= Conformal map of a circular lens
Two intersecting <circles> bound a lens. A <Möbius transformation> sending their intersection points to zero and infinity sends the two boundary arcs to rays, and the lens to a sector. A suitable power straightens the sector to a half-plane. The chosen sector and its branch must be identified by an interior test point; merely squaring an arbitrary boundary-straightening map need not be injective on the intended domain. A <Cayley transform> then gives a conformal bijection to a disc.
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