Pi Day 2022 - Buffon's Needles, calculating Pi Experimentally

Today it’s a bit of a different experiment where we’re going to calculate Pi by using an experimental method of dropping needles onto a bit of paper and seeing if they cross a line or not. The experiment is a problem called Buffons needle, and is one of the original geometry probability problems solved. The maths is a little bit tricky, but we both do it by hand, and then simulate the problem with a bit of python and jupyter.

On the 14th of March (3.14) lots of mathematicians on youtube like to calculate Pi, and I thought I would take part in this as well. Calculating Pi is usually done by measuring the diameter and circumference of a circle, but the number, being slightly magical, appears in all kinds of maths problems and puzzles. This one, is perhaps a little more obvious as any analysis quickly resolves into a triangle, and then where there is a triangle, theres a circle and maths with radians, and Pi is shortly behind.

Jupyter makes these kinds of experimental projects really easy, and for people wanting to play with maths, I can't think of a better language to play in - it lets you work with all kinds of fun numbers and is much easier (in my opinion) to read then other languages.