To celebrate π day we have offered our students a workshop to approximate the decimal value of π using familiar things. Our students threw 1kg of semolina to a square in whose base there was build a removable inscribed circle.
The experiment is based on Monte Carlo method which uses the Law of Large Numbers to obtain an empiric approximation of the number π. Assuming that all grains of semolina are placed randomly on the square, the ratio between the square and the circle is π/4. If we count the grains that are inside the circle and the total amount of grains that are thrown and divide the numbers, we'll have an approximation of π/4.
So it is enough to multiply by 4 to get an approximation of π. The more grains we throw, the more accurate is expected to be the approximation. Because it is an experiment based on randomness, result can fluctuate but due to the Law of Large Numbers, a fair approximation of π can be expected if the experiment is repeated enough.
A very huge number of grains are necessary to obtain a decent approximation of π and there could be technical difficulties to count the number of grains.
We have simplifie the experiment using their weight instead, assuming that all grains of semolina are identical for our purposes.
We are very happy with the result! We finally got an approximation of 3.1817!!!!
We also projected a computer program to simulate the experiment with millions of random grains to get a better approximation of π.
Scan the QR code to see it!