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A theorem on arrangements of lines in the plane

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Abstract

LetA be an arrangement ofn lines in the plane. IfR 1, …,R r arer distinct regions ofA, andR i is ap i-gon (i=1, …,r) then we show that\(\sum\limits_{i = 1}^r {P_i \leqq n + 4} \left( {_2^r } \right)\). Further we show that for allr this bound is the best possible ifn is sufficiently large.

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References

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Authors and Affiliations

  1. Michigan State University, 48823, East Lansing, Michigan

    R. J. Canham

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  1. R. J. Canham
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Financial support for this research was provided by the Carnegie Trust for the Universities of Scotland.

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Canham, R.J. A theorem on arrangements of lines in the plane. Israel J. Math. 7, 393–397 (1969). https://doi.org/10.1007/BF02788872

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  • DOI: https://doi.org/10.1007/BF02788872

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