Acute triangulations of convex quadrilaterals
An acute triangulation of a polygon ? ? is a triangulation of ? ? into acute triangles. Let f(?) f ( ? ) denote the minimum number of triangles necessary for an acute triangulation of ? ? . We prove that the maximum value of f(Q) f ( Q ) for all convex quadrilaterals Q Q is equal to 8. This solves a problem raised by Maehara (2001) in[4].
acute triangulations convex quadrilaterals size planar straight-line graphs