The two pictures of a knot, together with an explanation of what we can learn from them - for Prepare the Space.

Enlarged images of the two pictures are available by clicking the pdf link that is below the text

Introduce the pictures by saying 'Some people said that Jesus had uttered a hard saying. Here is a hard mathematical construction for you to puzzle over.'

An explanation of the drawing
We all know what it means to say that a loop of string is 'knotted' – it means you can't simply untie it without cutting it. But suppose a loop of string has two knots in it, like the diagram (fig. 1). How do you know that you can't somehow combine the two knots in such a way that one of them can be used to untie the other one?