Consider a square painting of size $1 \times 1$. A rectangular sheet of paper of area $2$ is called its “envelope” if one can wrap the painting with it without cutting the paper. (For instance, a $2 \times 1$ rectangle and a square with side $\sqrt2$ are envelopes.) a) Show that there exist other envelopes. (4) b) Show that there exist infinitely many envelopes. (3)