Research work · 1999
Hyperspheres And Tesseracts
Clifford A Pickover
Oxford University Press eBooks
Abstract
Abstract II FBI Headquarters, Washington, D.C., 8:00 P. M. You’ ve returned to your FBI office. “I want to talk more about hyperspheres and tesseracts, the 4-D counterparts to spheres and cubes.” You draw a circle on the board with a dot at its center. ‘ ‘ A circle is the collection of points (on a plane) all at the same distance r from a point. A sphere is the collection of points (in space) all at the same distance r from a point. Similarly, a hypersphere is the collection of points (in hyper space) all at the same distance r from a point.” Sally steps closer to the board. “If a hypersphere with a seventeen-foot radius came into our world, what points would be on it?” She points her finger in the air. ‘ ‘ Assume that its center is located at my fingertip.” For several seconds, you stare at Sally’ s elegantly manicured nails before taking a string from your drawer and measure off seventeen feet. “Sally, may I borrow one of your earrings?” She removes a small, golden earring from her left ear and hands it to you. You tie a knot around it. You tie the other end of the string to her finger and walk away until the string is taut. ‘ ‘ All the points that are seventeen feet from your fingertip would be on the hypersphere. Right now, your earring would touch the hypersphere’ s edge.