Universal Measuring Boxes

  • Jin Akiyama
  • Kiyoko Matsunaga


Since the old days of Japan, there were many ingenious convenient tools that applied mathematical ideas such as the right-angled scale (kanejaku), and the measuring box (masu). The kanejaku is a right-angled scale that was used to find the center and diameter of a circle (Fig. 11.1.1 (a)). On the other hand, the masu is a simple wooden box with no markings whose volume is, in this example, 6 dL. Using this box we can measure 1 dL, 2 dL, 3 dL, and so on in units of 1 dL up to 6 dL [1, 4].


Maximum Cardinality Rectangular Parallelepiped Triangular Prism Universal Measuring Triangular Basis 
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  1. [1]
    J. Akiyama et al., Math Wonderland (Wonder Sugaku Land) (in Japanese), 15-23, NHK (1998)Google Scholar
  2. [2]
    J. Akiyama, H. Fukuda and G. Nakamura, Universal Measuring Devices with Rectangular Base, LNCS 2866 (2003), 1-8MathSciNetMATHGoogle Scholar
  3. [3]
    J. Akiyama, H. Fukuda, G. Nakamura, T. Sakai, J. Urrutia and C. Zamora-Cura, Universal Measuring Devices without Gradations, Discrete and Computational Geometry, LNCS 2098 (2001), 31-40MATHGoogle Scholar
  4. [4]
    J. Akiyama, H. Fukuda, C. Nara, T. Sakai and J. Urrutia, Universal Measuring Boxes with Triangular Bases, Amer. Math. Monthly, 115, No. 3 (2008), 195-201MathSciNetMATHGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

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

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