The One they Didn't Teach You in School

Heron's formula is a classic taught in basic geometry for finding the area of a triangle from the perimeter. But Heron has a perhaps more impressive result called Heron's method, which is an algorithm for computing square roots. It is a highly effective method and we'll prove it today. #maths #mathematics Pick Up Jay Cummings's Math History book to support people who actually write real books: https://amzn.to/3YJGa0h Check out the coolest math clothes in the world: https://mathshion.com/ Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join More Math Chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Outro music: https://youtube.com/shorts/tfifiSdTZRg Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 1:24 Heron of Alexandria 2:59 Heron's Method 5:41 Intuition 6:46 More Facts 8:10 Proof Outline 10:09 Proof 14:47 Final Step 17:15 Conclusion