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geometryregioninversionprogramming-tools

Circle Inversion with programming languages

How can I find Circle Inversion of any region with programming tools?

For an example; consider problem of finding circle inversion for below region :

enter image description here

Any ideas or solution would be appreciated, thanks.

Solution

  • Inversions are easily described using complex numbers. We shall therefore assimilate points with complex numbers and represent hyperbolic points by complex numbers with modulus strictly less than one. The inversion with respect to a circle with center c and radius r is the function which transforms any complex z into a complex z' defined by :

    enter image description here