Unterhaltsame Geometrie

Paperback (3. Aufl. 1984)
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More About This Book

Product Details

  • ISBN-13: 9783528283148
  • Publisher: Vieweg+Teubner Verlag
  • Publication date: 1/1/1984
  • Language: German
  • Edition description: 3. Aufl. 1984
  • Edition number: 3
  • Pages: 110
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.26 (d)

Table of Contents

1. Etwas aus den Grundlagen.- 1.1 Ein praktisches Problem.- 1.2 Ein grundlegender Satz.- 1.3 Mittelwerte.- 2. Harmonische Teilung und Apollonios-Kreise.- 2.1 Konjugierte harmonische Punkte.- 2.2 Der Apollonios-Kreis.- 2.3 Koaxiale Figurenscharen.- 3. Inversion.- 3.1 Transformationen.- 3.2 Inversion.- 3.3 Invarianten.- 3.4 Doppelverhältnis.- 4. Anwendungen der Inversion.- 4.1 Zwei einfache Probleme.- 4.2 Der Inversor von Peaucellier.- 4.3 Das Apollonios-Problem.- 4.4 Steiner-Ketten.- 4.5 Schustermesser.- 5. Die Sechskugelfigur.- 5.1 Kegelschnitt-Definitionen.- 5.2 Eine Eigenschaft der Ketten.- 5.3 Soddys Sechskugelfigur.- 5.4 Einige neue Sechskugelfiguren.- 6. Die Kegelschnitte.- 6.1 Die Spiegel-Eigenschaft.- 6.2 Konfokale Kegelschnitte.- 6.3 Ebene Schnitte eines Kegels.- 6.4 Eine kennzeichnende Eigenschaft der Parabeln.- 7. Projektive Geometrie.- 7.1 Projektive Transformation.- 7.2 Die Grundlagen.- 7.3 Doppelverhältnis.- 7.4 Das vollständige Vierseit.- 7.5 Satz von Pascal.- 7.6 Dualität.- 8. Einige Euklidische Themen.- 8.1 Ein Navigationsproblem.- 8.2 Ein Dreikreis-Problem.- 8.3 Die Euler-Gerade.- 8.4 Der Neunpunktekreis.- 8.5 Ein Dreiecksproblem.- 9. Der Goldene Schnitt.- 9.1 Das Pentagramm.- 9.2 Ähnlichkeiten und Spiralen.- 9.3 Die regulären Polyeder.- 9.4 Die Kettenbrüche für—.- 10. Winkeldreiteilung.- 10.1 Die ungelösten Probleme des Altertums.- 10.2 Andere Arten der Dreiteilungen.- 11. Einige ungelöste Probleme der modernen Geometrie.- 11.1 Konvexe Mengen und geometrische Ungleichungen.- 11.2 Das Malfatti-Problem.- 11.3 Das Kakeya-Problem.- Anmerkungen.- Sachwortverzeichnis.

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