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Thread: Inversion and Poincare Models

  1. #1
    Junior Member
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    Inversion and Poincare Models

    I am trying to understand hypercycles and horocycles in the Poincare Disk Model and Upper-Half Plane Model.
    What I am wondering is if I have an understanding of the point of inversion that will take these hypercycles into the two models.
    Attached is a picture of what I am trying to understand if anyone can help explain it to me.
    Inversion and Poincare Models-img_0494.jpg
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  2. #2
    Junior Member
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    Re: Inversion and Poincare Models

    I may have started to answer my own question...but want to check to make sure.

    So I have in my notes if from the Poincaré Disk model we make the point of inversion an ideal point on the base circle, then the inversion will take the disk into the half plane.

    Therefore, what I should have said in the picture is, "another inversion with pole ON the boundary line" will take it into the disk.

    That means the first inversion would have been outside the boundary line. Correct?
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