## On acute triangulations of quadrilaterals.(English)Zbl 0998.52005

Akiyama, Jin (ed.) et al., Discrete and computational geometry. Japanese conference, JCDCG 2000, Tokyo, Japan, November 22-25, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 2098, 237-243 (2001).
Summary: An acute triangulation of a polygon $$\Gamma$$ is a triangulation of $$\Gamma$$ into acute triangles. Let $$f(\Gamma)$$ denote the minimum number of triangles for an acute triangulation of $$\Gamma$$, and let $$f(n)$$ denote the maximum value of $$f(\Gamma)$$ for all $$n$$-gons. We prove that $$f(4)=10$$.
For the entire collection see [Zbl 0968.00054].

### MSC:

 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)