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Hyperspace and the 4th Dimension

Date: 9/20/95 at 18:32:20
From: Anonymous
Subject: Hyperspace

May we have a general definition of hyperspace?  Our setting
is a tenth grade geometry class.

Date: 10/7/95 at 11:22:17
From: Doctor Andrew
Subject: Re: Hyperspace

Hi.  In all the science fiction I've read hyperspace has
seemed to be an area in the 4th dimension but not in our 3rd 
dimensional universe.  I think authors generally conceive of our
third dimensional universe as some really convoluted shape in the
4th dimension.  

An analogy would be to draw something looking like a small
intestine on a piece of paper and declare that in normal movement a
spacecraft has to stay  in the boundaries of this shape.  So, to get 
from one end to another could take a really long time.  When a 
spacecraft "goes into hyperspace" it crosses this boundary.  Since the 
shortest distance between two points on the piece of paper is a line, 
going through hyperspace can save a lot of time.  This is my 
impression from what I've read; it's not really mathematical.  There 
may be issues of relativity involved with how the shape of a 3 
dimensional universe fits into the 4th dimension.

If you are just wondering what the 4th dimension would be like, I 
would start by thinking of the simplest shape we know in 4 
dimensions: a sphere.  Imagine a set of points that is equidistant 
from a 4th dimensional point (w,x,y,z).  Distance is just the sum of 
the squares of the distances like in 3 dimensions.  This helped me 
think about it.  I remember that the book Flatland was fun to read; I 
read it in 9th grade.  It talks about the 4th dimension and how it 
would be perceived by three-dimensional creatures.

If we come up with something more formal about hyperspace we'll be 
glad to send it to you.  I haven't really come across anything about it 
in any math classes; I'm not really sure it is a useful notion in 

The 4th dimension is useful, as is any dimension, but I think 
hyperspace is more of a Physics/Sci Fi sort of thing.

-Doctor Andrew,  The Geometry Forum
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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