Geometry: A Comprehensive Course

Geometry: A Comprehensive Course
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作者:
出版社: Dover Publications
1988-12
版次: 1
ISBN: 9780486658124
定价: 181.50
装帧: 平装
开本: 其他
纸张: 其他
页数: 464页
正文语种: 英语
  • "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.
  • 内容简介:
    "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.
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