Generalizations of Casey’s Theorem for Higher Dimensions
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We give generalizations of Casey’s theorem and its converse for higher dimensions. We also present a multidimensional generalization for the problem of Apollonius. To do this we introduce a notion of ψ-tangent for a generalized k-sphere that touches a number of generalized n-balls in proper manner.
Keywords and phrasesCasey’s theorem Ptolemy’s theorem problem of Apollonius
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