Hardcopy books and articles with citations to
Hinged Dissections: Swinging & Twisting

(Early working title: Dissections Too! Swingin')

Citations in conference papers:

• Erik D. Demaine, Martin L. Demaine, David Eppstein, and Erich Friedman, "Hinged dissection of polyominoes and Polyiamonds," Proceedings of the 11th Canadian Conference on Computational Geometry, Vancouver, Canada, August 1999.
  
  
• Erik D. Demaine and Martin L. Demaine, "Puzzles, art, and magic with algorithms," Proceedings of the 3rd International Conference on Fun with Algorithms (FUN 2004), Isola d'Elba, Italy, May 26-28, 2004, pages 7-15.
  
  
• Michael Eisenberg, Ann Eisenberg, Glenn Blauvelt, Susan Hendrix, Leah Buechley, and Nwanua Elumeze, "Mathematical crafts for children: beyond scissors and glue," Proceedings of Art + Math = X, International Conference, University of Colorado, Boulder, June 2-5, 2005, pages 61-65.
  
  
• Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lindy, and Diane L. Souvaine, "Hinged dissection of polypolyhedra," in Proceedings of the 9th Workshop on Algorithms and Data Structures (WADS 2005), Waterloo, Ontario, Canada, August 15-17, 2005, pages 205-217.
  
  
• Robert Connelly, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Stefan Langerman, Joseph S. B. Mitchell, Ares Ribó and Günter Rote, "Locked and unlocked chains of planar shapes," in Proceedings of the ACM Symposium on Computational Geometry, June 2006, pages 61-70.
  
  
• Jin Akiyama, Midori Kobayashi, and Gisaku Nakamura, "Dudeney transformation of normal tiles," in Computational Geometry and Graph Theory, International Conference, KyotoCGGT 2007, Kyoto, Japan, June 2007, pages 1-13.
  
  
• Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott D. Kominers, "Hinged dissections exist," Proceedings of the 24th Annual ACM Symposium on Computational Geometry, College Park, Maryland, June 2008, pp. 110-119.
  
  
• Reza Sarhangi, "Making patterns on the surfaces of swing-hinged dissections," in Proceedings of Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, Leeuwarden, the Netherlands, July 2008.

  "During the 2007 Bridges Conference in Spain, Bridges Donostia, Greg N. Frederickson of the Department of Computer Science, Purdue University, presented a paper, titled Symmetry and Structure in Twist-Hinged Dissections of Polygonal Rings and Polygonal Anti-Rings. Frederickson showed a number of animations of different dissections including swing-, piano-, and twist-hinged dissections. His recent presentation, and another one during the 2005 Bridges Conference in Banff, Canada, motivated me to study this topic."

• Erik Demaine and Martin Demaine, "Mathematics is art," in Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture, Banff, Canada, July 2009, pp. 1-10.
  
  
• Jing Zhang, "To realize the diathetic education of mathematical education and CAI by network, mathematical experiment course," in 2nd International Conference on Education Technology and Computer ICETC), Shanghai, China, June 2010, pp. V4-467--V4-471.
  
  
• Daniel Wyllie Lacerda Rodrigues, "Detalhes acera da dissecçã do triângulo no quadrado" V Colóquio de História e Tecnologia no Ensino da Matemática, Recife, Brasil, de 26 a 30 de julho de 2010.
  
  
• Yahan Zhou and Rui Wang, "An algorithm for creating geometric dissection puzzles," in Proceedings 2012 of Bridges Towson: Mathematics, Music, Art, Architecture, Culture, Towson University, Maryland, July 2012, pp. 49-56.
  
  
• Rinus Roelofs, "Splitting tilings," in Proceedings 2012 of Bridges Towson: Mathematics, Music, Art, Architecture, Culture, Towson University, Maryland, July 2012, pp. 111-118.
  
