Calculate Pi With Chocolate

There are many silly ways to calculate Pi, from throwing sausages to filling plates with marbles, but this has got to be the tastiest method around.

You will need:

1. White chocolate chips
2. Milk chocolate chips
3. Printed out worksheet (attached to this step)

Print off the first worksheet or draw yourself a grid of 6 x 6 squares with a quarter of a circle drawn from corner to corner.

Place chocolate chips on all the squares which lie completely inside the circle.

Place white chocolate chips on the rest of the squares.

To find pi, count all the chips inside the circle, multiply by 4 and divide by the total number of chocolates (36).

Pi = 4 * milk chocolate / total chocolate

So for our 6 x 6 grid above this would be

Pi = 4 * 22/36 = 2.44

Which... isn't pi (3.1415926...).

To get a more accurate value we need to add more chocolate!

The second worksheet has a 12 x 12 grid, 144 squares in total.

Apply the same method of chocolate placement as above, placing milk chocolate on squares which are entirely within the circle and count again.

This time your equation becomes

Pi = 4 * 98 / 144

Pi = 2.7222

Which is better! But still not pi.

So far we've been keeping the maths simple, but we're still pretty far from the true value of pi.

The answer gets more accurate the more chocolate you use, but using this method we would need a 102 x 102 grid to get to a value of 3.1 and a 2529 x 2529 grid to get to 3.14! That's 6,395,841 chocolate chips!

Instead, we can get a more accurate value using the experiment we've already done but applying a slightly more complex equation.

This time, count all the squares which touch the line (23 squares in our example above) and use it in a new equation:

Pi = 4 * (milk chocolate + ½ squares which touch the line / total chocolate

Which gives us a new value of

Pi = 4 * (98 + 0.5*23)/144 = 3.041667

Which is pretty good for just counting chocolate!