How can you approximate Pi using Geometry?

Approximating Pi was a favourite pastime of many ancient mathematicians, none more so than Archimedes. Using his polygon approximation method we can get whole number bounds of 3 and 4 for the universal constant, with only high-school level geometry. This is the latest question from Tom Rocks Maths and I Love Mathematics - answering the questions sent in and voted for by YOU. Full playlist:    • How many ping-pong balls would it take to ...   Q1: What is the probability I have the same PIN as someone else? Q2: How long would it take to sink to the bottom of the ocean? Q3: What is the gravitational field of a hollow Earth? Q4: What is the best way to win at the board game Monopoly? Q5: What are the most basic Mathematical Axioms? Q6: How does Modular Arithmetic work? Q7: What is the Gamma Function? Q8: How many ping-pong balls would it take to lift the Titanic from the ocean floor? Q9: What is the graph of x^x? Q10: How can you show geometrically that Pi is between 3 and 4? Produced by Dr Tom Crawford at the University of Oxford. For more maths content check out Tom's website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths   / tomrocksmaths     / tomrocksmaths     / tomrocksmaths   Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collec...