# Brouwer's fixed point theorem

Is the statement is true or false, please explain the reason
Every continuous map $f \colon S^1 \to S^1$ has a fixed point where $S^1$ is a unit circle in $\mathbb R^2$ follows from Brouwer's fixed point theorem.

• Welcome to math.se! As in TeX you can use \$ for formatting of mathematics. – Smylic Apr 3 '17 at 7:33
• It doesn't. Consider rotating the circle by 45 degrees for example – mathworker21 Apr 3 '17 at 7:34
• If this is not the systematic outsourcing of one's homework, I don't know what is. – Did Apr 5 '17 at 7:04