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Math Help - Geometry/Topology: Hyperbolic Parametrization

  1. #1
    Junior Member
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    Geometry/Topology: Hyperbolic Parametrization

    Hi!

    I'm to find the hyperbolic length of a curve composed of three lines, from P=i, to R = ti, to S = 4 + ti, to Q = 4+i, where t>0, and then find which t makes this value minimal. I've got the formula for hyperbolic length, but it's in terms of x(t) and y(t), and I basically don't know how to actually parametrize the curve so I can fit it in the formula & integrate properly.

    ( L = [\int x'(t)^2 + y'(t)^2) / y(t)]

    I get the sense this is seriously basic stuff, but if anyone could help me out I'd really appreciate it. Thanks.
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  2. #2
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    PR: x(s)=0, y(s)=s s in [1,t]
    RS: x(s)= s, y(s)=t and s in [0,4]
    SQ: x(s)=4 y(s)=s s in [t,1]


    I changed your t (in the equation for L) with s, cause we have already t as a parameter and not as a dumby variable in the integral.
    and the fact that I wrote that s is in ___, is for the integration limits.
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