Simon talking about his favourite infinite sum at the circular room known as the “pi room” at the Palais de la Découverte (“Discovery Palace”) in Paris. Inscribed on the walls are 707 digits of the number π. The ratio of coprime pairs of numbers to pairs of numbers is 6/π^2. And 1/1^2 + 1/2^2 + 1/3^2 +… = π^2/6 So that means that the ratio of coprime pairs of numbers to pairs of numbers equals to 1 over Simon’s favourite infinite sum!
Simon made two more short videos at the pi room:
Proof that π is irrational: https://youtu.be/CUHgsCLxL0k
Looking for 2019 among the digits of π: https://youtu.be/5qIaA7MwzHY
Daniel Shiffman later showed Simon how to look for any number in the digits of Pi using this amazing project by Ben Fry: http://pi.fathom.info/