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The Mathematical Intelligencer

, Volume 40, Issue 2, pp 55–63 | Cite as

Equidecomposability of Polyhedra: A Solution of Hilbert’s Third Problem in Kraków before ICM 1900

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References

  1. [1]
    M. Aigner, G. M. Ziegler, Proofs from the Book, Springer-Verlag, Berlin Heidelberg 2001.Google Scholar
  2. [2]
    D. Benko, A New Approach to Hilbert’s Third Problem, The American Mathematical Monthly 114(2007), 665–676.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    L. A. Birkenmajer, Mikolaj Kopernik. Cz. 1.: Studya nad pracami Kopernika oraz materyaly biograficzne, Skład Główny w Księgarni Spółki Wydawniczej Polskiej, Kraków 1900.Google Scholar
  4. [4]
    L. Birkenmajer, O pewnem twierdzeniu z teoryi liczb, Prace Matematyczno-Fizyczne 7(1896), 12–14.Google Scholar
  5. [5]
    L. A. Birkenmajer, O związku twierdzenia Wilsona z teoryą reszt kwadratowych, Rozprawy Wydzialu Matematyczno-Przyrodniczego Akademii Umiejętności, 57A(1918), 137–149.Google Scholar
  6. [6]
    L. Birkenmajer, Zadanie konkursowe z geometryi podane przez p. Dra W. Kretkowskiego, Kraków 1883, Archives of PAN and PAU in Kraków. Ref. ms. 6828.Google Scholar
  7. [7]
    V. G. Boltianskii, Hilbert’s Third Problem, V. H. Winston & Sons (Halsted Press, John Wiley & Sons), Washington DC, 1978 (translated from the Russian version: Tret’ja problema Gil’berta, Nauka, Moscow 1977).Google Scholar
  8. [8]
    W. Bolyai de Bolya, Tentamen. Iuventutem studiosam in elementa matheseos purae, elementaris ac sublìmioris, methodo intuitiva, evidentiaque huic propria, introducendi. Cum appendice triplici, Maros Vásárhelyini; tomus primus 1932, tomus secudus 1933.Google Scholar
  9. [9]
    R. Bricard, Sur une question de géométrie relative aux polyedres, Nouvelles annales de mathématiques, Ser. 3, 15(1896), s. 331–334.Google Scholar
  10. [10]
    Briefwechsel zwischen Carl Friedrich Gauss und Christian Ludwig Gerling Correspondence of Gauss and Gerling), C. Schaeffer (ed.), Berlin 1927, Letter No. 343.Google Scholar
  11. [11]
    P. Cartier, Décomposition des polyèdres: Le point sur le troisième problème de Hilbert, Astérisque 133/134(1986), 261–288.Google Scholar
  12. [12]
    J.-L. Cathelineau, Quelques aspects du troisième problème de Hilbert, Gaz. Math., Soc. Math. Fr. 52(1992), 45–71.Google Scholar
  13. [13]
    D. Ciesielska, Sprawa doktoratu Władysława Kretkowskiego, Antiquitates Mathematicae 6(2012), 7–37.Google Scholar
  14. [14]
    M. Dehn, Ueber raumgleiche Polyeder, Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse 1900, 345–354.Google Scholar
  15. [15]
    M. Dehn, Über den Rauminhalt, Math. Ann. 55(1902), 465–478.CrossRefMATHGoogle Scholar
  16. [16]
    W. Folkierski, Zasady rachunku różniczkowego i całkowego, nakł. Biblioteki w Kórniku, Paris 1870.Google Scholar
  17. [17]
    P. Gerwien, Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke, Journal für die reine und angewandte Mathematik 10(1833), 228–234.MathSciNetCrossRefGoogle Scholar
  18. [18]
    A. Goddu, Ludwik Antoni Birkenmajer and Curtis Wilson on the Origin of Nicholas Copernicus’s Heliocentrism, Isis 107(2016), 225–253.CrossRefGoogle Scholar
  19. [19]
    H. Guggenheimer, The Jordan Curve Theorem and an unpublished manuscript by Max Dehn, Archive for History of Exact Sciences, 17(1977), 193–200.Google Scholar
  20. [20]
    H. Hadwiger, Zum Problem der Zerlegungsgleichheit der Polyeder, Arch. Math, 2(1950), 441–444.MathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    D. Hilbert, Mathematical Problems. Lecture delivered before the International Congress of Mathematicians at Paris 1900 (translated by M. W. Newson), Bulletin of American Mathematical Society 19(1902), 437–479.CrossRefMATHGoogle Scholar
  22. [22]
    B. Kagan, Über die Transformation der Polyeder, Math. Ann. 57(1903), 421–424.MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    R. Kellerhals, Old and new about Hilbert’s Third Problem, in: European women in mathematics (Loccum, 1999), 179–187, Hindawi Publ. Corp., Cairo, 2000.Google Scholar
  24. [24]
    L. Kretkowski, Question 769 et 770, Nouvelles Annales de Mathématiques sér. 2, 6(1867), 227–231.Google Scholar
  25. [25]
    W. Kretkowski, Rozwiązanie pewnego zadania z geometryi wielowymiarowej, Pamiętnik Towarzystwa Nauk Ścisłych 12(1880), 3 pages.Google Scholar
  26. [26]
    M. Laczkovich, Equidecomposability and discrepancy: a solution to Tarski’s circle squaring problem, Journal für die reine und angewandte Mathematik 404(1990), 77–117.MathSciNetMATHGoogle Scholar
  27. [27]
    M. Laczkovich, Paradoxical decompositions: a survey of recent results, Proc. First European Congress of Mathematics, Vol. II (Paris, 1992), Progress in Mathematics 120, Birkhäuser, Basel 1994.Google Scholar
  28. [28]
    T. Muir, The Theory of Determinant in the historical order of development, vol. III, The period 1861 to 1880, Macmillan, London 1920.Google Scholar
  29. [29]
    Rozprawy i Sprawozdania z Posiedzeń Wydzialu Matematyczno-Przyrodniczego Akademii Umiejętności 11(1884), 87–92.Google Scholar
  30. [30]
    G. Sforza, Un’ osservazione sull’ equivalenza dei poliedri per congruenza delle parti, Periodico di matematica 12(1897), 105–109.MATHGoogle Scholar
  31. [31]
    J.-P. Sydler, Conditions nécessaires et suffisantes pour l’équivalence des polyedres de l’espace euclidean a trois dimensions, Comment. Math. Helv. 40(1965), 43–80.MathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    W. Wallace, J. Lowry, Question 269, New Series of the Mathematical Repository 3(1814). Thomas Leybourn (ed.), 44–46.Google Scholar

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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Ludwik and Aleksander Birkenmajer Institute for the History of SciencePolish Academy of SciencesWarszawaPoland
  2. 2.Mathematics Institute, Jagiellonian UniversityKrakówPoland

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