References
J. J. Sylvester, Question No. 1229,Educational Times,18, 111 (1865).
M. W. Crofton, Probability,Encyclopedia Britannica,19, 768–788 (1885).
E. Czuber,Wahrscheinlichkeiten und ihre Anwendung auf Fehlerausgleichung, Statistik und Lebensversicherung, Vol. 1, Teubner, Leipzig (1903).
R. Deltheil, Sur le théorie des probabilités géométriques,Ann. Fac. Sci. Univ. Toulouse,XI, 1–65 (1920).
R. Deltheil,Probabilités Géométriques, Gauthier-Villars, Paris (1926).
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).
W. Blaschke,Vorlesungen über Differentialgeometrie II:Affine Differentialgeometrie, Springer, Berlin (1923).
H. A. Alikoski, Über das Sylvestersche Vierpunktproblem,Ann. Acad. Sci. Fenn.,51(7), 1–10 (1939).
H. Solomon,Geometric Probability, SIAM, Philadelphia (1978).
J. F. C. Kingman, Random secants of a convex body,J. Appl. Probab.,6(3), 660–672 (1969).
H. Groemer, On some mean values associated with a randomly selected simplex in a convex set,Pacific J. Math.,45(2), 525–533 (1973).
M. G. Kendall and P. A. P. Moran,Geometrical Probability [in Russian], Nauka, Moscow (1972).
E. Gečiauskas, On the second moment in Blaschke's problem,Lith. Math. J.,34, 122–125 (1994).
L. A. Santalo,Introduction to Integral Geometry [in Russian], Moscow (1956).
Additional information
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