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Möbius transformations are conformal, bilinear functions of the form
 
Möbius transformations are conformal, bilinear functions of the form
   −
f(z) = (az + b)/(cz + d)
+
:<math>f(z) = \frac{a z + b}{c z + d}</math>
    
where a, b, c, d are real numbers, and ad - bc =\= 0.  It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.
 
where a, b, c, d are real numbers, and ad - bc =\= 0.  It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]
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