  
• Jin Akiyama, Ikuro Sato and Hyunwoo Seong, "On Reversibility among parallelohedra," in XIV Spanish Meeting on Computational Geometry, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Alcalá de Henares, Spain, June 27-30, 2011, Revised Selected Papers, Lecture Notes in Computer Science, 2012, Volume 7579, pp. 14-28.
  
  
• Jin Akiyama and Hyunwoo Seong, "Operators which preserve reversibility," in Computational Geometry and Graphs, Thailand-Japan Joint Conferenece, TJJCCGG 2012, Springer Lecture Notes in Computer Science 8296, Bangkok, Thailand, December 6-8, 2012, pp. 1-19.
  
  
• Jin Akiyama and Hyunwoo Seong, "On a Mechanism of Reversibilities among Polygons and Polyhedra," in The 5th International Symposium on Graph Theory and Combinatorial Algorithms (GTCA2013), Tongliao, Inner Mongolia, China, July 12-14, 2013.
  
  
• Jin Akiyama, Ikuro Sato and Hyunwoo Seong, "Tessellabilities, reversibilities, and decomposabilities of polytopes," Geometric Science of Information - First International Conference, Paris, France, August 20-30, 2013, Lecture Notes in Computer Science, Vol. 8085, 2013, pp. 215-223.
  
  
• Hans Walser, Puzzle (pdf), Puzzle (htm), at the Forum für Begabtenförderung, Pädagogische Hochschule Karlsruhe, March 27-29, 2014.
  
  
• Vincent Kee, Nicolas Rojas, Mohan Rajesh Elara, and Ricardo Sosa, "Hinged-Tetro: A Self-reconfigurable Module for Nested Reconfiguration," 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Besançon, France, July 8-11, 2014, pp. 1539-1546.
  
  
• Hans Walser, Puzzle (pdf), at the SLA-Tagung, in Bern, Switzerland, November 15, 2014.
  
  
• Jin Akiyama, Stefan Langerman, and Kiyoko Matsunaga, "Reversible Nets of Polyhedra", JCDCGG 2015: Discrete and Computational Geometry and Graphs, pp. 13-23.
  
  
• Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Jayson Lynch, Pasin Manurangsi, Mikhail Rudoy, and Anak Yodpinyanee, "Dissection with the Fewest Pieces is Hard, Even to Approximate", Discrete and Computational Geometry and Graphs: 18th Japan Conference 2015, 2016, LNCS 9943, pp. 37-48.
  
  
• Veerajagadheswar Prabakaran, Rajesh Elara Mohan, Thejus Pathmakumar, and Shunsuke Nansai, "Htetro: A Tetris Inspired Shape Shifting Floor Cleaning Robot," 2017 IEEE International Conference on Robotics and Automation," Singapore, 2017.
  
  
• Andrew Sniderman, "4-3 Dissection Tiling System", Proceedings of Bridges Conference, 2018, pp. 31--38.
  
  
• Prabakaran Veerajagadheswar, Mohan Rajesh Elara, Pathmakumar Thejus, and Sivanantham Vinu, "A Tromino Tiling Theoretic Approach to Path Planning in a Reconfigurable Floor Cleaning Robot," 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR), Delft, Netherlands.
  
  

Citations in journal papers:

• "In memory of Anton Hanegraaf," Cubism for Fun, no. 56, October 2001, p. 39.
  
  
• Erik D. Demaine and Martin Demaine, "Hinged dissection of the alphabet," Journal of Recreational Mathematics, vol. 31, no. 3, 2003, pages 204-207.
  
  
• Jin Akiyama and Gisaku Nakamura, "Determination of all convex polygons which are chameleons--congruent Dudeney dissections of polygons--," IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E86-A, no. 5 (2003), 978-986.
  
  
• Joseph O'Rourke, "Computational geometry column 44," International Journal of Computational Geometry and Applications (IJCGA), vol. 13, no. 3 (June 2003), pp. 273-275, and SIGACT News, vol. 34, no. 2 (June 2003), pages 58-60.
  
