Israel Journal of Mathematics

, Volume 7, Issue 4, pp 393–397

A theorem on arrangements of lines in the plane

  • R. J. Canham

DOI: 10.1007/BF02788872

Cite this article as:
Canham, R.J. Israel J. Math. (1969) 7: 393. doi:10.1007/BF02788872


LetA be an arrangement ofn lines in the plane. IfR1, …,Rr arer distinct regions ofA, andRi is api-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.

Copyright information

© The Weizmann Science Press of Israel 1969

Authors and Affiliations

  • R. J. Canham
    • 1
  1. 1.Michigan State UniversityEast Lansing