Calculate Pi With a Dartboard

You can try this at home, but do it the easy way

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Imagine a special, square dartboard, say exactly 2 meters by 2 meters in size, with a giant bullseye circle inscribed within its borders.

If you throw darts as randomly as inhumanly possible at this dartboard, the total number of hits and misses can be used to estimate pi. But before we start throwing those darts, let’s simplify the board even more.

A Very Special Dartboard

Saw off the upper right corner of the dartboard to reduce the result to a 1 meter by 1 meter square, with a quarter of the original circle in it.

This dartboard simplifies the math, and that’s always a good thing. The area of the circular segment is a fraction of the total area of the square, and the value of pi works into the ratio. Let’s start with the formula for the area of a circle given its radius.

Do the math and you’ll see the area of the square is 1, and the area of the quarter circle part…