An area-maximizing curve
3,100 views · Published 5 November 2018 · 44:12 · Indexed 6 October 2026
Channel: Dr Peyam · 2018 · Education
Suppose you have a simple closed curve of a given length and suppose that the region inside the curve has maximal area. What can you say about this curve? In this video, using Fourier series, we’ll show that the curve must be a circle and the area must be a disk! This is sometimes called the isoperimetric problem in two dimensions. Enjoy!