  
• Jin Akiyama and Gisaku Nakamura, "Determination of All Convex Polygons which are Chameleons--Congruent Dudeney Dissections of Polygons--," IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E86-A, No. 5, pp. 978-986.
  
  
• J. Akiyama, F. Hurtado, C. Merino, and J. Urrutia, "A problem on hinged dissections with colours," Graphs and Combinatorics, vol. 20, no. 2 (June 2004), pp. 145-159.
  
  
• D. G. Rogers, "Pythagoras framed, cut up Liu Hui," (Norwegian. English summary) Normat, vol. 52, no. 2 (2004), 71-78.
  
  
• Alfinio Flores, "Hinged geometry," ON-Math Online Journal for School Mathematics, vol. 4, no. 1 (2006).
  
  
• Erik D. Demaine, Martin L. Demaine, and A. Laurie Palmer, "The helium stockpile: A collaboration in mathematical folding sculpture," Leonardo, vol. 39, no. 3 (2006), pages 233-235.

  For a comprehensive book on hinged dissections see G. N. Frederickson, Hinged Dissections: Swinging and Twisting (Cambridge, U.K.: Cambridge Univ. Press, 2002).

• Erik D. Demaine and Martin L. Demaine, "Puzzles, art, and magic with algorithms," Theory of Computing Systems, vol. 39, no. 3 (June 2006), pages 473-481.
  
  
• Kamran Sedig and Mark Sumner, "Characterizing interaction with visual mathematical representations," International Journal of Computers for Mathematical Learning, vol. 11, no. 1 (April 2006), pp. 1-55.
  
  
• Izidor Hafner and Tomislav Zitko, "Hinged dissection of a rhombic solid to the truncated cuboctahedron," Visual Mathematics vol. 8, no. 4 (2006).
  
  
• Izidor Hafner and Tomislav Zitko, "Equidecomposition of rhombohedron, hexagonal prism, and rhombic dodecahedron," Visual Mathematics vol. 8, no. 4 (2006).
  
  
• M. Kano, Mari-Jo Ruiz, and Jorge Urrutia, "Jin Akiyama: a friend and his mathematics," Graphs and Combinatorics, vol. 23[Suppl] (2007), pp. 1-39.
  
  
• Alexander Drohobyczer, "Another look at dissecting three equal squares into one," Journal of Recreational Mathematics, vol. 34, no. 1 (2005-2006), pp. 24-34.
  
  
• Joseph O'Rourke, "Computational geometry column 50," ACM SIGACT News, vol. 39, no. 1 (2008), pp. 73-76.
  
  
• Jean-Paul Delahaye, "La géométrie du bricolage," Pour la Science, no. 374 (Décembre 2008), pp. 100-105.
  
  
• N. J. A. Sloane and Vinay A. Vaishampayan, "Generalizations of Schöbi's tetrahedral dissection," Discrete and Computational Geometry, vol. 41, no. 2 (March 2009), pp. 232-248.
  
  
• Guillaume Reuiller, "(Encore) des maths «façon puzzle»," Découverte, no. 364 (Septembre-Octobre 2009), pp. 68-71.
  
  
• Robert Connelly, Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Stefan Langerman, Joseph S. B. Mitchell, Ares Ribó and Günter Rote, "Locked and unlocked chains of planar shapes," Discrete & Computational Geometry, vol. 44, no. 2 (March 2010), pp. 439-466.
  
  
• Christian Blanvillain and János Pach, "Square trisection, dissection of a square in three congruent partitions," Bulletin d'Informatique Approfondie et Applications, no. 86 (Juin 2010), pp. 7-17.
  
  
• Tiina Hohn and Andy Liu, "Polyomino dissections," College Mathematics Journal, vol. 43, no. 1 (January 2012), pp. 88-94.

