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Math Help - Hyperbolic Geometry

  1. #1
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    Hyperbolic Geometry

    I am taking my first class with Hyperbolic Geometry and I need some help with the basics.

    I am asked to find the hyperbolic line through i and 2+2i. I understand that this line is going to be represented in the shape of a Euclidean Circle and I am able to draw this circle but I'm not sure how to express it. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by zebra2147 View Post
    I am taking my first class with Hyperbolic Geometry and I need some help with the basics.

    I am asked to find the hyperbolic line through i and 2+2i. I understand that this line is going to be represented in the shape of a Euclidean Circle and I am able to draw this circle but I'm not sure how to express it. Any help would be appreciated.

    I supose you're working with the Poincare's half (upper) plane model of a dimension 2 hyperbolic geometry,and thus you'd need a

    half circle through 1,\,2+2i with center on the real axis. There are infinite such circles, of course, but here's a

    geometric easy way to choose a "nice" one: find the equation of the perpendicular bisector of the segment determined by

    i,\,2+2i , and find its intersection with the real axis, which will be our half circle's center...

    Tonio
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  3. #3
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    Alright great...That's the process I had started. But then I guess my question is... Am I suppose to use the formula for a euclidean circle?
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    Quote Originally Posted by zebra2147 View Post
    Alright great...That's the process I had started. But then I guess my question is... Am I suppose to use the formula for a euclidean circle?

    Yes, of course...that's what we do in that Poincare's model of hyp. geometry.

    Tonio
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