Creating N-cubes: An Overview
Make-em yourself and then find their Snakes
Dennis Clark
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Creating N-cubes: An OverviewMake-em yourself and then find their SnakesDennis Clark |
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A 5-space cube with colored line sets. |
A 5-space cube with a snake. |
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Do you think you could draw a square on a blackboard? Certainly. Could you
draw a two-dimensional hypercube; a 2-space cube? You bet. A square is a
two-dimensional hypercube or 2-space cube. Can you draw a normal cube on the blackboard?
I think so. You might draw two overlapping diamonds (squares) and then draw a line from
each corner of one diamond to its corresponding corner on the other diamond. You just drew
a cube; a 3-space cube. Now, you're ready for a 4-space cube called a tesseract.
Draw two normal cubes (two 3-space cubes) close to each other and connect each corner of
one cube to its corresponding corner on the other cube. That's a tesseract, an n-space cube
where n=4. So you already know the secret of drawing an n-space cube. Just take two
(n-1)-space cubes and connect their corresponding corners together. That's how to draw an
n-space cube.
Well, that's one way to draw an n-space cube. There are many different ways! If you're interested in an elegant, simple, mathematical way of drawing orderly looking Ncubes, these web pages show you one way that it can be done. The idea is to demonstrate some binary arithmetic and perverted geometry (topology) in a fascinating, graphic way. If you're a High School teacher, you might like the included lesson plan. There's even an included research project on finding maximal length closed paths or loops (snakes) in N-space cubes. |
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| Creating N-cubes: An Overview | Creating N-cubes is easy. I can show you how. |
| Making Tesseracts | Pictures of an N-cube classroom experience. |
| How to Draw N-space Cubes | 71 large 200k web pages. |
| How to Draw N-space Cubes | A 439k PowerPoint file (includes all 71 slides). |
| Chasing Snakes in N-space Cubes | 53 large web pages. |
| Chasing Snakes in N-space Cubes | A 502k PowerPoint file (includes all 53 slides). |
| Ncubes.exe | A 348k Visual Basic program to draw N-cubes. |
| Ncubes.exe Program Description | Web page that shows big (80k) captured ncubes.exe screens. |
| 7-space Snakes | 326,105 7-space snakes found so far. *** 16 mb *** |
| Unique Snake data | A list of the unique 3,4,5, and 6-space snakes. |
| Ncube Lesson Plan | appropriate for grades 9 through 12 |
| Ncube Author bio | My life in a very small nutshell. |
