🚀 go-pugleaf

asimov@nas.nasa.gov (Dan Asimov) writes:
>Yet a third notion is a manifold which happens to be a metric space which
>arose through embedding the manifold in Euclidean space, by measuring the
>distance across the Euclidean space.  Interestingly enough, this is not
>very often considered in math research.

>But as *such*, with the extrinsic metric (the one obtained from the
>distance across R^3), your helix will, of course, *not* embed
>"isometrically" in R^2, which I believe is your point.

That was indeed my point, although from the rest of your message, I
had misunderstood what the manifold really was. However, I had thought
that "embedding" really meant in R^n with the appropriate n-dimensional
Cartesian metric: each point described with the corresponding n-tuple.

The thing I really misunderstood seems to have been the theorem. In my
sense of embedding, is there a known minimum N for which *any* 1-D
manifold will extrinsically embed in R^N?

Gruss,
Dr Bruce Scott                             The deadliest bullshit is
Max-Planck-Institut fuer Plasmaphysik       odorless and transparent
bds at spl6n1.aug.ipp-garching.mpg.de                 -- W Gibson

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