In this set of activities students approximate Pi by rolling dice and spotting factors between pairs of numbers.
Two D12s (fair dice with numbers 1 – 12) per pair of students, or a random number generator which can simulate this
Curriculum Topics Covered
Randomness; properties of numbers and their factors; π; manipulation of equations
Students investigate the probability that two integers chosen randomly are coprime (do not share a factor other than one) by generating numbers with dice and counting coprime pairs. Amazingly, for an infinitely large set of integers, this probability can be found using a formula that involves Pi. Pi appears in an unexpected place! Students can discover what the formula is, and then with some re-arrangement and use of their probability value find an estimate for Pi.
This set of activities is inspired by the video below, ‘Generating π from 1,000 random numbers’, which Matt Parker released on his YouTube channel for Pi Day 2017.