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  "body": "\n## Summary\n\nA Möbius transformation is a map $z \\mapsto \\frac{az + b}{cz + d}$ of the Riemann sphere to itself, with $ad - bc \\neq 0$, see the [[definition|0B346DDAM5]].\nThese maps are bijective and holomorphic, they preserve angles, and they [[map circles and lines to circles and lines|0SXDHQM2MH]].\n",
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