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Re: kuen surface

  • To: mathgroup at
  • Subject: [mg48109] Re: kuen surface
  • From: mathma18 at (Narasimham G.L.)
  • Date: Thu, 13 May 2004 00:08:57 -0400 (EDT)
  • References: <c7nng0$dn0$> <c7q68e$rop$>
  • Sender: owner-wri-mathgroup at

"Peltio" <peltio at> wrote in message news:<c7q68e$rop$1 at>...
> "Wolf, Hartmut" wrote
> >Yes, a single view is not enough to look at this marvelleous thing.
> I remember an article in an old issue of the Mathematica Journal that
> illustrated a function to 'cut into' 3D graphics. For a given surface an
> animation was generated with two view of the surface cut at a plane that
> gradually moved from one end to the other of the enclosing box.
> IIRC, one of the surfaces used to test this function was Kuen's surface.
> I guess the package was/is downloadable from the Mathsource, but I don't
> remember which issue it was in. The name should be Slice or SliceShow.

My suggestion instead would be to use isometric bending of surfaces of
constant negative Gauss Curvature.This is possible starting with
Sine-Gordon soliton solutions suggested by Roger Bagula as above and
also Richard Palais in 3DExplorMath.

A series of animated frames that curl the surface in ond out like
warped scrolls would give a marvellous demonstration and feel of 3D
objects rather than static slices of the same. This is perhaps because
3D perception is an assembly of  2D surfaces whose connections are
grasped together for the whole object e.g.,when bent isometrically.
Richard Palais had shown me bending among all (Jacobi function)
meridians of a Sphere (the cone,sphere and ring types). I am prepared
to work further together with anyone interested.

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