Liping Yuan: Acute Triangulations of Pentagons, p.393-410

Abstract:

An acute triangulation is a triangulation whose triangles have all their angles less than $\frac{\pi}{2}$. In this paper we prove that $i)$ every planar pentagon can be triangulated into at most 54 acute triangles, and $ii$) every double pentagon can be triangulated into at most 76 acute triangles.

Key Words: Acute triangulation; pentagon; double pentagon; Helly's theorem.

2000 Mathematics Subject Classification: Primary: 52A15;
Secondary: 53A05.

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