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Re: D=5



At 9:57 AM -0400 9/19/02, Robert Cohen wrote:
Am I the only one
to suffer from this limitation in this company?

No. I'm with you.

If I never experienced a 3-dimensional object, I would see the drawing above
as two 2-D squares with their corners connected. Since I know what a cube
looks like, I can visualize what the 3-D image "looks like" (in 3-D) that
has the 2-D projection drawn above.

If I draw two 2-D cubes (like that above) side by side and connect their
corners, I see two 2-D representations of cubes with their corners
connected. I acknowledge that it is represents the 2-D projection of a 4-D
image but I can't visualize what the 4-D image "looks like" (in 4-D).

I think it helps to have a 2-D image of a 4-D cube _rotate_ and/or view it
with 3-D glasses, and there are various web sites and computer programs
(http://www.nucalc.com/) that will do that for you.

<http://darkwing.uoregon.edu/~koch/java/FourD.html>
<http://dogfeathers.com/java/hyprcube.html>
<http://www.flowerfire.com/ferrar/java/hypercuber/HyperCuber.html>
<http://www.geom.umn.edu/docs/holt/tesseract/top.html>

Sagan also shows you a 3-D projection of a 4-D cube in Cosmos.

Larry