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The 4th Dimension

Date: 2/10/96 at 15:39:37
From: Anonymous
Subject: 4th Dimension, the Over-Sphere.

In my Geometry class, about two weeks ago, we read the book, 
_Sphereland_.  In it, when it talked about Overcubes and 
Overspheres, I couldn't visualize this. Even though I know 
we really shouldn't be able to see 4d figures, just as 2d creatures 
can't visualize 3d creatures, is there any way you could describe 
an oversphere?

Thank you in advance,
Mike L.

Date: 3/8/96 at 23:14:23
From: Doctor Jodi
Subject: Re: 4th Dimension, the Over-Sphere.

Hi Mike! Thanks for your question! I love thinking about the 
fourth dimension.  For reading about the fourth dimension, there 
are a few other good books around.  The classic, called _Flatland_ 
(by Edwin Abbott), talks mostly about a 2D world, but the 2D hero, 
a Square, also travels into a 1D world and has an encounter with a 
sphere that might help you relate to questions about the oversphere.

Another book I'd particularly recommend is _Planiverse_, which 
talks about lots of technical details from zippers and doors to playing 
volleyball in a 2D universe.  It's an awesome story and again should 
give you ideas about 4D.

For pictures on the web, try   

which will give you a sense of what 4-D polyhedra, like the 
hypercube, the four-dimensional analogue of the cube, might look 

Good luck and please let us know how it goes!  Feel free to write 
back with more questions!

-Doctor Jodi,  The Math Forum

Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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