Unexpected Twists in Geometric Dissections

• Abu’l-Wafā’ al-Būzjānī: Kitāb fīmā yahtāju al-sāni‘ min a‘ māl al-handasa (On the Geometric Constructions Necessary for the Artisan). Mashdad: Imam Riza 37, copied in the late 10th or the early 11th century. Persian manuscript

• Akiyama, J., Nakamura, G.: Dudeney dissection of polygons. In: Akiyama, J., Kano, M., Urabe, M. (eds.) Discrete and Computational Geometry, Japanese Conference, JCDCG’98, LNCS, vol. 1763, pp. 14–29. Springer, (2000)

• Allman, G. J.: Greek Geometry from Thales to Euclid. Hodges, Figgis, Dublin (1889)

• Anonymous: Fī tadākhul al-ashkāl al-mutashābiha aw al-mutawāfiqa (Interlocks of Similar or Complementary Figures). Bibliothèque Nationale, ancien fonds Paris. Persan 169, ff. 180r–199v

• Bolyai, F.: Tentamen juventutem. Typis Collegii Reformatorum per Josephum et Simeonem Kali, Maros Vasarhelyini (1832)

• Bruyr, D. L.: Geometrical Models and Demonstrations. J. Weston Walch, Portland, Maine (1963)

• Cantor, M.: Vorlesungen über Geschichte der Mathematik, vol. 1, 3rd edn. B. G. Teubner, Stuttgart (1907)

• Dudeney, H. E.: Perplexities. Monthly puzzle column. In: The Strand Magazine from May 1910 through June 1930

• Dudeney, H. E.: Puzzles and prizes. Column in the Weekly Dispatch, April 19, 1896–March 27, 1904

• Dudeney, H. E.: The Canterbury Puzzles and Other Curious Problems. W. Heinemann, London (1907)

• Esser, W. L. III: Jewelry and the like adapted to define a plurality of objects or shapes. U.S. Patent 4,542,631, 1985

• Frederickson, G. N.: Dissections Plane and Fancy. Cambridge University Press, New York (1997)

• Frederickson, G. N.: Geometric dissections that swing and twist. In: Akiyama, J., Kano, M., Urabe, M. (eds.) Discrete and Computational Geometry, Japanese Conference, JCDCG’00, Lecture Notes in Computer Science, LNCS, vol. 2098, pp. 137–148. Springer, Berlin (2000)

• Frederickson, G. N.: Geometric dissections now swing and twist. Math. Intel. 23(3), 9–20 (2001)

  Google Scholar 

• Frederickson, G. N.: Hinged Dissections: Swinging and Twisting. Cambridge University Press, New York (2002)

• Frederickson, G. N.: Piano-hinged dissections: now let’s fold. In: Akiyama, J., Kano, M. (eds.) Discrete and Computational Geometry, Japanese Conference, JCDCG 2002 Revised Papers, LNCS, vol. 2866, pp. 159–171. Springer, Berlin (2003)

• Frederickson, G. N.: The heptagon to the square, and other wild twists. November 2005. Accepted for publication in the Mathematical Intelligencer

• Frederickson, G. N.: Hinged dissections: Swingers, twisters, flappers. In: Cipra, B., Demaine, E. D., Demaine, M. L., Rodgers, T. (eds.) A Tribute to a Mathemagician, pp. 185–195. A K Peters, Wellesley (2005)

• Frederickson, G. N.: Piano-hinged Dissections: Time to Fold. A K Peters, Wellesley (2006)

• Gerwien, P.: Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke. J. f. Die Reine angew. Math. (Crelle’s J.) 10, 228–234 and Taf. III (1833)

• Hanegraaf, A.: The Delian altar dissection. Elst, The Netherlands (1989)

• Lindgren, H.: Geometric dissections. Aust. Math. Teacher. 7, 7–10 (1951)

• Lindgren, H.: A quadrilateral dissection. Aust. Math. Teacher. 16, 64–65 (1960)

  Google Scholar 

• Lindgren, H.: Geometric Dissections. D. Van Nostrand, Princeton, (1964)

• Lowry: Solution to question 269, [proposed] by Mr. W. Wallace. In: Leybourn, T. (ed.) Mathematical Repository, vol. III, pp. 44–46 of Part I. W. Glendinning, London (1814)

• Loyd, S.: Weekly puzzle column in Tit-Bits, starting in October 3, 1896 and continuing into 1897

• Loyd, S.: Mental Gymnastics. Puzzle column in Sunday edition of Philadelphia Inquirer, October 23, 1898–1901

• Lurker, E.: Heart pill. 7 inch tall model in nickel-plated aluminum, limited edition of 80 produced by Bayer, in Germany, 1984

• Özdural, A.: Mathematics and arts: Connections between theory and practice in the medieval Islamic world. Historia Math. 27, 171–201 (2000)

  Google Scholar 

• Rubik, E.: Toy with turnable elements for forming geometric shapes. U.S. Patent 4,392,323, 1983

• Sayili, A.: Thâbit ibn Qurra’s generalization of the Pythagorean theorem. Isis, 51, 35–37 (1960)

  Google Scholar 

• Taylor, H. M.: On some geometrical dissections. Messenger Math. 35, 81–101 (1905)

  Google Scholar 

• Theobald, G.: Geometric dissections. http://home.btconnect.com/GavinTheobald/ HTML/Index.html

• Wallace, W. (ed.): Elements of Geometry, 8th edn. Bell & Bradfute, Edinburgh (1831)

• Yates, R. C.: Geometrical Tools, a Mathematical Sketch and Model Book. Educational Publishers, St. Louis (1949)

Download references