On acute triangulations of quadrilaterals. (English) Zbl 0998.52005

Maehara, Hiroshi

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.)

Keywords:

quadrilaterals; acute triangulation