Talk:Spherical Geometry: Isometry Exploration

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Why do we have questions 6 and 7 both? Rotations are translations. --Steve

I put the question this way because it "mimics" what you ask students when studying Euclidean geometry. You are absolutely right of course in stating that rotations are translations and vice versa.

What do you think Steve? Should we rewrite the last problem and ask them to "show" that rotations are translations (and hence reflections)? Feel free to rewrite that last question :-) --Barta 10:35, 22 October 2007 (CDT)

I changed both questions so as to highlight differences from and similarties to the plane. I don't recall having shown the relations between reflections and either translations or rotations in the plane, so I added that as part of the questions. --Steve 19:04, 22 October 2007 (CDT)

Excellent idea. This way the exploration is independent from what was done before. --Barta 08:46, 23 October 2007 (CDT)

I just added a question addressing the fact that on the sphere translations and rotations are the same thing. IF I have time I will write up some solutions. (unless someone beats me to it...) --Barta 08:55, 23 October 2007 (CDT)

I wonder if we really want to say that on the sphere, translations are rotations. The way I think of it, a translation should move every point along a geodesic, so that there are no translations in anything except flat surfaces (plane and its quotients); a sphere has rotations, but no translations. I wonder if we should strive for that viewpoint instead of treating spherical translations as being the same as rotations. --Steve 12:13, 24 October 2007 (CDT)

glide-reflection problem

I think the line (i.e., great circle) segment specified in the glide-reflection problem ought, instead, to be a full line (i.e., great circle). But I don't know how to create these images. --Steve 13:29, 29 October 2007 (CDT)