Oct 2002: Hyperspace: Up, Out, and Away
|
|
|
THE DISCOVER BOGGLER Oct 2002: Hyperspace: Up, Out, and Away |
 |
|
| Ever since I read Flatland in 8th grade I have been entranced by the idea of four-dimensional space. Over the years I have written a paper about four-dimensional optical illusions, consulted on visual effects for feature films involving the fourth dimension, and made models of 4-d figures. My favorite 4-d creations by other people include documentary films by Brown math professor Thomas Banchoff, the novel The Boy who Reversed Himself, and Canadian animator Norman McLaren's whimsical drawings of 4-d tennis courts and houses.
Tesseract: Cube to the Fourth. A rather standard explanation of four-dimensional space by generalizing from square to cube to hypercube. Not a lot of fun as a puzzle, but important background. 4D Tictacktoe. The challenge for me was to make 4-space fun and understandable. I don't think I succeeded entirely, but I'm pleased to have found a 4-d game that I could explain in a magazine. You don't really have to understand 4-space to solve this puzzle, but it helps. HyperCross. Martin Gardner posed the problem of counting ways of unfolding a hypercube many years ago in his column in Scientific American. One of my puzzle testers solved this difficult problem independently before finding that Gardner had already published the answer. |
|
Copyright 2000 Scott Kim. All rights reserved. |
