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Unterhaltsame Geometrie

Unterhaltsame Geometrie


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About the Book

Was ist Geometrie? Eine junge Dame, so gefragt, antwortet ohne Zagern: "Oh, das ist das, wo etwas bewiesen wird." Gedrar.gt, ein Beispiel fUr so ein zu beweisendes Etwas zu geben, muBte sie passen. Auch war ihr entgangen, warum es eine gute Sache war, etwas z-u beweisen. Die Reaktion der Dame ist typisch fUr viele Menschen, die meinen, auf der Schule Geometrie gelernt zu haben. Sie vergessen aile die Hauptsache und ver- gegenwartigen sich nicht, warum dieser Stoff durchgenommen worden ist. Das Vergessen der Satze ist keine Tragadie. Wir vergessen vieles von dem, was wir wahrend unserer Schulzeit lernten - oder sollte ich sagen, was uns dort begegnete? Nichtsdesto- weniger ist es bedauerlich, wenn ein ganzer Unterricht so langweilig ist, daB es nicht gelingt, irgendetwas daraus in dem Gedachtnis der SchUler einzupragen. Zugegeben, die traditionelle Geometrie war selbst an diesem Mangel schuld (und ist es noch). Und warum wurde sie gelehrt? Weil man meinte, dem jungen Menschen ein einheitliches logisches System auf einem ihm gemaBen Niveau bieten zu mUssen. Vermutlich erreichten einige SchUler das gewUnschte Ziel, aber viele andere wurden so durch die Einzelheiten abge- lenkt, daB sie den Blick fur die Hauptsache verloren.

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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Product Details
  • ISBN-13: 9783528283148
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Edition: Revised edition
  • Language: German
  • Returnable: N
  • Width: 152 mm
  • ISBN-10: 3528283149
  • Publisher Date: 01 Jan 1984
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 110
  • Returnable: N


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