But what's the BIGGEST Triangle?

🛍 Check out my math fashion brand! https://mathshion.com/ ❤️ Join the channel to get exclusive and early videos, original music, math lectures, and more!    / @wrathofmath   What triangle is the biggest? The 'optimal' triangle in some sense. This certainly depends on the specifics of what we mean. Today we'll consider the isoperimetric problem for triangles, a type of problem dating back to 19 BC with Dido's Problem in Virgil's Aenid. Our problem is: of all triangles with a given perimeter, which has the biggest area? We'll prove the intuitive answer is correct using Heron's formula and one extra result. #mathproblems #geometry Outro Song:    • ♪ Northumberland Ending ♪ (2026 Outro)   (Longer Version:    • ♪ Northumberland ♪   ) More Math Chats:    • Math Chats   Business Inquiries: [email protected] SOURCES https://www.liverpool.ac.uk/~maryrees... Non–Euclidean versions of some classical triangle inequalities by Svrtan and Veljan Geometric Inequalities by Kazarinoff The Isoperimetric Inequality by Robert Osserman An Introduction to Inequalities by Beckenbach and Bellman Dido’s Problem and Its Impact on Modern Mathematics by Catherine Bandle 0:00 Intro 0:59 Isoperimetric 4:23 Preliminary Result 10:53 Isoperimetric Inequality 14:48 Conclusion