Autoreference and magnetization in dynamic geometry

II.3 Rolling up on the pseudosphere

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Yves Martin - University of La Réunion

Laboratory of Computer Science and Mathematics (LIM, EA 2525)

ICTMT9, Metz, July 8, 2009

1. On the pseudosphere

The uniformization of the circle is used on the ellipse of equal latitudes for the vertices of the triangle. So when a point moves on more than one sheet of the pseudosphere, we can see how the covering works with continuity in direct manipulation.

2. On the hyperbolic speuddosperical surface

This Malffati's construction is made by conjugation : points A, B and C are on the surface. They are sent to Klein-Beltrami's disk. The construction is made in this hyperbolic (projective) model and sent back on the pseudospherical surface.

More about the geometry of Beltrami's surfaces in dynamic geometry (26 files in direct manipulation)

On line constructions by macros on the pseudospherical surfaces (after looking for the previous link) : you can build lines on the surfaces by yourself.

Previous work on these surfaces (2001) with Cabri-geometre.

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