Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

March 28, 2007

Glitter Trap

You've probably looked at your distorted reflection in one of the shiny ornaments that decorate shops and homes during the holiday season. But you may be surprised to learn what the reflections in a pyramid of silvery balls are like.

You can try this at home with four round Christmas tree ornaments and a small flashlight. Large, silver balls work best.

Place three of the balls on a table so they touch one another and form a triangle. Position the fourth ball on top of the other three to create a pyramid. In a darkened room, shine the flashlight through the opening in between the ornaments and into the center of the pile. You'll see an intricate pattern of light and dark patches among the balls.

University of Maryland student David Sweet has taken this procedure one step further. He's photographed the patterns that appear when the four-ball pyramid is lit from below and has blue and red poster boards placed outside two of the faces. The reflections of the colors bounce back and forth among the mirror-like balls and create striking patterns of blue, red, white, and black.

It turns out that the boundary between the colored patches is very complicated. If you magnify a part of the boundary, you see a patchy pattern that looks like the original, unmagnified image. Zooming in further, you see even more of the same patchy pattern. A pattern that looks similar at different magnifications is known as a fractal.

But this "glitter trap" is more than a toy for creating colorful patterns. Among other things, the behavior of light in a stack of mirrored balls can help mathematicians and physicists picture how electrons wander through the materials used to make transistors, computer chips, and other electronic devices.

Muse, December 1999, p. 37.

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