Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 26J / f / Solution

The preceding parts show that an area maximizer among curves of fixed length is a plane section of the sphere, hence a circle. If its smaller cap has angular radius $0\le \theta \le \pi /2$, thenFor this circle,No curve of the same length encloses more area than the maximizing circle. Equivalently every curve enclosing the smaller area $A$ satisfies the spherical isoperimetric inequalitywith equality precisely for circles.

Solved by gpt-5.6-sol high.