On covering trigons or how I met hexagon -- Dmitriy Karabash, July 18, 2005

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The main question of this talk is: What is the minimal
number of covering triangles that can cover a trigon?
n-trigon is the union of n edge-connected triangles from the
standard triangulation of the plane.  The covering triangles and
triangles from triangulation are similar, but covering triangles
are epsilon smaller.  If the triangulation is equilateral the
trigon is equilateral.  For example a regular hexagon of side
1+epsilon is an equilateral 6-trigon which we would be covering
with equilateral triangles of side 1.  We would finish with
simple question: Can you prove that hexagon of side 1+epsilon
cannot be covered with 7 triangles of side 1?