Commentary on Menger’s Path Length Papers

  • Lester Senechal


The determination of the length of a path in a metric space is a variational problem that can be treated by direct methods, without invoking the more extensive machinery of the calculus of variations. In the series of papers [1-10], Menger treated these ideas with increasing generality.


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  1. 1a.
    Ein Theorem über die Bogenlänge. Anz. Oster. Akad. Wiss. 65 (1928) 264–266;Google Scholar
  2. 1b.
    Die Halbstetigkeit der Bogenlänge, Anz. Oster. Akad. Wiss 65 (1928) 271–281;Google Scholar
  3. 1c.
    Über eine neue Definition der Bogenlänge. Eine weitere Verallgemeinerung des Längenbegriffes, ibid 66 (1929) 23–25.Google Scholar
  4. 2.
    Untersuchungen über allgemeine Metrik. Vierte Untersuchung. Zur Metrik der Kurven. Mathematischen Annalen 103 (1930) 467–501.Google Scholar
  5. 3.
    Metrische Geometrie und Variationsrechnung. Fundamenta Mathematicae XXV (1935) 441–458.Google Scholar
  6. 4.
    ATheory of Length and its Applications to the Calculus of Variations, Proceedings of the National Academy of Sciences 25 (1939) 474–478.MathSciNetCrossRefGoogle Scholar
  7. 5.
    On Shortest Polygonal Approximations to a Curve, Notre Dame University, Reports of a Mathematical Colloquium 2 (1940) 33–39.MathSciNetGoogle Scholar
  8. 6.
    Définition intrinsique de la notion de chemin, Comptes rendus 221 (1946) 739–741.Google Scholar
  9. 7.
    Stieltjes integrals considered as lengths, Annales de la Société Polonaise de Mathématique XXI (1948) 173–175.Google Scholar
  10. 8.
    What paths have length? Fundamenta Mathematicae VI (1949) 109–118.Google Scholar
  11. 9.
    A topological characterization of the length of paths, Proceedings of the National Academy of Sciences 38 (1952) 66–69.MathSciNetCrossRefGoogle Scholar
  12. 10.
    Geométrie générale. Mémorial des Sciences Mathématiques CXXIV (1954) 55–61.Google Scholar

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© Springer-Verlag Wien 2003

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  • Lester Senechal

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