Advertisement

Reversible Pairs of Figures

  • Jin Akiyama
  • Kiyoko Matsunaga
Chapter

Abstract

I have here two figures: one is a shrimp and the other is a bream (Fig. 4.1.1). In Japan, there is a well-known saying, “throw a shrimp to catch a bream” which has same meaning as “throw a sprat to catch a mackerel” in English.

Keywords

Equilateral Triangle Convex Polygon Reversible Transformation Checkerboard Pattern Reversible Figure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T. Abbott, Z. Abel, D. Charlton, E. Demaine, M. Demaine, S. Kominers, Hinged dissections exist, Discrete & Computational Geometry 47 (1) (2012), 150-186.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    J. Akiyama, Catalog of the Exhibition Held at Yoshii Gallery in Paris (2012)Google Scholar
  3. [3]
    J. Akiyama, F. Hurtado, C. Merino and J. Urrutia, A Problem on Hinged Dissections with Colours, Graphs and Combinatorics 20 (2), (2004), 145-159MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    J. Akiyama and S. Langerman, Parcel Magic, to be publishedGoogle Scholar
  5. [5]
    J. Akiyama and G. Nakamura, Dudeney Dissections of Polygons. Discrete and Computational Geometry, Lecture Notes in Computer Science, 1763, (2000), 14-29, SpringerMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    J. Akiyama and G. Nakamura, Congruent Dudeney Dissections of Triangles and Convex Quadrangles—All Hinge Points Interior to the Sides of the Polygons, Discrete and Computational Geometry, The Goodman-Pollack Festschrift. (B. Aronov, S. Basu, J. Pach and M. Sharir, eds.), Algorithms and Combinatorics, 25 (2003), 43-63, SpringerGoogle Scholar
  7. [7]
    J. Akiyama and G. Nakamura, Congruent Dudeney Dissections of Polygons – All the Hinge Points on Vertices of the Polygon, Discrete and Computationa1 Geometry, Lecture Notes in Computer Science, 2866 14-21 (2003), SpringerMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    J. Akiyama, D. Rappaport and H. Seong, A decision algorithm for reversible pairs of polygons, Disc. Appl. Math. 178, (2014), 19-26MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    J. Akiyama and H. Seong, A criterion for a pair of convex polygons to be reversible, Graphs and Combinatorics 31(2) (2015), 347-360.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    J. Akiyama and T. Tsukamoto, Envelope Magic, to appearGoogle Scholar
  11. [11]
    E. D. Demaine, M. L. Demaine, D. Eppstein, G. N. Frederickson, E. Friedman, Hinged dissection of polynominoes and polyforms, Comput. Geom. Theory Appl., 31 (3) (2005), 237-262CrossRefMATHGoogle Scholar
  12. [12]
    H. E. Dudeney, The Canterbury Puzzles and Other Curious Problems, W. Heinemann (1907)Google Scholar
  13. [13]
    G. N. Frederickson, Hinged Dissections: Swinging and Twisting, Cambridge University Press, 2002.MATHGoogle Scholar
  14. [14]
    R. Sarhangi, Making patterns on the surfaces of swing-hinged dissections, in Proceedings of Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, Leeuwarden, the Netherlands, July 2008.Google Scholar
  15. [15]
    D. Schattschneider, Will It Tile? Try the Conway Criterion, Mathematics Magazine Vol. 53 (Sept. 1980), No. 4, 224-233MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Wikipedia, Conway Criterion, http://en.wikipedia.org/wiki/Conway-criterion

Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Jin Akiyama
    • 1
  • Kiyoko Matsunaga
    • 2
  1. 1.Tokyo University of ScienceTokyoJapan
  2. 2.YokohamaJapan

Personalised recommendations