Pi Approximation Using Factors Activities

In this set of activities students approximate Pi by rolling dice and spotting factors between pairs of numbers. 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 ‘Generating π from 1,000 random numbers’ that Matt Parker released on his YouTube channel (www.youtube.com/standupmaths) for Pi Day 2017.

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