What is symmetry?

The chapter begins with four beautiful things: a flower, a butterfly, a rangoli and a pinwheel. What makes them so pleasing to look at? Not only their colours. In each of them, some parts of the figure are repeated, and the repeats happen in a definite pattern. Try it with your own hands: press your palms together, and every finger meets its partner exactly.

Look at each one closely.

• The flower looks the same from many different angles, because its petals are all alike and are spread evenly around the centre.
• In the rangoli, the red petals come back onto themselves when the rangoli is turned by 90° (a quarter turn) around its centre, and so do its other parts.
• The pinwheel has a hexagon in the middle, and the same shape is stuck onto each of the hexagon's sides, so the pattern repeats as you go round.

Now think of a picture of clouds. Clouds have lovely shapes, but no part of them repeats in a definite pattern. So the book says the first four figures are symmetrical and the clouds are not.

A symmetry is a part, or parts, of a figure that are repeated in some definite pattern. When a figure is made of parts that repeat in a definite pattern, we say it has symmetry, or that it is symmetrical. Great buildings such as the Taj Mahal and a temple gopuram are built with symmetry too.