  "The torch has now been passed on to Greg Frederickson, with three outstanding books so far."

• Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott Duke Kominers, "Hinged dissections exist," Discrete & Computational Geometry, vol. 47, no. 1 (2012), pp. 150-186.
  
  
• Andrew Jobbings, "Dissecting polyominoes," Mathematics in School, vol. 2, no. 2 (March 2013), pp. 30-33.

  "No discussion of dissections would be complete without mentioning Greg Frederickson, whose two books and associated web pages are very thorough."

• Jin Akiyama, David Rappaport, Hyunwoo Seong, "A decision algorithm for reversible pairs of polygons," Discrete Applied Mathematics, vol. 178, (2014), pp. 19-26.
  
  
• Roger B. Nelsen, "Proof without words: The area of a regular dodecagon," College Mathematics Journal, vol. 46, no. 1 (January 2015), p. 10.
  
  
• Jin Akiyama and Hyunwoo Seong, "A criterion for a pair of convex polygons to be reversible," Graphs and Combinatorics, online, February 26, 2015.
  
  
• Jean-Paul Delahaye, "Dissections géométriques," Encyclopaedia Universalis, consulté le juin 2015.

  "Le second ouvrage, paru cinq ans plus tard, s'intitule Hinged Dissections: Swinging and Twisting. Il traite principalement des découpages avec charnières, c'est-à-dire tels que les pièces restent liées les unes aux autres lors de la transformation d'une première figure en une seconde. Un exemple de dissection avec charnières est celui tout à fait remarquable du carré en triangle équilatéral."

  which is translated as:

  "Hinged Dissections: Swinging and Twisting ... mainly deals with hinged dissections, that is to say such that the pieces remain linked to one another when transforming a first figure into a second. An example of a dissection with hinges is that quite remarkable one of the square to an equilateral triangle."

  
  
• Ning Tan, Nicolas Rojas, Rajesh Elara Mohan, Vincent Kee, and Ricardo Sosa, "Nested reconfigurable robots: Theory, design and realization," International Journal of Advanced Robotic Systems, vol. 12, no. 110 (2015), pp. 1-12.
  
  
• Yi-Jheng Huang, Shu-Yuan Chan, Wen-Chieh Lin, and Shan-Yu Chuang, Making and animating transformable 3D models, Computers & Graphics, vol. 54, February 2016, pages 127-134.
  
  
• Alfinio Flores, "Hinged tilings," North American GeoGebra Journal, vol. 6, no. 1 (2017), pp. 1-11.
  
  
• Jas Paul Singh, "Concept of Pythagorean Theorem's New Proof and Pythagorean's Triple With Ancient Vedic Investigation," International Journal of Scientific Research and Education, vol. 5, issue 4 (April 2017), pages 6326-6338.
  
  
• Noah Duncan, Lap-Fai Yu, Sai-Kit Yeung, Demetri Terzopoulos, "Approximate Dissections," ACM Transactions on Graphics, vol. 36, no. 6, article 182, November 2017.
  
  
• Veerajagadheswar Prabakaran, Rajesh Elara Mohan, Vinu Sivanantham, Thejus Pathmakumar, and Suganya Sampath Kumar, "Tackling area coverage problems in a reconfigurable floor cleaning robot based on polyomino tiling theory," Applied Sciences, vol. 8, no. 3, 342, February 2018.
  
  
• Veerajagadheswar Prabakaran, Mohan Rajesh Elara, Thejus Pathmakumar, and Shunsuke Nansai, "Floor cleaning robot with reconfigurable mechanism," Automation in Construction, vol. 91, pages 155-165, July 2018.
  
  
• Prabakaran Veerajagadheswa, Mohan Rajesh Elara, Thejus Pathmakumar, and Vengadesh Ayyalusami, "A Tiling-Theoretic Approach to Efficient Area Coverage in a Tetris-Inspired Floor Cleaning Robot", IEEE Access vol. 6, 2018.
  
