## Acute triangulations of convex quadrilaterals.(English)Zbl 1250.52001

An acute triangulation of a polygon $$P$$ is a triangulation of $$P$$ into acute triangles. Let $$f(P)$$ be the minimum number of triangles necessary for an acute triangulation of $$P$$.
Solving a problem raised by H. Maehara [Lect. Notes Comput. Sci. 2098, 237–243 (2001; Zbl 0998.52005)], the author proves that the maximum value of $$f(Q)$$ for all convex quadrilaterals $$Q$$ is equal to 8.

### MSC:

 52A10 Convex sets in $$2$$ dimensions (including convex curves) 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry) 05C10 Planar graphs; geometric and topological aspects of graph theory

Zbl 0998.52005
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### References:

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