RE: need mathematica's help for exploring a certain type of mapping
- To: mathgroup at smc.vnet.net
- Subject: [mg68576] RE: need mathematica's help for exploring a certain type of mapping
- From: "David Park" <djmp at earthlink.net>
- Date: Wed, 9 Aug 2006 23:57:37 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I thought that the definition of an isometry was that it preserved
A mapping that did a 3D rotation of the xy-plane, plus translations in 3D
space, plus reflections in a plane would cover the isometries if we use the
Euclidean metric in both 2D and 3D.
But suppose you wanted to map onto a specific curved surface. Then are you
going to allow a different distance measuring function on the surface, a
different metric? Are we allowed to design a metric for any given mapping?
Is it possible to have an isometry then? I don't know.
djmp at earthlink.net
From: Nabeel Butt [mailto:nabeel.butt at gmail.com]
To: mathgroup at smc.vnet.net
I need to use mathematica's graphics to explore a certain
kind of problem.The following theorem is not yet proven nor disproven and
mathematica might proof useful in disproving it though.
Hypothesis:If a mapping from R^2->R^3 is unit distance preserving then it
must be an isometry.
The real issue at hand is for mathematica to generate a mapping that
preserves unit distance but is not an isometry so in the process disproving
The real problem is that R^2 consists of infinite points and it might
not be possible to check all of them.What i suggest is that you apply the
unit preserving maps to special type of figures in R^2 like the circumfrence
of the circle,square,isoceles triangle etc.
Any ideas are welcome.Thanks in advance.
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