  
• Recep Aslaner and Aziz Ilhan, "Pythagoras Connection Expressed for Square Application of Other Plain Polygons and Appliances," Journal of Buca Faculty of Education, Say1 45, p. 55-67 (June 2018).
  
  
• Meng Wang and Haipeng Mi, "Tangible Tetris," Leonardo, accepted and posted online July 31, 2018.
  
  
• Shuhua Li, Ali Mahdavi-Amiri, Ruizhen Hu, Han Liu, Changqing Zou, Oliver van Kaick, Xuiping Liu, Hui Huang, and Hao Zhang, "Construction and Fabrication of Reversible Shape Transforms," ACM Transactions on Graphics, vol. 37, No. 6, Article 190.
  
  
• Zach Rueger, Chan Soo Ha, and Roderic S. Lakes, "Flexible Cube Tilt Lattice with Anisotropic Cosserat Effects and Negative Poisson's Ratio," physica status solidi (b) basic solid state physics, November 23, 2018.
  
  
• Eunji Jin, In Seong Lee, Dongwook Kim, Hosoowi Lee, Woo-Dong Jang, Myung Soo Lah, Seung Kyu Min, and Wonyoung Choe, "Metal-organic framework based on hinged cube tessellation as transformable mechanical metamaterial," Science Advances, Vol. 5, no. 5, May 10, 2019.
  
  
• Keke Tang, Peng Song, Xiaofei Wang, Bailin Deng, Chi-Wing Fu, and Ligang Liu, "Computational Design of Steady 3D Dissection Puzzles," Computer Graphics Forum, vol. 38, Issue 2 (May 2019), pp. 291-303.
  

Citations in books:

• David W. Henderson and Daina Taimina, Experiencing Geometry: Euclidean, Non-Euclidean, with History (3rd Edition of Experiencing Geometry), 2004.

  The book explores all manner of dissections whose pieces are hinged together, along with techniques that allow you to design them. It is a nice sequel to Dissections: Plane & Fancy.

• Ivan Moscovich, Leonardo's Mirror & Other Puzzles, Sterling Publishing, 2004.
  
  
• Jean-Paul Delahaye, Les inattendus mathématiques: Art, casse-tête, paradoxes, superstitions, Belin, Pour la Science, 2004.
  
  
• Claudi Alsina and Roger B. Nelsen, Math Made Visual: Creating Images for Understanding Mathematics, Mathematical Association of America, 2006.

  "Readers interested in plane dissections and their mathematical properties will find the books by G. Frederickson [Frederickson, 1997 and 2002] of interest."

• Eli Maor, The Pythagorean Theorem: A 4,000-Year History, Princeton University Press, 2007.
  
  
• Erik D. Demaine and Joseph O'Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Cambridge University Press, 2007.
  
  
• John A. Pelesko, Self Assembly: The Science of Things That Put Themselves Together, Chapman and Hall/CRC, 2007.

  "Very little has been done with regards to designing self-reconfiguring hinged dissections. The interested reader will find the book by Frederickson invaluable."

• John Bryant and Chris Sangwin, How Round is Your Circle?: Where Engineering and Mathematics Meet, Princeton University Press, 2008.

  "The solution to this problem [of a dissection of an equilateral triangle into pieces that can be rearranged to form a square] is often attributed to Henry Ernest Dudeney (1857-1930), one of the greatest nineteenth-century puzzlers. This dissection appears in his book (Dudeney 1907) as the haberdasher's problem, although it had previously been posed in his puzzle column in Weekly Disaotch on 6 April 1902. Two weeks later he reported that many people had spotted that this was possible using five pieces, beginning by cutting the triangle into two right triangles. The only person to correctly send in a solution using four pieces was a Mr. C. W. McElroy of Manchester. Interestingly, Frederickson (2002) leaves us in doubt as to whether Dudeney knew how to solve the puzzle using only four pieces before he posed it."

