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Die Euklidische Ebene Und Ihre Verwandten by Heinz Lüneburg

Die Euklidische Ebene Und Ihre Verwandten

by Heinz Lüneburg
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Book cover type: Paperback
  • ISBN13: 9783764356859
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 216
  • Original Price: EUR 46.72
  • Language: German
  • Edition: 1999
  • Item Weight: 359 grams
  • BISAC Subject(s): Geometry / General

Your aid I want Nine trees to plant In rows just half a score, And let there be In each row three. Solve this. I ask no more. ( J. J ackson, Rational Amusements for Winter Evenings. London 1821) Beim Beweise vieler Sätze der Elementargeometrie nutzt man nur sehr unvollkom- men aus, da es der Körper der reellen Zahlen ist, welcher der Geometrie zugrunde liegt. Mal sind es nur die Körpereigenschaften, die man benötigt, mal da die mul- tiplikative Gruppe abelsch ist. Manchmal braucht man auch nur, da die Charak- teristik nicht zwei ist, ein andermal, da R eine Anordnung besitzt. Gelegentlich genügt es sogar zu wissen, da die euklidische Ebene eine affine Ebene ist. Diese wenigen Andeutungen machen schon ein wenig deutlich, worum es bei un- serem Thema gehen wird: Wir werden uns einerseits erheblich einschränken, indem wir hier unter Elementargeometrie nur die ebene euklidische Geometrie verstehen, also auf alles Räumliche verzichten, andererseits eine wesentliche Erweiterung des Themas Elementargeometrie vornehmen, indem wir zumindest zu Beginn unserer Untersuchungen auch beliebige projektive Ebenen in sie einbeziehen, da wir uns dieses Hilfsmittels nicht werden begeben wollen. Wir werden jedoch nicht eine The- orie der projektiven Ebenen entwickeln, wie sie etwa in den im Literaturverzeichnis aufgeführten Büchern von P. Dembowski, Hughes und Piper, Pickert oder auch von mir dargestellt wird.

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