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Thread: Hyperbolic plane

  1. #1
    Jun 2011

    Hyperbolic plane

    1) Explain what is meant by a hyperbolic line

    2) Explain what it means for two hyperbolic lines to be parallel

    3) Let R donate a mapping of the upper half plane onto itself, RoR = id. State three additional properties which R possesses if it is a hyperbolic reflection. If R(z) = 3zbar-5/zbar-3, show that RoR = id and give a precise geometric description of this.

    Ok for 1), I don't know the definition and google gives me nothing. Something to do with being a line in the hyperbolic plane which is a sphere? But how to put it formally?
    2) Parallel lines doesn't meet, but how to explain that in a hyperbolic sense? 3) I tried multiplying but I got no where? I don't think I understand this question too well. Unfortunately I don't know where to go to look as I don't have any book with this in. Please help professors.
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  2. #2
    Junior Member
    May 2011

    Re: Hyperbolic plane

    Check here.

    "Because there is no precise hyperbolic analogue to Euclidean parallel lines, the hyperbolic use of parallel and related terms varies among writers."

    But there's definitely info out there. Sorry I can't help more!
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