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parallel lines in hyperbolic geometry

Defines: 
asymptotically parallel, asymptotically parallel lines, hyperparallel, hyperparallel lines, disjointly parallel, disjointly parallel lines, ultraparallel, ultraparallel lines
Major Section: 
Reference
Type of Math Object: 
Topic

Mathematics Subject Classification

51-00 no label found51M10 no label found

Comments

For the time being, I am leaving this open for world editing, as I am unsure about the clarity of the presentation of the two kinds of parallel lines (which has the added complication that each kind has at least two names). Also, if someone wants to add pstricks pictures about how these relate to other models of hyperbolic geometry, feel free to do so! Otherwise, I would greatly appreciate it if you would not edit the pictures without obtaining my consent first.

In any case, I plan on adding entries on the Poincar\'{e} disc model and the Poincar\'{e} upper half plane model later on today and, if it has not been done already, I will add what these parallel lines can look like in these models.

Warren

I have decided to remove the option of world editing from this entry. If anyone adds alternative models of hyperbolic geometry and can incorporate graphics, I will allow him/her to edit this entry appropriately.

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