Let and be geodesic segments of equal length. Prove that there is a hyperbolic rigid motion that maps and onto and , respectively.

Once again, completely lost. (Headbang)

Printable View

- Mar 25th 2010, 12:51 PMPinkkHyperbolic rigid motion
Let and be geodesic segments of equal length. Prove that there is a hyperbolic rigid motion that maps and onto and , respectively.

Once again, completely lost. (Headbang) - Mar 29th 2010, 07:00 PMPinkk
Any suggestions?

- Apr 5th 2010, 04:48 PMPinkk
Okay, so I know the cases will probably have to divided up depending on if the geodesic segments are vertical lines or arcs of circles centered on the x-axis, and there has to be some inversion(s), but after that point I am just not sure.

- Apr 5th 2010, 07:21 PMxxp9
so you're using the upper plane model of the hyperbolic geometry, are you?

- Apr 5th 2010, 07:24 PMPinkk
Yes, the upper half plane, so the hyperbolic rigid motions we have covered so far are inversions where the center is located on the x-axis, horizontal translations, and reflections across vertical lines.