Pi Approximation Using Factors

In this set of activities students approximate Pi by rolling dice and spotting factors between pairs of numbers.

Equipment needed

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.