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Die Crofton-Formel

In: Ein Schaubild der Mathematik

Author

Listed:
  • Dmitry Fuchs

    (University of California Davis, Dept. Mathematics)

  • Serge Tabachnikov

    (Pennsylvania State University, Dept. Mathematics)

Abstract

Zusammenfassung Die Crofton-Formel bezieht sich auf die Menge orientierter Geraden in der Ebene. Wie in der geometrischen Optik werden wir orientierte Geraden mitunter als Lichtstrahlen betrachten und sie als Strahlen bezeichnen. Eine orientierte Gerade ist durch ihre Richtung φ und ihren Abstand p om Ursprung O definiert. Dieser Abstand ist vorzeichenbehaftet (siehe Abbildung 19.1). Der Strahlenraum ist also ein Zylinder mit den Koordinaten (φ,p) (den wir uns als vertikalen Einheitszylinder im Raum vorstellen).

Suggested Citation

  • Dmitry Fuchs & Serge Tabachnikov, 2011. "Die Crofton-Formel," Springer Books, in: Ein Schaubild der Mathematik, chapter 0, pages 307-321, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-12960-5_19
    DOI: 10.1007/978-3-642-12960-5_19
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