Symmetrie Gruppe Dualitt: Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des ,Used

Symmetrie Gruppe Dualitt: Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des ,Used

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Diese Arbeit enthiilt zwei grof3ere Fallstudien zur Beziehung zwischen theo retischer Mathematik und Anwendungen im 19. Jahrhundert. Sie ist das Ergebnis eines mathematikhistorischen Forschungsprojekts am Mathemati schen Fachbereich der UniversitiitGesamthochschule Wuppertal und wurde dort als Habilitationsschrift vorgelegt. Ohne das wohlwollende Interesse von Herrn H. Scheid und den Kollegen der Abteilung fUr Didaktik der Mathema tik ware das nicht moglich gewesen: Inhaltlich verdankt sie direkt oder indirekt vielen Beteiligten et was. So wurde mein Interesse an den kristallographischen Symmetriekon zepten, dem Thema der ersten Fallstudie, durch Anregungen und Hinweise von Herrn E. Brieskorn geweckt. Sowohl von seiner Seite als auch von Herrn J. J. Burckhardt stammen uberdies viele wert volle Hinweise zum Manuskript von Kapitel I. Herrn C. J. Scriba mochte ich fur seine die gesamte Arbeit betreffenden priizisen Anmerkungen danken und Herrn W. Borho ebenso fUr seine ubergreifenden Kommentare und Vorschlage. Beziiglich der in Kapitel II behandelten projektiven Methoden in der Baustatik des 19. Jahrhunderts gilt mein besonderer Dank den Herren K. E. Kurrer und T. Hiinseroth fUr ihre zum Teil sehr detaillierten Anmerkungen aus dem Blickwinkel der Geschichte der Bauwissenschaften. Schliefilich geht mein Dank an alle nicht namentlich Erwiihnten, die in Gesprachen, technisch oder auch anderweitig zur Fertig stellung dieser Arbeit beigetragen haben. Fur die vorliegende Publikation habe ich einen Anhang mit einer Skizze von in unserem Zusammenhang besonders wichtig erscheinenden Aspekten der Theorie der kristallographischen Raumgruppen hinzugefUgt. Ich hoffe, daB er zum Verstiindnis des mathematischen Hintergrunds der historischen Arbeiten des ersten Kapitels beitragt.

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