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A Kind of Triangle Covering and Packing Problem

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Computational Geometry, Graphs and Applications (CGGA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7033))

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Abstract

In 2000, H.L. Abbott and M.Katchalski [1] discussed a problem on covering squares with squares. They defined the function f(x) to be the side length of the largest open axis-parallel square that can be covered by the set of closed axis-parallel squares \(\{Q_n\}_{n=1}^\infty\) with side length x n. In this paper, we study this kind of covering problem for equilateral triangles. And we also discuss its dual problem.

(2000)Mathematics Subject Classification. 52C15

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References

  1. Abbott, H.L., Katchalski, M.: Covering squares with squares. Discrete and Computational Geometry 24, 151–169 (2000)

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  2. Moser, W., Pach, J.: Recent developement in combinatorial Geometry. In: New Trends in Discrete and Computational Geometry, Algorithms and Combinatorics, vol. 10, pp. 281–302. Springer, Berlin (1993)

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  3. Shan, Z.: Combinatorical Geometry. Shanghai Educational Press (1995) (in Chinese)

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  4. Zhang, Y.Q., Wang, G.S., Zhang, G.S.: A problem on packing a square with sequence of squares. Journal of Hebei Normal University (Natural Science Edition) 32, 10–11 (2008) (in Chinese)

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tianjin University, 300072, Tianjin, China

    Yuqin Zhang

  2. Shijiazhuang Posts and Telecommunications Technical Collage, 050021, Shijiazhuang, China

    Guishuang Wang

Authors
  1. Yuqin Zhang
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  2. Guishuang Wang
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Tokio, Shibuya-ku, Japan

    Jin Akiyama

  2. School of Computer Science and Technology, Dalian Maritime University, 116026, Dalian, China

    Jiang Bo

  3. Ibaraki University, Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Mikio Kano

  4. Tokai University, 4-1-1 Kitakaname, 259-1292, Hiratsuka, Japan

    Xuehou Tan

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© 2011 Springer-Verlag Berlin Heidelberg

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Cite this paper

Zhang, Y., Wang, G. (2011). A Kind of Triangle Covering and Packing Problem. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_21

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  • DOI: https://doi.org/10.1007/978-3-642-24983-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24982-2

  • Online ISBN: 978-3-642-24983-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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