Path: utzoo!utgpu!news-server.csri.toronto.edu!mailrus!wuarchive!cs.utexas.edu!rutgers!cbmvax!mitchell
From: mitchell@cbmvax.commodore.com (Fred Mitchell - Product Assurance)
Newsgroups: comp.graphics
Subject: Re: 4-Space Basis Rotation Matrices
Message-ID: <13857@cbmvax.commodore.com>
Date: 17 Aug 90 02:09:06 GMT
References: <2494@ryn.esg.dec.com>
Reply-To: mitchell@cbmvax (Fred Mitchell - Product Assurance)
Organization: Commodore, West Chester, PA
Lines: 20

In article <2494@ryn.esg.dec.com> jroth@allvax.dec.com (Jim Roth) writes:
>
>The conceptual problem is that one cannot rotate "about" an axis; rather
>one can rotate "in a plane" or 2 dimensional subspace in n dimensions.

Or more to the point, one rotates ABOUT a plane in 4-space, as one
rotates ABOUT a line in 3-space. One would also rotate about a 3-space
in 5-space, etc. The dimension of your 'axis' of rotation in n-space
is always n-2.

In the 4-space example, rotating about a plane is fun to try to 
conceptualize. You dont pass thru the plane-axis of rotation, as
one might at first think; rather you go around it. It only appears
that you pass through it when looking at it from a 3-space (shadow)
perspective. You need a 4th-dimensional eye to truly visualize
this nightmare! :-)

-Mitchell

We are trapped in our lonely 3-D world. We miss out on so much.