Abstract
In his legendary address to the International Congress of Mathematicians at Paris in 1900 David Hilbert asked — as the third of his twenty-three problems — to specify
“two tetrahedra of equal bases and equal altitudes which can in no way be split into congruent tetrahedra, and which cannot be combined with congruent tetrahedra to form two polyhedra which themselves could be split up into congruent tetrahedra.”
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References
V. G. Boltianskii: Hilbert’s Third Problem, V. H. Winston & Sons (Halsted Press, John Wiley & Sons), Washington DC 1978.
M. Dehn: Ueber raumgleiche Polyeder, Nachrichten von der Königl. Gesellschaft der Wissenschaften, Mathematisch-physikalische Klasse (1900), 345–354.
M. Dehn: Ueber den Rauminhalt, Mathematische Annalen 55 (1902), 465–478.
C. F. Gauss: “Congruenz und Symmetrie”: Briefwechsel mit Gerling, pp. 240–249 in: Werke, Band VIII, Königl. Gesellschaft der Wissenschaften zu Göttingen; B. G. Teubner, Leipzig 1900.
D. Hilbert: Mathematical Problems, Lecture delivered at the International Congress of Mathematicians at Paris in 1900, Bulletin Amer. Math. Soc. 8 (1902), 437–479.
G. M. Ziegler: Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, New York 1995/1998.
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© 2004 Springer-Verlag Berlin Heidelberg
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Aigner, M., Ziegler, G.M. (2004). Hilbert’s third problem: decomposing polyhedra. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05412-3_8
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DOI: https://doi.org/10.1007/978-3-662-05412-3_8
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