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Discussion: Roundtable
Topic: Virtual Reality Technology


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Subject:   My interpretation, Dennis,
Author: Gayla
Date: Mar 20 2003
of what you are suggesting is getting to look at different objects in different
geometries, i.e., a sphere in spherical geometry versus a sphere in hyperbolic
geometry, is that what you mean?  How trees, valleys, and mountains would form
in different geometric spaces?  I contacted Mattias Weber, who works with
hyperbolic geometry and provided the following url for a program called Snappea,
which does computations and visualizations in hyperbolic space:
http://humber.northnet.org/weeks/index/SnapPea.html

My question to M. Weber was about landscapes in hyperbolic space, but also, as
regards shapes, would a sphere look the same, and/or would there be points of
singularity...  His answer was that "spheres in hyperbolic space look exactly
the same as spheres in euclidean space", and as regards my question about points
of singularity he said: "In neighborhoods of points hyperbolic space is
indistinguishable from euclidean space,
and therefore point singularities will look exactly the same, too."  

If this is the kind of transformations you were talking about, then I, too, am
very interested to know about software out there that might let a person go
between different geometries.



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