Eight and seven point degenerations of Miquel's Theorem in Laguerre planes |
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Authors: | Olaf Bröcker |
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Affiliation: | Universit?t Hamburg, Fachbereich Mathematik, Bundesstraβe 55, 20146 Hamburg, Germany, DE
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Abstract: | For M?bius planes Schaeffer [9] has proved that all seven point degenerations of Miquel's Theorem characterize miquelian M?bius planes. For Laguerre planes we have several degenerations of Miquel's Theorem with eight and seven points. We prove that all except one of these degenerations characterize miquelian Laguerre planes. The remaining degeneration characterizes elation Laguerre planes. Received 14 September 2001; revised 1 September 2002. |
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Keywords: | Mathematics Subject Classification (2000): 51B05 51B15.?: Nonlinear incidence geometry Laguerre planes Miquel's Theorem. |
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