← The Folded Line · Lesson 1 of 4
A fold is a mirror
Put a dot near each of two corners of a sheet and fold so one dot lands exactly on the other. Unfold it. The crease runs exactly halfway between the dots, and square to the line joining them.
That is all a fold is: a mirror. Every point on one side lands on its reflection on the other side, the same distance from the crease. Folding edge onto edge does the same for lines — the crease splits the angle between them in half, with no protractor.
Mathematicians have listed the ways a single fold can line things up — seven of them. One can bring two points onto two lines at once, and with it a sheet of paper can trisect an angle, which a compass and ruler cannot.
You fold one dot exactly onto another. Where does the crease lie?