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Code Golf

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    \$\begingroup\$ Interesting challenge, but of course, it's equivalent to Monte - Carlo integration of that curve, which is a traditional "toy" method for calculating pi. (If you aren't familiar with it throw random darts at the one by one square, count the ratio which fall within or outside one unit of the origin, derive area of that quarter circle from that ratio. Accuracy is limited by the quality of your random number generator, the number of digits your calculations can be carried out to, and how long you are willing to repeat the experiment while waiting for the result to stabilize. Common homework!) \$\endgroup\$
    – keshlam
    Commented Sep 17 at 17:35