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Record Nr. |
UNINA9910460700503321 |
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Autore |
Bachmann Friedrich <1909-> |
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Titolo |
N-gons / / Friedrich Bachmann and Eckart Schmidt ; translated by Cyril W. L. Garner |
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Pubbl/distr/stampa |
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Toronto, [Ontario] ; ; Buffalo, [New York] : , : University of Toronto Press, , 1975 |
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©1975 |
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ISBN |
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Descrizione fisica |
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1 online resource (208 p.) |
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Collana |
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Mathematical Expositions, , 0076-5333x ; ; Number 18 |
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Disciplina |
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Soggetti |
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Polygons |
Set theory |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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 |
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included throughout, and two appendixes, by Henner Kinder and Eckart Schmidt, provide background material on lattices and cyclotomic polynomials.(Mathematical Expositions No. 18) |
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