# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sun, 26 May 2013 07:07:13 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Hyperbolic Geometry...Posted: Fri, 20 Mar 2009 01:42:07 UTC
 Senior Member

Joined: Thu, 5 Mar 2009 14:02:53 UTC
Posts: 75
Hi guys,

How do you go about showing that a hyperbolic isometry of is determined uniquely by the images of any 3 non-collinear points?

Further more, how can you show from this that every hyperbolic isometry is the product of at most 3 reflections in lines?

Many thanks. x

PS - we are using the half plane model for hyperbolic space.

Top

 Post subject: Re: Hyperbolic Geometry...Posted: Fri, 20 Mar 2009 01:55:27 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6010
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Hi guys,

How do you go about showing that a hyperbolic isometry of is determined uniquely by the images of any 3 non-collinear points?

Further more, how can you show from this that every hyperbolic isometry is the product of at most 3 reflections in lines?

Many thanks. x

PS - we are using the half plane model for hyperbolic space.

(1) Just like the Euclidean case --- first show that it must fix the three lines, and extend from there.

(2) Find a line that reflect i to f(i), then it remains to either reflect in a line through f(i) or rotate about f(i), both possible with at most 2 reflections.

Top

 Post subject: Posted: Fri, 20 Mar 2009 02:07:03 UTC
 Senior Member

Joined: Thu, 5 Mar 2009 14:02:53 UTC
Posts: 75
Thanks outermeasure, but could you please be a little more explicit?

Many thanks.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous