# Acute Triangulations of Doubly Covered Convex Quadrilaterals

Liping Yuan; Carol T. Zamfirescu

Bollettino dell'Unione Matematica Italiana (2007)

- Volume: 10-B, Issue: 3, page 933-938
- ISSN: 0392-4041

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topYuan, Liping, and Zamfirescu, Carol T.. "Acute Triangulations of Doubly Covered Convex Quadrilaterals." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 933-938. <http://eudml.org/doc/290433>.

@article{Yuan2007,

abstract = {Motivated by various applications triangulations of surfaces using only acute triangles have been recently studied. Triangles and quadrilaterals can be triangulated with at most 7, respectively 10, acute triangles. Doubly covered triangles can be triangulated with at most 12 acute triangles. In this paper we investigate the acute triangulations of doubly covered convex quadrilaterals, and show that they can be triangulated with at most 20 acute triangles.},

author = {Yuan, Liping, Zamfirescu, Carol T.},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {10},

number = {3},

pages = {933-938},

publisher = {Unione Matematica Italiana},

title = {Acute Triangulations of Doubly Covered Convex Quadrilaterals},

url = {http://eudml.org/doc/290433},

volume = {10-B},

year = {2007},

}

TY - JOUR

AU - Yuan, Liping

AU - Zamfirescu, Carol T.

TI - Acute Triangulations of Doubly Covered Convex Quadrilaterals

JO - Bollettino dell'Unione Matematica Italiana

DA - 2007/10//

PB - Unione Matematica Italiana

VL - 10-B

IS - 3

SP - 933

EP - 938

AB - Motivated by various applications triangulations of surfaces using only acute triangles have been recently studied. Triangles and quadrilaterals can be triangulated with at most 7, respectively 10, acute triangles. Doubly covered triangles can be triangulated with at most 12 acute triangles. In this paper we investigate the acute triangulations of doubly covered convex quadrilaterals, and show that they can be triangulated with at most 20 acute triangles.

LA - eng

UR - http://eudml.org/doc/290433

ER -

## References

top- BAKER, B. S. - GROSSE, E. - RAFFERTY, C. S., Nonobtuse triangulations of polygons, Discrete Comput. Geom., 3 (1988), 147-168. Zbl0634.57012MR920700DOI10.1007/BF02187904
- BERN, M. - MITCHELL, S. - RUPPERT, J., Linear-size nonobtuse triangulations of polygons, Discrete Comput. Geom., 14 (1995), 411-428. Zbl0841.68118MR1360945DOI10.1007/BF02570715
- BURAGO, Y. D. - ZALGALLER, V. A., Polyhedral embedding of a net (Russian), Vestnik Leningrad. Univ., 15 (1960), 66-80. Zbl0098.35403MR116317
- CASSIDY, C. - LORD, G., A square acutely triangulated, J. Recreational. Math., 13 (1980/81), 263-268. MR625260
- GARDNER, M., New Mathematical Diversions, Mathematical Association of America, Washington D.C., 1995. Zbl0842.00006MR1335231
- GOLDBERG, M., Problem E1406: Dissecting an obtuse triangle into acute triangles, American Mathematical Monthly, 67 (1960), 923.
- HANGAN, T. - ITOH, J. - ZAMFIRESCU, T., Acute triangulations, Bull. Math. Soc. Sci. Math. Roumanie, 43 (91) No. 3-4 (2000), 279-285. Zbl1048.51501MR1837482
- ITOH, J. - ZAMFIRESCU, T., Acute triangulations of the regular dodecahedral surface, Europ. J. Combinatorics, to appear. Zbl1115.52004MR2305575DOI10.1016/j.ejc.2006.04.008
- ITOH, J. - ZAMFIRESCU, T., Acute triangulations of the regular icosahedral surface, Discrete Comput. Geom., 31 (2004), 197-206. Zbl1062.51014MR2060635DOI10.1007/s00454-003-0805-8
- MAEHARA, H., On acute triangulations of quadrilaterals, Proceedings of JCDCG 2000, Lecture Notes in Computer Science, 2098 (2001), 237-354. Zbl0998.52005MR2043655DOI10.1007/3-540-47738-1_22
- MAEHARA, H., Acute triangulations of polygons, Europ. J. Combinatorics, 23 (2002), 45-55. Zbl1006.65019MR1878775DOI10.1006/eujc.2001.0531
- YUAN, L., Acute triangulations of polygons, Discrete Comput. Geom., 34 (2005), 697- 706. Zbl1112.52002MR2173934DOI10.1007/s00454-005-1188-9
- ZAMFIRESCU, C., Acute triangulations of the double triangle, Bull. Math. Soc. Sci. Math. Roumanie, 47, No. 3-4 (2004), 189-193. Zbl1114.52012MR2121985
- ZAMFIRESCU, T., Acute triangulations: a short survey, Proc. 6th Annual Conference Romanian Soc. Math. Sciences, I (2002), 10-18. MR2017183

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