Show that when n lines in general position in the real affine plane (no two parallel, no three concurrent)...

geometry/triangular.regions New

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Problem

Show that when n lines in general position in the real affine plane (no
two parallel, no three concurrent) divide the plane into regions, then
at least n-2 of these regions are triangular.

-- David Robbins <robbins@runner.ccr-p.ida.org>, February 1995

Show solution

I sent email to Branko Grunbaum inquiring about this problem.  He has
informed me this conjecture was proved by R. W. Shannon.  The proof was
published in Geometriae Dedicata 8(1979), 179-187.  Another proof was
announced recently by a Russian mathematician (A. Ya. Belov, Uspehi
Mathematicheskih Nauk 47(2)(1992), 151-152).

-- David Radcliffe <radcliff@csd.uwm.edu>, March 1995