From Point to Hypercube
By moving an object in any dimension, you can create an object in the next dimension. Here is how to move from a point to a line segment to a cube to a four-dimensional hypercube.
A two-dimensional picture of a three-dimensional model of a four-dimensional hypercube.
- A point has zero dimensions.
- Moving a point in a straight line generates a line segment. A line segment is a fundamental one-dimensional object.
- Shifting a line segment at right angles to its length generates a square. A square is a basic two-dimensional object.
- Moving the square at right angles to its plane produces a cube, a basic three-dimensional object.
- What would appear if you could move a cube in a fourth direction, at right angles to all its edges? The result would be a hypercube.
Moving from a point to a line segment to a square to a cube to a hypercube, or tesseract.
A hypercube is also called a tesseract, a term used by science-fiction writers, such as Robert Heinlein in his story "—And He Built a Crooked House" and Madeleine L'Engle in A Wrinkle in Time.
A hypercube looks mind-boggling in a two-dimensional drawing on paper (above), but the fancy graphics of modern computers have allowed mathematicians to create fascinating images on a screen that make it possible to visualize and understand objects such as hypercubes and hyperspheres in higher and higher dimensions!
A computer-generated image showing torus-shaped "slices" of a four-dimensional hypersphere.
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