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HAIT Journal of Science and Engineering C Volume 4, Issues 1-2, pp. 5-108 © 2007 Holon Institute of Technology |
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Packing of complex spheresDov Aharonov |
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Department of Mathematics Technion - Israel Institute of Technology, Haifa 32000, Israel e-mail: dova@techunix.technion.ac.il Received 22 March 2006, accepted 24 June 2006 |
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In what follows we deal with a "complex version" of packing of spheres. Among other things we present a "complex" generalization of the beautiful "Four Circle Theorem of Descarte" for arbitrary finite dimension. The "Boul Of Integer Property" (BOIP) of F. Soddy is extended in various directions. We also present a new approach to "Mauldon Inclination Theorem". This includes a consideration of the hyperbolic space as a projection of a "complex sphere" in an higher dimension. Our methods are mainly geometrical, but in some cases it is more natural to use the classical "Darboux-Frobenious" theorem, which is purely algebraic. |
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