The Isoperimetric Inequality скачать в хорошем качестве

The Isoperimetric Inequality

We prove the isoperimetric inequality. This states that if we are give a smooth closed curve that encloses an area of A, the A is not more than the length of the curve squared divided by 4pi. The area, A, can actually achieve this value if the curve is a circle since both expressions are pi*r^2 in that case. We use the arclength parameter formula, Green's Theorem, Parseval's Theorem and the Plancherel in the proof. The proof is an excellent examples of using different branches of mathematics together! #mikethemathematician, #mikedabkowski, #profdabkowski