Geometry: A Comprehensive Course

"Alucidandmasterlysurvey."—MathematicsGazetteProfessorPedoeiswidelyknownasafineteacherandafinegeometer.Hisabilitiesinbothareasareclearlyevidentinthisself-contained,well-written,andlucidintroductiontothescopeandmethodsofelementarygeometry.Itcoversthegeometryusuallyincludedinundergraduatecoursesinmathematics,exceptforthetheoryofconvexsets.BasedonacoursegivenbytheauthorforseveralyearsattheUniversityofMinnesota,themainpurposeofthebookistoincreasegeometrical,andthereforemathematical,understandingandtohelpstudentsenjoygeometry.Amongthetopicsdiscussed:theuseofvectorsandtheirproductsinworkonDesargues'andPappus'theoremandthenine-pointcircle;circlesandcoaxalsystems;therepresentationofcirclesbypointsinthreedimensions;mappingsoftheEuclideanplane,similitudes,isometries,mappingsoftheinversiveplane,andMoebiustransformations;projectivegeometryoftheplane,space,andndimensions;theprojectivegenerationofconicsandquadrics;Moebiustetrahedra;thetetrahedralcomplex;thetwistedcubiccurve;thecubicsurface;orientedcircles;andintroductiontoalgebraicgeometry.Inaddition,threeappendicesdealwithEuclideandefinitions,postulates,andpropositions;theGrassmann-PlueckercoordinatesoflinesinS3,andthegroupofcirculartransformations.Amongtheoutstandingfeaturesofthisbookareitsmanyworkedexamplesandover500exercisestotestgeometricalunderstanding.