\section{Reidemeister moves}

\begin{problems}
\item
Are the two trefoils the same?
How do you know?
How could you convince someone else of your answer?
\item
Are the two figures-of-eight the same?
How do you know?
How could you convince someone else of your answer?
\item
What is involved in showing that two knot diagrams represent the
same knot, and in showing that two knot diagrams do not represent the
same knot?
\item
Make a Reidemeister movie to show that the figure-of-eight is
amphicheiral.
\end{problems}
