Re: Re: need mathematica's help for exploring a certain type of mapping

*To*: mathgroup at smc.vnet.net*Subject*: [mg68593] Re: [mg68578] Re: need mathematica's help for exploring a certain type of mapping*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 11 Aug 2006 04:40:00 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200608090820.EAA21373@smc.vnet.net> <NDBBJGNHKLMPLILOIPPOMELCFBAA.djmp@earthlink.net> <200608100357.XAA21852@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

Unless I misunderstand what you say, it is not possible that a map R^3 -> R^2 could be an isometry. After all, such a map would be a homeomorphism -- a topological embedding of R^3 into R^2. As such, the map would preserve topological dimension. But dim(R^3) = 3 whereas dim(S) <= 2 for every subspace of R^2. Nabeel Butt wrote: > Dear David, > Keep the metric Eucilidean(easy to visualise in mathematica). > Also,i want a map that preserves unit distances but not necessarily all > distances. > It may happen that a mapping from R^2->R^3 that preserves unit distances > preserves all distances and hence,is an isometry. > It is proven in mathematical literature that a unit preserving map from > R^3->R^2 is an isometry. > However, for f:R^2->R^3 this is still an open question. -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**need mathematica's help for exploring a certain type of mapping***From:*"Nabeel Butt" <nabeel.butt@gmail.com>

**Re: need mathematica's help for exploring a certain type of mapping***From:*"Nabeel Butt" <nabeel.butt@gmail.com>