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Re: kuen surface
"Peltio" <peltio at twilight.zone> wrote in message news:<c7q68e$rop$1 at smc.vnet.net>... > "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.