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

Abstract

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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.

How to cite

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Yuan, 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

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  8. ITOH, J. - ZAMFIRESCU, T., Acute triangulations of the regular dodecahedral surface, Europ. J. Combinatorics, to appear. Zbl1115.52004MR2305575DOI10.1016/j.ejc.2006.04.008
  9. 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
  10. 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
  11. MAEHARA, H., Acute triangulations of polygons, Europ. J. Combinatorics, 23 (2002), 45-55. Zbl1006.65019MR1878775DOI10.1006/eujc.2001.0531
  12. YUAN, L., Acute triangulations of polygons, Discrete Comput. Geom., 34 (2005), 697- 706. Zbl1112.52002MR2173934DOI10.1007/s00454-005-1188-9
  13. ZAMFIRESCU, C., Acute triangulations of the double triangle, Bull. Math. Soc. Sci. Math. Roumanie, 47, No. 3-4 (2004), 189-193. Zbl1114.52012MR2121985
  14. ZAMFIRESCU, T., Acute triangulations: a short survey, Proc. 6th Annual Conference Romanian Soc. Math. Sciences, I (2002), 10-18. MR2017183

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