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The radius of image of a circle under mobius transformation

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  • 1.  The radius of image of a circle under mobius transformation

    Posted Aug 11, 2021 08:04 AM

     

    A Mobius transformation of the plane takes z↦az+bcz+dz↦az+bcz+d. These are known to take circles to circles, but given an explicit circle, how do we compute the radius.

    Let's parameterize our circle by z(t)=z0+re2πintz(t)=z0+re2πint. What is the radius and center of the image circle?

     

    az(t)+bcz(t)+daz(t)+bcz(t)+d

     

    I am looking for a computational proof that the image is a circle so I can find the (Euclidean) radius and centerIn my application, I have an approximate circle {z0+e2πint:t∈1NZ}{z0+e2πint:t∈1NZ} where NN is a large number. If we act the Mobius transformation pointwise, these spaces will no longer be evenly spaced out. So I decided it's better to compute the Euclidean center and radius if possible.



  • 2.  RE: The radius of image of a circle under mobius transformation

    EMPLOYEE
    Posted Aug 11, 2021 08:07 AM

    Hello @ObviousKiwi !

    It's really fascinating what you are doing, but how is it related to the HPE Networking?