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Regularizing quadrangles in the Möbius plane
For any given cross ratio $$\delta \in \mathbb C$$ we define a non-linear Möbius-invariant procedure creating vertices of a new quadrangle from a given quadrangle. Reiterating the process we discover a remarkable regularizing property. The values $$\delta \in \mathbb C$$ for which this phenomenon of regularization develops are examined. The …