  "Perhaps a more interesting problem would be to find the minimum number of pieces needed for a dissection between two polygonal shapes. This problem appears to be very difficult and is currently unsolved in the general case. An extensive treatment of the history and mathematics of dissections is given in Frederickson (1997), with special hinged dissections covered in Frederickson (2002)."

• Martin Gardner, Origami, Eleusis, and the Soma Cube: Martin Gardner's Mathematical Diversions, (The New Martin Gardner Mathematical Library), Cambridge University Press, 2008.
  
  
• Anker Tiedemann, Pythagoras' Firkant: Matemagi for talfreaks (Pythagoras's Square: Mathemagic for Number Freaks), Samsø, Denmark: Danmarks Matematiklærerforenings forlag Matematik, 2008.
  
  
• Robert A. Hearn and Erik D. Demaine, Games, Puzzles, and Computation, A K Peters, 2009.
  
  
• Satyan L. Devadoss and Joseph O'Rourke, Discrete and Computational Geometry, Princeton University Press, 2011.
  
  
• Joseph O'Rourke, How to Fold It: The Mathematics of Linkages, Origami and Polyhedra, Cambridge University Press, 2011.

  "Hinged dissections are described in Frederickson's delightful book."

• Edward J. Barbeau, More Fallacies, Flaws & Flimflam, Mathematical Association of America, Spectrum, 2013.

  "It provides an excellent comprehensive survey of the art and science of dissecting polygons and rearranging the pieces to form other polygons or sets of polygons."

• I. E. Leonard, J. E. Lewis, A. C. F. Liu, and G. W. Tokarsky, Classical Geometry: Euclidean, Transformational, Inversive, and Projective, John Wiley & Sons, 2014.
  
  
• Martin Gardner, Knots and Borromean Rings, Rep-Tiles, and Eight Queens, Mathematical Association of America, 2014.
  
  
• Hans Walser, Symmetrie in Raum und Zeit, B. G. Teubner: Leipzig, 2014.
  
  
• Hans Walser, EAGLE-MALBUCH Formen und Farben, Geometrische Figuren zum Ausmalen, Eagle 084, Leipzig 2015.
  
  
• Claudi Alsina and Roger B. Nelsen, A Mathematical Space Odyssey: Solid Geometry in the 21st Century, MAA Press: 2015.
  
  
• Jin Akiyama and Kiyoko Matsunaga, Treks into Intuitive Geometry: The Worlds of Polygons and Polyhedra, Springer Japan: 2015.
  
  
• Jay Friedenberg, Tattoo Patterns From Around the World, 2015.
  
  
• Hans Walser, EAGLE-MALBUCH Zöpfe-Zerlegungen-Zehnecke: Geometrische Figuren zum Ausmalen, Eagle 094, Leipzig 2016.
  
  
• Andy Liu, "Area and dissection," S.M.A.R.T. Circle Minicourses, Springer: 2018, pp. 3-28.
  
  
• "Découpages & pavages, Entre art et géométrie," Tangente Hors-série no. 64. Éditions POLE, Paris, France, Septembre 2018.

  See references on pages 40 and 67.
  
  Note that the hinged dissection of an octagon to a square on page 41 should be attributed to me. I gave that hinged dissection on page 120 of my (2002) book, Hinged Dissections, and I also displayed a translucent plastic model of it on my (2003) webpage https://www.cs.purdue.edu/homes/gnf/book2/modphoto.html .
  
  On page 40, there is a photograph of a table based on my hinged dissection of an octagon to a square, which is not explained in the text. Bernard Lalanne was an aerospace engineer based in the south of France, who got sent me that photo and also one of the square top in October 2003. My webpage describing Bernard's table has been at https://www.cs.purdue.edu/homes/gnf/book2/Booknews2/lalanne.html since October 2003.
  
