Article PDF
Avoid common mistakes on your manuscript.
References
M. Aigner, G. M. Ziegler, Proofs from the Book, Springer-Verlag, Berlin Heidelberg 2001.
D. Benko, A New Approach to Hilbert’s Third Problem, The American Mathematical Monthly 114(2007), 665–676.
L. A. Birkenmajer, Mikolaj Kopernik. Cz. 1.: Studya nad pracami Kopernika oraz materyaly biograficzne, Skład Główny w Księgarni Spółki Wydawniczej Polskiej, Kraków 1900.
L. Birkenmajer, O pewnem twierdzeniu z teoryi liczb, Prace Matematyczno-Fizyczne 7(1896), 12–14.
L. A. Birkenmajer, O związku twierdzenia Wilsona z teoryą reszt kwadratowych, Rozprawy Wydzialu Matematyczno-Przyrodniczego Akademii Umiejętności, 57A(1918), 137–149.
L. Birkenmajer, Zadanie konkursowe z geometryi podane przez p. Dra W. Kretkowskiego, Kraków 1883, Archives of PAN and PAU in Kraków. Ref. ms. 6828.
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).
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.
R. Bricard, Sur une question de géométrie relative aux polyedres, Nouvelles annales de mathématiques, Ser. 3, 15(1896), s. 331–334.
Briefwechsel zwischen Carl Friedrich Gauss und Christian Ludwig Gerling Correspondence of Gauss and Gerling), C. Schaeffer (ed.), Berlin 1927, Letter No. 343.
P. Cartier, Décomposition des polyèdres: Le point sur le troisième problème de Hilbert, Astérisque 133/134(1986), 261–288.
J.-L. Cathelineau, Quelques aspects du troisième problème de Hilbert, Gaz. Math., Soc. Math. Fr. 52(1992), 45–71.
D. Ciesielska, Sprawa doktoratu Władysława Kretkowskiego, Antiquitates Mathematicae 6(2012), 7–37.
M. Dehn, Ueber raumgleiche Polyeder, Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse 1900, 345–354.
M. Dehn, Über den Rauminhalt, Math. Ann. 55(1902), 465–478.
W. Folkierski, Zasady rachunku różniczkowego i całkowego, nakł. Biblioteki w Kórniku, Paris 1870.
P. Gerwien, Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke, Journal für die reine und angewandte Mathematik 10(1833), 228–234.
A. Goddu, Ludwik Antoni Birkenmajer and Curtis Wilson on the Origin of Nicholas Copernicus’s Heliocentrism, Isis 107(2016), 225–253.
H. Guggenheimer, The Jordan Curve Theorem and an unpublished manuscript by Max Dehn, Archive for History of Exact Sciences, 17(1977), 193–200.
H. Hadwiger, Zum Problem der Zerlegungsgleichheit der Polyeder, Arch. Math, 2(1950), 441–444.
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.
B. Kagan, Über die Transformation der Polyeder, Math. Ann. 57(1903), 421–424.
R. Kellerhals, Old and new about Hilbert’s Third Problem, in: European women in mathematics (Loccum, 1999), 179–187, Hindawi Publ. Corp., Cairo, 2000.
L. Kretkowski, Question 769 et 770, Nouvelles Annales de Mathématiques sér. 2, 6(1867), 227–231.
W. Kretkowski, Rozwiązanie pewnego zadania z geometryi wielowymiarowej, Pamiętnik Towarzystwa Nauk Ścisłych 12(1880), 3 pages.
M. Laczkovich, Equidecomposability and discrepancy: a solution to Tarski’s circle squaring problem, Journal für die reine und angewandte Mathematik 404(1990), 77–117.
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.
T. Muir, The Theory of Determinant in the historical order of development, vol. III, The period 1861 to 1880, Macmillan, London 1920.
Rozprawy i Sprawozdania z Posiedzeń Wydzialu Matematyczno-Przyrodniczego Akademii Umiejętności 11(1884), 87–92.
G. Sforza, Un’ osservazione sull’ equivalenza dei poliedri per congruenza delle parti, Periodico di matematica 12(1897), 105–109.
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.
W. Wallace, J. Lowry, Question 269, New Series of the Mathematical Repository 3(1814). Thomas Leybourn (ed.), 44–46.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This 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.
About this article
Cite this article
Ciesielska, D., Ciesielski, K. Equidecomposability of Polyhedra: A Solution of Hilbert’s Third Problem in Kraków before ICM 1900. Math Intelligencer 40, 55–63 (2018). https://doi.org/10.1007/s00283-017-9748-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00283-017-9748-4