Problems

Take a straight string of finite length. Put the right half on top of the left half to form a hoop, and then pass it (the piece now on top) through the hoop from underneath. Glue the two ends together to form the trefoil knot.

Draw a sequence of pictures to illustrate the formation of the trefoil knot.

In the picture below, the each side is glued in the same direction as its opposite side. Draw a sequence of pictures to show the gluing process and the final shape.

Take a straight string of finite length. Wrap the right half around the left half so that it is pointing to the right again and there is a hoop. Pass the right pointing piece through the hoop from above. Glue the two ends together to form the figure-8 knot.

Draw a sequence of pictures to illustrate the formation of the figure-8 knot.

Explain why it is possible to have a picture of a figure-8 knot with 100 crossings.