. However, in theory, it should get closer and closer to a match and, if it ran for infinity, it would come infinitely close to matching Pi.
wisekidk Featured By Owner Feb 25, 2010  Student Filmographer
Yea, it would take a looooong time. Mine went well over 3000 and it was oy just past the 4 digit, and it was getting very slow since it was almost out of spots.
gadgetsguru Featured By Owner Dec 17, 2005  Professional Photographer
So... much... math... :omg:
DovSherman Featured By Owner Dec 17, 2005  Professional Digital Artist
Ah, but it's really, really simple math. The formula is....

4 x (number of shots that hit pond) / (number of shots total) = something close to PI
gadgetsguru Featured By Owner Dec 18, 2005  Professional Photographer
For me, math ≠ simple.
heterodox13 Featured By Owner Nov 26, 2005   Interface Designer
wow, can you do my homework? lol
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Submitted on
November 25, 2005
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