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Proceedings of the American Mathematical Society

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On the impossibility of ruler-only constructions


Authors: V. J. Baston and F. A. Bostock
Journal: Proc. Amer. Math. Soc. 110 (1990), 1017-1025
MSC: Primary 51M15
MathSciNet review: 1034882
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Abstract | References | Similar Articles | Additional Information

Abstract: The paper points out that there are several interpretations in the literature of what is meant by a geometric construction. It is shown that these differences in interpretation are important, since certain classic results (including the Mohr-Mascheroni Theorem) are true under one but false under another.


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  • [1] Ludwig Bieberbach, Theorie der geometrischen Konstruktionen, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften. Mathematische Reihe, Band 13, Verlag Birkhäuser, Basel, 1952 (German). MR 0052796
  • [2] Heinrich Dörrie, 100 great problems of elementary mathematics: Their history and solution, Translated by David Antin, Dover Publications, Inc., New York, 1965. MR 0183598
  • [3] Howard Eves, A survey of geometry, Revised edition, Allyn and Bacon, Inc., Boston, Mass., 1972. MR 0322653
  • [4] B. V. Kutuzov, Studies in mathematics, vol. IV, Geometry (L. I. Gordon and E. S. Shater, transls.), School Mathematics Study Group, University of Chicago, Chicago, 1960.
  • [5] Peter Schreiber, Theorie der geometrischen Konstruktionen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1975 (German). Studienbücherei. MR 0640443

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1034882-3
Keywords: Geometric construction, ruler-only constructions, impossibility proof, Mohr-Mascheroni Theorem
Article copyright: © Copyright 1990 American Mathematical Society