Monthly Archives: December 2007

Calling a mathematician!

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So, I saw this the other day:
Xkcd Infinite Resistor Grid
I’m sure this problem has a solution. There’s an infinite number of variables, but there’s a more infinite number of equations that relate them together, so I’d imagine in principle there’s a solution.

Of course, infinity is weird, so I guess that might not be true? Clearly, I’m going to try solving this though.

Approximating π the Monte Carlo Way

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  1. Draw a square on the ground, and within it, inscribe a circle.
  2. Throw rice into the square, as randomly as you can, counting how many grains of rice you’ve thrown.
  3. Count how many land in the circle.
  4. Divide by the number you threw, and multiply by 4.

Congratulations, you have estimated π. The more rice you throw, and the more randomly and uniformly you do it, the better the approximation. There’s something almost unsettling about this method…