What is the area of a Squircle?

Check out https://www.kiwico.com/standupmaths and get 50% off your first month of any crate! Maybe enjoy making a pencil sharpener! Not that I'd know what that's like... This is the GeoGebra file Sam Hartburn made for me: https://www.geogebra.org/m/pffgbck8 Here is The Coding Train's first part of the Super Shape series. https://www.youtube.com/watch?v=z86cx2A4_3E I mentioned the these old videos of mine: Ellipses and perimeters https://www.youtube.com/watch?v=5nW3nJhBHL0 Generalising fibonacci https://www.youtube.com/watch?v=ghxQA3vvhsk Lemniscate on MathWorld https://mathworld.wolfram.com/Lemniscate.html This is a really good write-up about Gauss and the Arithmetic-Geometric Mean. https://homepage.univie.ac.at/tomack.gilmore/papers/Agm.pdf This is a nice related problem about the area v perimeter of a squircle. https://www.johndcook.com/blog/2019/04/11/dido-problem/ Cheers to my Patreon supporters for whom I have dedicated one digit of Gauss's constant each. It was their inspiration who made me do the 'multiple Matts' thing. You can also help support and shape the videos I make! https://www.patreon.com/standupmaths CORRECTIONS - If you feel a sense of déjà vu: yes, the two sections at 16:13 and 16:45 cover the same content. I tried saying it two different ways and we accidentally left both in the edit. So, let's call that 'buy one get one free' sale on learning. - At 21:42 I say "geometric mean" instead of "arithmetic mean". And that is probably not the only time. These words have lost all meaning to me. - The Patreon credits stop early! Long story. I'll explain on Patreon. - Let me know if you spot any other mistakes. Crazy amount of editing and meshing of footage by Alex Genn-Bash Maths graphics by Sam Hartburn and Matt Parker Kitchen by Carrie and Nina Music by Howard Carter Design by Simon Wright and Adam Robinson MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/ US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/ UK book: https://mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback