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

Видео What is the area of a Squircle? канала Stand-up Maths