Calculating Pi with Skittles and Census Data - Numberphile

TL;DR

Pi can be estimated by randomly distributing Skittles in a circle inscribed in a square, then scaling up using UK census population data.

Key Points

• 1.- The method works because a unit circle inscribed in a square has area π vs. 4, so the ratio of items inside the circle to total items equals π/4 — multiply by 4 to get π.
• 2.- Physical Skittles experiment at Numberphile yielded 562 inside the circle, 159 outside (721 total), giving an estimate of 3.1 for π.
• 3.- Scaling up with UK Office of National Statistics census data: a 100km radius circle centered on Nottingham contained ~16.2 million people vs. ~20.4 million in the square, estimating π as 3.18.
• 4.- Anfield (Liverpool) at 100km radius gave a worse estimate of 3.27, attributed to the irregular UK coastline skewing population distribution in the circle vs. square.
• 5.- The center of England (a farm in Leicestershire) at 100km gave the best census result of 3.049, though still worse than the physical Skittles experiment.