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Original Articles

On the Division of the Plane by Lines

Pages 647-656 | Published online: 11 Apr 2018

References

  • G. L. Alexanderson and John E. Wetzel, Arrangements of planes in space (in preparation).
  • G. L. Alexanderson and John E. Wetzel, Dissections of a plane oval, this Monthly, 84 (1977) 442–449.
  • G. L. Alexanderson and John E. Wetzel, Simple partitions of space, to appear in Math. Mag.
  • G. L. Alexanderson and John E. Wetzel, Three m-point plane partition problems (in preparation).
  • Albert A. Blank, Mathematical induction, in Enrichment Mathematics for High School, 28th Yearbook, National Council of Teachers of Mathematics, Washington, D.C., 1963, 118–140.
  • Bro. U. Alfred (Brousseau), A mathematician's progress, Math. Teacher, 59 (1966) 722–727.
  • J. W. Freeman, The number of regions determined by a convex polygon, Math. Mag., 49 (1976) 23–25.
  • L. I. Golovina and I. M. Yaglom, Induction in Geometry (trans, by A. W. Goodman and Olga A. Titelbaum), Heath, Boston, 1963.
  • Branko Grünbaum, Arrangements and Spreads, Conference Board of the Mathematical Sciences, Regional Conference Series in Math. No. 10, Amer. Math. Soc., Providence, R.I., 1972.
  • H. Hadwiger, Eulers Charakteristik und kombinatorische Geometrie, J. Reine Angew. Math., 194 (1955) 101–110.
  • Jeanne W. Kerr and John E. Wetzel, Dissections of a polygon, Elem. Math., 33 (1978) 1–7.
  • Jeanne W. Kerr and John E. Wetzel, Dissections of a triangular prism, Geometriae Dedicata, 4 (1975) 279–289.
  • Jeanne W. Kerr and John E. Wetzel, Platonic divisions of space, to appear in Math. Mag.
  • G. Pólya, Induction and Analogy in Mathematics, Vol. 1 of Mathematics and Plausible Reasoning, Princeton Univ. Press, 1954.
  • S. Roberts, On the figures formed by the intercepts of a system of straight lines in a plane, and on analogous relations in space of three dimensions, Proc. London Math. Soc., 19 (1889) 405–422.
  • J. Steiner, Einige Gesetze über die Theilung der Ebene und des Raumes, J. Reine Angew. Math., 1 (1826) 349–364.
  • Thomas Zaslavsky, Facing up to arrangements: Face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. No. 154, Amer. Math. Soc., Providence, R.I., 1975.
  • Thomas Zaslavsky, A combinatorial analysis of topological dissections, Advances in Math., 25 (1978) 267–285.

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