## Department of Mathematics

Indian Institute Of Technology Madras , Chennai

### An infinite flock of pigeons.

#### Abstract :

We take a glimpse of the pigeonhole principle in its infinite avatar. We prove the Bolzano - Weierstrass theorem and some generalisations from analysis using infinite P. H. P. We then use it to prove that circle has the most area among all figures with same perimeter.

Key Speaker N Narayanan, IITM.