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Hole dissections for planar figures

Published online by Cambridge University Press:  21 June 2021

Greg N. Frederickson
Greg N. Frederickson*
Affiliation:
Department of Computer Science, Purdue University, West Lafayette, IN47907, USA e-mail:[email protected]
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Extract

A geometric dissection is a cutting of a geometric figure (or a finite set of figures) into pieces that we can rearrange to form another geometric figure (or finite set of figures). If our figures are required to be polygons, then there is always a dissection that has just a finite number of pieces. This was established by John Lowry [1], William Wallace [2], Farkas Bolyai [3], and Karl Gerwien [4]. The American Sam Loyd [5] and the Englishman Henry Ernest Dudeney [6, 7] emphasised the goal of minimising the number of pieces that resulted from such a standard dissection.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 563 , July 2021 , pp. 237 - 244
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Copyright
© Mathematical Association 2021

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References

Mr, Lowry, Solution to question 269, by Mr W. William. In Leybourn, T. (ed.), Mathematical Repository, Vol. III, pp. 44-46 of Part I, W. Glendinning (1814).Google Scholar
William, Wallace, (ed.), Elements of geometry (8th ed.), Bell & Bradfute (1831).Google Scholar
Farkas, Bolyai, Tentamen juventutem, Maros Vasarhelyini: Typis Collegii Reformatorum (1832).Google Scholar
Karl, Gerwien, Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke, Journal für die reine und angewandte Mathematik (Crelle’s Journal) 10, pp. 228–234 and Taf. III (1833).Google Scholar
Sam, Loyd, Cyclopedia of puzzles, Frank Bigelow Corporation (1914).Google Scholar
Dudeney, Henry E. , The Canterbury puzzles and other curious problems, W. Heinemann (1907). Google Scholar
Dudeney, Henry E., Amusements in mathematics: Thomas Nelson and Sons (1917).Google Scholar
Frederickson, Greg N., Dissections: plane & fancy, Cambridge University Press (1997).CrossRefGoogle Scholar
Henry, Perigal, On geometric dissections and transformations, Messenger of Mathematics 2 (1873) pp. 103–105.Google Scholar
Harry, Lindgren, Geometric dissections, D. Van Nostrand Company (1964).Google Scholar
Frederickson, Greg N., Hinged dissections: swinging & twisting, Cambridge University Press (2002).Google Scholar
Gavin, Theobald, Geometric dissections, accessed November 2020 at www.gavin-theobald.uk/HTML/HoleIndex.html Google Scholar
Loomis, E. S. . The Pythagorean proposition: its demonstration analyzed and classified and bibliography of sources for data of the four kinds of proofs (2nd edn.) National Council of Teachers of Mathematics, (1968). Google Scholar
Sam, Loyd, Mental gymnastics, Philadelphia Inquirer (26 May, 1901).Google Scholar
Noam, Elkies, Noam’s mathematical miscellany: Geometric morsels, accessed November 2020 at http://people.math.harvard.edu/elkies/Misc/index.html#geom Google Scholar
Leonard, Sohncke, Die regelmässigen ebenen Punksysteme von un begrenzter Ausdehnung, Journal für die reine und angewandte Mathematik (Crelle’s Journal) 77 (1874) pp. 47–101.Google Scholar