Ann Van Hierden, age 15, of Picture Butte, Alta., Canada, for her question:

WHAT CAUSES THE SHAPE OF THE RAINBOW?

Almost all nature's wonders contain concealed lessons in mathematics. For example, the colors and shape of the glimmering rainbow are based on indisputable rules of geometry. Behind the scenes, the whole thing depends on the assorted wavelengths of light, plus angles created by a circle.

Actually the rainbow resembles a magician's trick on a grand scale. It depends on light beams, mirrors and even has a dark curtain to show off the dazzling display to its best advantage. The lights are sunbeams, the mirrors are falling raindrops, and the backdrop is a dark, weeping cloud.

    When all these items are in place, an observer on the ground may behold the glimmering arch of the rainbow. The sun and the cloud must be rather low and facing each other from opposite sides of the sky. For example, if the sun is almost at the top of the sky, then the rainbow barely peeks above the horizon.

The colored bands form definite angles with the sunbeams as they zoom across the sky. The red band forms angles of about 42 degrees, and the blue bands about 40 degrees. When a second bow appears, its larger circle forms angles of about 50 degrees.