One early autumn, I found myself at a school in rural Norfolk, watching a lesson on two-dimensional shapes. The teacher was giving key facts about particular shapes and the pupils had to work out what the shape was. She started easy with square, circle, triangle but eventually found her way to the kite, the mathematical name for a four-sided shape which has two pairs of equal, adjacent sides (yes, it looks like a kite!).
Teacher: OK, I’m thinking of a shape. It has four sides. Anyone want to guess?
Pupil: Is it a square?
Teacher: No, but good guess because a square does have four sides. Anyone else?
Teacher: No… let me tell you something else about it: it has two pairs of equal length sides.
Pupil: It could be a rectangle, Miss!
Teacher: Yes, it could be, but it could be other things too…
Pupil: I think it could be a parallelogram, Miss.
Teacher: That’s a good guess, it could be, because parallelograms have two pairs of equal length sides don’t they?
Pupil: Is it a rhombus?
Teacher: No… here’s another clue… the equal sides are not opposite each other.
There is silence, save for the sound of heads being scratched. Headlice were common in rural East Anglia at the time.
Teacher: Hmm, let’s see if I can help with another clue. You might see some string attached to one of these.
Pupil: Miss! Miss! I know it! It’s a conker!