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Johann Sebastian Bach und der Zwei-Quadrate-Satz: Über Fermats Weihnachtstheorem in Schemellis Gesangbuch

Johann Sebastian Bach und der Zwei-Quadrate-Satz: Über Fermats Weihnachtstheorem in Schemellis Gesangbuch

          
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About the Book

Johann Sebastian Bach als Mathematiker für Mathematiker, Weihnachtstheorem statt Weihnachtsoratorium, Fermat statt Fermate, Kleiner Satz statt große Besetzung, so lauten die Denkanstöße des Buches bei der Beschreibung mathematischer Strukturen in den Kompositionen Bachs, die sich jenseits einer mystifizierenden Zahlensymbolik alleine auf Basis der Zahlentheorie des 17. und 18. Jahrhunderts interpretieren lassen. Untersuchungsgegenstand ist vor allem Schemellis Gesangbuch (BWV 439 - 507) aus dem Jahre 1736 mit insgesamt 954 geistlichen Liedern. Für 69 davon hat Bach Noten beigesteuert und dabei eine zahlentheoretisch höchst bemerkenswerte Auswahl getroffen von Primzahlen, Pseudoprimzahlen und nach Fermats Verfahren zerlegbaren Zahlen. Vor allem aber zeigt die konkrete Gestaltung der Auswahl der Primzahlen unter den Liednummern, dass Bach das sog. Weihnachtstheorem von Pierre de Fermat (1607 - 1665) kannte, dem genialen französischen Amateur-Mathematiker, dessen Zwei-Quadrate-Satz beschreibt, wann eine Primzahl als Summe zweier Quadratzahlen dargestellt werden kann. Das Wissen, das Bach hier demonstriert, reicht an das höchste Niveau der seinerzeitigen Mathematik und umfasst Beobachtungen, die heute als Bausteine des modernen Beweises für diesen wegweisenden Satz der Zahlentheorie aus dem 17. Jahrhundert dienen. Auch in der Chaconne für Violine solo (BWV 1004) und im Wohltemperierten Klavier Teil 2 (BWV 870 - 893) finden sich grundlegende Konstruktionen der Zahlentheorie wieder, wie der Satz von Euklid oder Beispiele für Kongruenz und Restklassen. Im Wohltemperierten Klavier Teil 1 (BWV 846 - 869) hat Bach alle Fäden zusammengeführt und seine Zahl, die Bach-Zahl 14, als quadratische Form inverser Restklassen dargestellt, was eine mathematische Meisterleistung ist.


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Product Details
  • ISBN-13: 9783749425839
  • Publisher: Books on Demand
  • Publisher Imprint: Books on Demand
  • Height: 203 mm
  • No of Pages: 260
  • Spine Width: 14 mm
  • Weight: 263 gr
  • ISBN-10: 3749425833
  • Publisher Date: 05 Aug 2019
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Sub Title: Über Fermats Weihnachtstheorem in Schemellis Gesangbuch
  • Width: 127 mm


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