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Piano-Hinged Dissections: Now Let’s Fold!

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Discrete and Computational Geometry (JCDCG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2866))

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Abstract

A new type of hinging is explored for geometric dissections of two-dimensional figures. The figures are represented by pieces on two adjacent levels. Piano hinges are used to rotate a piece B from being next to a piece A on one level to being above or below piece A on another level. Techniques are presented and analyzed for designing piano-hinged dissections. These include the use of polygon structure, the conversion from twisted-hinged dissections, the folding analogue of a P-slide, the folding analogue of a step dissection, and the use of tessellations. Properties of piano-hinged dissections are explored. An open problem relating to the possible universality of such hingings is posed.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Purdue University, West Lafayette, IN, 47907, USA

    Greg N. Frederickson

Authors
  1. Greg N. Frederickson
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Editor information

Editors and Affiliations

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

    Jin Akiyama

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

    Mikio Kano

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© 2003 Springer-Verlag Berlin Heidelberg

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Frederickson, G.N. (2003). Piano-Hinged Dissections: Now Let’s Fold!. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_16

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  • DOI: https://doi.org/10.1007/978-3-540-44400-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20776-4

  • Online ISBN: 978-3-540-44400-8

  • eBook Packages: Springer Book Archive

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