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Math Help - poincare: find the distance between the points

  1. #1
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    poincare: find the distance between the points

    I need some help finding the Poincare distance
    I have tried to do this problem, but I know my answer is wrong!
    Please Help me:

    Let Gamma be the interior of the unit disk centered at the origin in the xy-plane, (x^2+y^2 <1). Find the poincare distance between the following pairs of points.
    (0,0) and (1/2,0).
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    I need some help finding the Poincare distance
    I have tried to do this problem, but I know my answer is wrong!
    Please Help me:

    Let Gamma be the interior of the unit disk centered at the origin in the xy-plane, (x^2+y^2 <1). Find the poincare distance between the following pairs of points.
    (0,0) and (1/2,0).
    Okay, what have you done to get your "wrong" answer? In particular, what formulas are you using?

    I assume you are talking about the Poincare disk model for hyperbolic geometry.
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  3. #3
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    Find A
    TU is the line x=
    T= ( , (√3)/2)
    U=( , - (√3)/2)
    Find the equation of the line tangent to gamma at T (Perpendicular to radius of T)
    o The slope of point T is √3
    o Slope of the perpendicular to the radius is -1/√3
    o Equation of the line: y = -1/√3 x + 2/√3
    A
    o 0= -1/√3 x + 2/√3
    o X=2
    o A =(2,0)
    Find midpoint of AA
    ( 5/4 , 0)
    Equation of the perpendicular bisector
    X= 5/4
    Midpoint of BA
    ( , 0)
    Intersection of midpoint and perpendicular bisector
    (5/4, 0)
    Find the radius (r)
    r =
    delta( the other circle)
    o y + (x- 5/4) = 9/16
    So P and Q are the simultaneous Solutions of
    x + y =1
    y + (x- 5/4) = 9/16

    Then we find P and Q and then the cross ratio, but my problem is that the circle delta creates doesnt include B, so I feel I did something wrong along the way. I feel my A is wrong. I really dont know Please help me.

    Thanks
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