Comment on Calculating Pi with a Cannon by ~DovSherman

wow, can you do my homework? lol

In theory, if this cannon fires enough times (for instance, infinity), it will get the exact number of Pi, right?


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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.

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.

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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.

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.

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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]

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.

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So... much... math...


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FAQ #123: I want to see a great artist on deviantART. Where do I go?
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Artwork © 1985 - 2008, Jeffrey Bennett