Classifying two-dimensional shapes

Prepare to be amazed!

There is a fascinating way of forming the regular polygons, using the fact that the number of lines of symmetry increases as the number of sides increases. (For example, a regular triangle has three lines of symmetry, a regular quadrilateral has four, and so on.) You need two mirrors taped together, so that they can open out like the covers of a book. Draw a straight line on a sheet of paper and place the two mirrors, opened at 120 degrees across the line, so that you can see the reflections in the mirrors. With care, you should be able to arrange the mirrors so that you can see a regular triangle in them. Then slowly close the two mirrors. As you do this, the image will successively form each of the regular polygons. This is a delightful experience, not to be missed!

Incidentally, as the number of sides increases the polygon approximates more and more closely to a circle. This is why mathematicians like to think of a circle as a regular polygon with an ‘infinite’ number of sides.