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November 25, 2005
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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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:iconnightingale2012:
how long can this go on??!! I left it on left and came back and it was still shooting! Is there a limit??!!
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:iconavoidingcliches:
Very nice. We'll keep working on the "random" bit. What did you use for this?
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:icondovsherman:
I'm sorry but I don't understand the question. Use for what?
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:iconavoidingcliches:
As in, did you write the code for this? And what program did you use for the graphics?

I'm no computer guy, just mathy and physicsy. I am interested in what exactly you're running here...

I'm afraid my questions are vague because my understanding is similarly vague...
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:icondovsherman:
Oh, I see. It's a very simple Flash-based program, written with Flash Actionscript. I made the graphics myself - the canon using Swift3D and the rest with the simple graphics editor built into Flash.
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:iconmimin-photography:
This is so amazing...so simple and yet - brilliant.
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:iconbozar88:
isn't it somehow connected with the integral over the circular path?
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:icontapeking:
Wow... Thats an interesting way to calculate pi. I wish we did something like this in my math class.
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