Why is there no equation for the perimeter of an ellipse

Applications for paid internships at Jane Street are open! A Podcast of Unnecessary Detail is out now: Come for the Unnecessary Detail, stay for the A Podcast Of. These are my approximation equations: perimeter ≈ π[53a/3 717b/35 - √(269a^2 667ab 371b^2)] perimeter ≈ π(6a/5 3b/4) If you can do better, submit it to Matt Parker's Maths Puzzles. This was my pervious video featuring ellipsoids: You can buy the ellipse from this video on eBay. I've written on my two new equations and signed it. All money goes to charity (the fantastic Water Aid). Bonus content and a deleted scene are available on my Patreon.