  Note that the hinged dissection of three hexagons to one hexagon, on page 63, had already been described by me in my (2002) book, Hinged Dissections, on pages 62-63.
  
  On page 9, there is a dissection to an "approximate rectangle", which motivates the formula for the area of a circle. This was discussed already over a decade ago in https://www.cs.purdue.edu/homes/gnf/book2/Booknews2/formumod.html .

• "Maths Jeux Culture Express", CIJM (Comité International des Jeux Mathématiques), Paris, France, Mai 2019.

  See the bibliography on page 97.
  
  On page 23, we see Gavin Theobald's dissection of a globular Greek Cross to a square. This dissection was explained already in Hinged Dissections: Swinging and Twisting on page 137.
  
  On page 27, we see Henry Dudeney's legendary hinging of the dissection of an equilateral triangle to a square. It is very similarly displayed as in Hinged Dissections: Swinging and Twisting, on page 2.

Citations in theses:

• Robert Aubrey Hearn, Games, Puzzles, and Computation, Ph.D. dissertation, Massachusetts Institute of Technology, 2006.
  
  
• Paul Garcia, Life and Work of Major Percy Alexander MacMahon, Ph.D. dissertation, Open University, 2006.
  
  
• Noah Duncan, Zoomorphic Design, Interchangeable Components, and Approximate Dissections: Three New Computational Tools for Open-Ended Geometric Design, Ph.D. dissertation, University of California, Los Angeles, 2017.
  
  
• Masoud Matinpour, An Investigation on the Potentials of Islamic Geometric Patterns Regarding Kinetic Surface Design (Islami Geometrik Oruntulerin Kinetik Yuzey Olusturma Potansiyelleri Uzerinde Bir Deneme), M.Sc. thesis, Gazi University, Ankara, Turkey, June, 2019. (See Sekil 2.33, on page 59, which reproduced Figure T8, on page 117, from "Turnabout 3: Hinged Tessellations", and Sekil 2.34, on page 60, which reproduced Figure T9, on page 118, also from "Turnabout 3: Hinged Tessellations".)
  
  

Citations in book chapters:

• Jin Akiyama and Gisaku Nakamura, "Congruent Dudeney Dissections of Triangles and Convex Quadrilaterals - All Hinge Points Interior to the Sides of the Polygons", in Discrete and Computational Geometry: The Goodman-Pollack Festschrift, ed. B. Aranov, S. Basu, and J. Pach, 2003, Springer, pp. 43-63.
  
  
• Joseph O'Rourke and Subhash Suri, "Polygons," in Handbook of Discrete and Computational Geometry, second edition, ed. Jacob E. Goodman and Joseph O'Rourke, 2004, CRC Press.
  
  
• Jean-Paul Delahaye, "Dissections géométriques," in Encyclopédie Universalis.
  
  
• Tiina Hohn and Andy Liu, "Polyomino dissections," in Martin Gardner in the Twenty-First Century, ed. Michael Henle and Brian Hopkins, Mathematical Association of America, Washington, DC, 2012, pp. 135-141.

  "The torch has now been passed on to Greg Frederickson, with three outstanding books so far."

• Joseph O'Rourke, Subhash Suri, and Csaba D. To'th, chapter 30, "Polygons", in Handbook of Discrete and Computational Geometry, third edition, edited by Jacob E. Goodman, Joseph O'Rourke, and Csaba D. To'th, CRC Press LLC, 2016.

Citations in Web Columns:

• Joseph Malkevitch, "Are precise definitions a good idea?", feature column for the American Mathematical Society, 2016.
  
  
• Alexander Bogomolny, "Pythagorean Theorem", 2016.
• Christian Blanvillain, "Quadratum Cubicum".

  "For more information on the fabulous history of this problem, and on dissections in general, we refer the reader to the bibliography's links and the three excellent books by Prof. Greg N. Frederickson, that will present to you the puzzle solutions throughout the ages and much more!"

