But what's the BIGGEST Triangle?

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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

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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