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An inverse problem for circle packing and conformal mapping

An inverse problem for circle packing and conformal mapping

Figure 1.1 illustrates the fact that if a region is almost packed with circles of radius <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon"> <mml:semantics> <mml:mi>ε<!-- ε --></mml:mi> <mml:annotation encoding="application/x-tex">\varepsilon</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the hexagonal pattern and if the unit disk is packed in an isomorphic pattern with circles of varying radii …