15068

1442 دكتري

دكتري

هندسه تصويري

اصفهان : دانشگاه صنعتي اصفهان

1398

هفت، [87]ص.

قهرمان طاهريان

اعظم اعتماد

واژه نامه

محمدرضا ودادي، مهدي شريف زاده، اسماعيل حسيني، احسان ممتحن

1398/06/31

كتابنامه

رياضي محض

رياضي

1398/06/31

2559718

Degenerate Forms of Miquel Axiom in Benz Planes Sajad Mohseni Takaloo s mohseni@math iut ac ir 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Sayed Ghahreman Taherian taherian@cc iut ac ir Advisor Dr Azam Etemad Dehkordy ae110mat@cc iut ac ir 2010 MSC 51B20 51H15 51A20 Keywords Miquel axiom Benz planes ovoidal Laguerre planes dilatation Apol lonius Problem stereographic projection Abstract1 AbstractWe study Benz planes with dilatations and show that for a Benz plane B P C G the following statements are equivalent B satis es a degenerate form of Miquel axiom called MIII and for each point 6 W P the a ne derivation W B is desarguesian For each two non parallel points P Q P there exists an automorphism of P Q B such that Fix P Q and in the a ne derivation Q B the map is P Q P Q the point re ection at P Hence by 15 if L is an ovoidal Laguerre plane where the associated skew eld hascharacteristic 2 and satis es MIII then it is a miquelian Laguerre plane i e for 6these planes MIII and M8 are equivalent cf theorem 5 6 After that we deal about a classical geometrical problem about triangles and circlescalled Apollonius Problem

قهرمان طاهريان

اعظم اعتماد

محمدرضا ودادي، مهدي شريف زاده، اسماعيل حسيني، احسان ممتحن