Chapter 5.4, Problem 1MS

Fixed things first. What does the Brouwer Fixed Point Theorem assert?

To determine

To explain: The Brouwer Fixed point theorem.

Explanation of Solution

Consider the two disks as black and blue color.

The Brouwer Fixed point theorem states that “the two disks of the same size are placed on each other such that the black disk is exactly on the top of blue disk. If the black disk is stretched, shrunked, rotated, folded without cutting is placed on the blue disk such that the disk does not hang off from blue disk then there is a point on the black disk that must be fixed”.

Therefore, there must be at least one point on the black disk that is exactly at the same position when the black disk is originally placed.