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Sylvester's problem and random chords

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References

  1. J. J. Sylvester, Question No. 1229,Educational Times,18, 111 (1865).

    Google Scholar 

  2. M. W. Crofton, Probability,Encyclopedia Britannica,19, 768–788 (1885).

    Google Scholar 

  3. E. Czuber,Wahrscheinlichkeiten und ihre Anwendung auf Fehlerausgleichung, Statistik und Lebensversicherung, Vol. 1, Teubner, Leipzig (1903).

    Google Scholar 

  4. R. Deltheil, Sur le théorie des probabilités géométriques,Ann. Fac. Sci. Univ. Toulouse,XI, 1–65 (1920).

    Google Scholar 

  5. R. Deltheil,Probabilités Géométriques, Gauthier-Villars, Paris (1926).

    Google Scholar 

  6. W. Blaschke, Über affine Geometrie XI: Lösung des “Vierpunktproblem” von Sylvester aus der Theorie der geometrischen Wahrscheinlichkeiten,Berichte Verh. Sachs. Ges. Wiss.,69, 436–453 (1917).

    MATH  Google Scholar 

  7. W. Blaschke,Vorlesungen über Differentialgeometrie II:Affine Differentialgeometrie, Springer, Berlin (1923).

    Google Scholar 

  8. H. A. Alikoski, Über das Sylvestersche Vierpunktproblem,Ann. Acad. Sci. Fenn.,51(7), 1–10 (1939).

    MATH  Google Scholar 

  9. H. Solomon,Geometric Probability, SIAM, Philadelphia (1978).

    Google Scholar 

  10. J. F. C. Kingman, Random secants of a convex body,J. Appl. Probab.,6(3), 660–672 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  11. H. Groemer, On some mean values associated with a randomly selected simplex in a convex set,Pacific J. Math.,45(2), 525–533 (1973).

    MATH  MathSciNet  Google Scholar 

  12. M. G. Kendall and P. A. P. Moran,Geometrical Probability [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  13. E. Gečiauskas, On the second moment in Blaschke's problem,Lith. Math. J.,34, 122–125 (1994).

    Article  Google Scholar 

  14. L. A. Santalo,Introduction to Integral Geometry [in Russian], Moscow (1956).

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Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 37, No. 3, pp. 327–330, July–September, 1997.

Translated by E. Gečiauskas

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Gečiauskas, E. Sylvester's problem and random chords. Lith Math J 37, 243–245 (1997). https://doi.org/10.1007/BF02465354

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  • DOI: https://doi.org/10.1007/BF02465354

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