Abstract: Recently, there has been a lot of interest in Apollonian circle packings where the curvatures turn out to be integers, and the properties of the integers that occur as curvatures. We shall reframe this in terms of the binary hermitian forms corresponding to generalized circles and use that theory to derive the Descartes Four Circle Theorem, and similar theorems for other kleinian circle packings. We shall use this to prove the curvatures in other kleinian circle packings are algebraic integers in certain number fields.
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