03411nam 2200637 450 991046070050332120200917021826.01-4426-5644-110.3138/9781442656444(CKB)3710000000433123(EBL)3431994(OCoLC)929153286(MiAaPQ)EBC4669449(CEL)447499(OCoLC)918588755(CaBNVSL)kck00235790(DE-B1597)465700(OCoLC)944178742(DE-B1597)9781442656444(Au-PeEL)EBL4669449(CaPaEBR)ebr11255982(OCoLC)958557737(EXLCZ)99371000000043312320160920h19751975 uy 0engur|n|---|||||rdacontentrdamediardacarrierN-gons /Friedrich Bachmann and Eckart Schmidt ; translated by Cyril W. L. GarnerToronto, [Ontario] ;Buffalo, [New York] :University of Toronto Press,1975.©19751 online resource (208 p.)Mathematical Expositions,0076-5333x ;Number 18Includes index.1-4426-5154-7 Includes bibliographical references and index.Frontmatter -- Contents -- Authors' preface -- Translator's preface -- Summary of contents -- Introduction -- 1. Cyclic classes of n-gons -- 2. Cyclic mappings of n-gons -- 3. Isobaric cyclic mappings -- 4. Averaging mappings -- 5. Idempotent elements and Boolean algebras -- 6. The main theorem about cyclic classes -- 7. Idempotent-transfer. Residue class rings of principal ideal domains -- 8. Boolean algebras of the n-gonal theory I -- 9. Boolean algebras of the n-gonal theory II -- 10. Rational components of an n-gon -- 11. Complex components of an n-gon -- 12. The real components of an n-gon -- 1. Lattices -- 2. Cyclotomic polynomials -- List of symbols and notations -- Index This book, a translation of the German volume n-Ecke, presents an elegant geometric theory which, starting from quite elementary geometrical observations, exhibits an interesting connection between geometry and fundamental ideas of modern algebra in a form that is easily accessible to the student who lacks a sophisticated background in mathematics. It stimulates geometrical thought by applying the tools of linear algebra and the algebra of polynomials to a concrete geometrical situation to reveal some rather surprising insights into the geometry of n-gons. The twelve chapters treat n-gons, classes of n-gons, and mapping of the set of n-gons into itself. Exercises are included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.(Mathematical Expositions No. 18)Mathematical expositions ;Number 18.PolygonsSet theoryElectronic books.Polygons.Set theory.516/.22Bachmann Friedrich1909-983272Schmidt EckartGarner Cyril W. L.MiAaPQMiAaPQMiAaPQBOOK9910460700503321N-gons2244590UNINA