- M. Bern and D. Eppstein.
Polynomial size non-obtuse
triangulation of polygons.
*Proc. 7th ACM Symp. Comp. Geom.*, 1991, pp. 342-350;*Int. J. Comp. Geom. & Appl.*, vol. 2, 1992, pp. 241-255. Shows that any simple polygon can be triangulated with O(*n*^{2}) non-obtuse triangles. - M. Bern, D. Eppstein, and J. Gilbert.
Provably good mesh generation.
*Proc. 31st IEEE Symp. Foundations of Comp. Sci.*, 1990, vol. I, pp. 231-241;*J. Comp. Sys. Sci.*, vol. 48, 1994, pp. 384-409. Figure 5 of the journal version includes a tile (labeled*bbbb*) triangulating the square with all angles at most 80 degrees. - M. Bern, S. Mitchell, and J. Ruppert.
Linear-size non-obtuse triangulation of polygons.
*Proc. 10th ACM Symp. Comp. Geom.*, 1994, pp. 221-230;*Disc. Comp. Geom.*, vol. 14, 1995, pp. 411-428. - Charles Cassidy and Graham Lord.
A square acutely triangulated.
*J. Rec. Math.*, vol. 13, no. 4, 1980/81, pp. 263-268.Summary (from

*Math. Reviews*84j:51036): We examine the problem of triangulating the square into acute-angled triangles. By a proper triangulation we mean a subdivision of the square and its interior into nonoverlapping triangles in such a way that any two distinct triangles are either disjoint, have a single vertex in common, or have one entire edge in common; and by an interior vertex we mean a vertex (of a triangle) which lies inside the square but not on its boundary. We begin with a proof, alternative to that of Lindgren, of the minimality-uniqueness of eight. Then we show there is no triangulation into nine triangles! And finally we demonstrate that there is a triangulation of the square into*n*acute-angled triangles for all*n*greater than or equal to ten. - J. L. Gerver.
The dissection of a polygon into nearly equilateral triangles.
*Geom. Dedicata*, vol. 16, 1984, pp. 93--106. Shows how to compute a*dissection*of a polygon (that is, vertices embedded within sides of triangles are allowed) with no angles larger than 72 degrees, assuming all interior angles of the input measure at least 36 degrees. - H. Lindgren.
*Austral. Math. Teacher*, vol. 18, 1962, pp. 14-15. Cited by Cassidy and Lord.

From the Geometry Junkyard,
computational
and recreational geometry.

David Eppstein,
Theory Group,
ICS,
UC Irvine.

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