Newton’s Approximation for Pi

In 1666 Newton found Pi to sixteen decimal places by evaluating the first twenty-two terms of an infinite sum. Celebrate Pi Day with your students by following in Newton’s footsteps and doing the maths to derive his sum, or by evaluating many, many terms of the sum by hand, and getting an approximation for Pi.

Curriculum Topics Covered

Evaluating terms of the sum by hand can be done with a variety of written calculation methods so is accessible from Key Stage 3 upwards. 

Deriving Newton’s sum involves A-Level maths knowledge, including the following topics: equation of a circle, binomial expansion, finding definite integrals, areas of sectors of circles, index laws, trigonometry, Pythagoras’ theorem.

More information

See our Teacher Notes first to get more information about the activities you could do with your class. 

For Pi Day Matt followed in Newton’s footsteps and evaluated twenty terms of this sum by hand to get an approximation for Pi. Matt had help from schools across the world who evaluated some of the terms for him. It truly was a mass participation calculation! Watch the video below.