## MatheMUSEments

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

## April 4, 2007

### Tesseracts: Cubes Get Hyper

Madeleine L'Engle, who wrote these words in A Wrinkle in Time, used tesseract to mean a shortcut through space and time. In her story, space-time wrinkles, or folds onto itself, creating new paths that allow characters to tesser, or travel from one end of the galaxy to the other in an instant.

Mathematicians also use the word tesseract, but they mean something different. A tesseract is another name for a four-dimensional cube, or a hypercube.

Here's one way to picture what this strange object might look like. You can start by imagining a point floating in space. A mathematical point has no length or width. Mathematicians say the point has no dimension. Moving the point along a straight path to a new position traces out a line. That line is a one-dimensional object. Shifting the line at right angles to its length traces out a square, and a square is a two-dimensional object. Moving the square at right angles to its flat surface traces out a cube—a three-dimensional object.

Here's the mind-boggling part. You have to try to imagine what would happen if you could move the cube in a new, fourth dimension at right angles to the three you've already used. Any drawing or model you might make of the resulting object would look horribly distorted. But you can still get an idea of what a tesseract would look like and even sometimes "see" it in flashes.

How might you recognize a tesseract if you ever encountered one in your multidimensional travels? Well, in our three-dimensional world, it might look something like a large cube that seemed to be spitting out a smaller one.

Even though L'Engle's concept of a tesseract is different, her book has inspired many readers to think more deeply about time and space and mathematics.

Muse, September 2000, p. 18.