Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Recreational Mathematics Magazine

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.05

Open Access
Online
ISSN
2182-1976
See all formats and pricing
More options …

Rules for folding polyminoes from one level to two levels

Julia Martin / Elizabeth Wilcox
Published Online: 2018-01-11 | DOI: https://doi.org/10.1515/rmm-2017-0020

Abstract

Polyominoes have been the focus of many recreational and research investigations. In this article, the authors investigate whether a paper cutout of a polyomino can be folded to produce a second polyomino in the same shape as the original, but now with two layers of paper. For the folding, only “corner folds” and “half edge cuts” are allowed, unless the polyomino forms a closed loop, in which case one is allowed to completely cut two squares in the polyomino apart. With this set of allowable moves, the authors present algorithms for folding different types of polyominoes and prove that certain polyominoes can successfully be folded to two layers. The authors also establish that other polyominoes cannot be folded to two layers if only these moves are allowed.

Keywords: Folding polyominoes

References

  • [1] Brzustowski, J. "Can you win at Tetris?", Master's thesis, The University of British Columbia, Canada, March 1992.Google Scholar

  • [2] Burgiel, H. "How to Lose at Tetris", The Mathematical Gazette, 81(491), 194-200, July 1997.Google Scholar

  • [3] Frederickson, G. N. Dissections: Plane & Fancy. Cambridge University Press, 1997.Google Scholar

  • [4] Frederickson, G. N. "Folding Polyominoes from One Level to Two", The College Math Journal, 42(4), 265-274, September 2011.Google Scholar

  • [5] Golomb, S. W. Polyominoes: Puzzles, Patterns, Problems, and Packings, Princeton University Press, 1994.Google Scholar

  • [6] Martin, G. E. Polyominoes: A guide to puzzles and problems in tiling, The Mathematical Association of America, 1987.Google Scholar

About the article

Published Online: 2018-01-11

Published in Print: 2017-12-20


Citation Information: Recreational Mathematics Magazine, Volume 4, Issue 8, Pages 47–58, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2017-0020.

Export Citation

© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in