Citations in unpublished papers:

• David Eppstein, Hinged kite mirror dissection.
  
  
• Yahan Zhou and Rui Wang, "A Computational Algorithm for Creating Geometric Dissection Puzzles"
  
  
• Izidor Hafner, "Dissection of rhombic solids with octahedral symmetry to Archimedean solids, Part 1".
  
  
• Izidor Hafner, "Dissection of rhombic solids with octahedral symmetry to Archimedean solids, Part 2".
  
  
• Frank Moeckel, "Kinematische Architektur," Technische Universität Darmstadt , Fachbereich Architektur, October 2006. (no longer active)
  
  
• Alfinio Flores Penafiel, "Geometría con bisagras". ("Geometría con bisagras".)
  
  
• Leonardo Bobadilla, "Assembly of Hinged Polygon Triangulations".
  
  
• Mircea Pitici, "Geometric Dissections", Cornell University, 2008.
  
  
• Yoshihisa Sato, Megumi Ishida, Takafumi Kitamura, and Ryuji Suga, "Dudeney dissections of polygons as mathematical teaching materials in the elementary or secondary education", in a Japanese-language journal, pp. 113-127. (Received 2009).
  
  
• Giuseppe Dattoli, Elio Sabia, and Mario Del Franco, Triangoli e la Notazione di Conway, 2009.
  
  
• Erik D. Demaine, Joseph S. B. Mitchell, and Joseph O'Rourke, "The Open Problems Project", December 8, 2012.
  
  
• Serge Perrine, "Trigonométrie pythagoricienne", Campus de Metz de Supélec, France, July 2014.
  
  
• Jeffrey Bosboom, Erik D. Demaine, Martin L. Demaine, Jayson Lynch, Pasin Manurangsi, Mikhail Rudoy, and Anak Yodpinyanee, "Dissection with the Fewest Pieces is Hard, Even to Approximate", arXiv Dec 2015.
  
  
• David McKenzie, "The Histories of Common Forms of Tiling Puzzles", Blog, 2016.
  
  
• Jin Akiyama, Stefan Langerman, and Kiyoko Matsunaga, "Reversible Nets of Polyhedra", arXiv, July 2, 2016.
  
  
• Jin Akiyama, Erik D. Demaine, Stefan Langerman, Polyhedral characterization of reversible hinged dissections," arXiv, March 3, 2018.

Citations in presentations:

• Joel Reyes Noche, An Invitation to Research, Department of Mathematics and Natural Sciences, Ateneo de Naga University, Philippines, July 4, 2007.
  
  
• Hans Walser, "Puzzles: Mathematik und Schule," Mathematisches Institut der Johannes Gutenberg Universität;t Mainz, December 16, 2015.
  
  

Citations to "Geometric dissections that swing and twist":

• J. Akiyama, F. Hurtado, C. Merino, J. Urrutia, "A problem on hinged dissections with colours," Graphs and Combinatorics, vol. 20 (2004), pp. 145-159.
  
  

Citations to "Designing a table both swinging and stable":

• Andrew Percy and Alistair Carr, Leaning on Socrates: to derive the pythagorean theorem, Australian Mathematics Teacher, Vol. 66, No. 2 (2010), pages 8-12.

  "The version that we give below can be constructed as a wooden "toy" used to demonstrate the derivation. Similar hinged "toys", such as the Dudeney dissection, transforming an equilateral triangle into a square, are charming in their appeal to all ages (de Mestre 2003, Frederickson 2008)."

• Barbara Geometry: From Triangles to Quadrilaterals and Polygons, (powerpoint) Broward County Public Schools, January 2011.
  
  

Citations to "Unexpected twists in geometric dissections":

• Dan Ismailescu and Adam Vojdany, Class Preserving Dissections of Convex Quadrilaterals, Forum Geometricorum, vol. 9 (2009), pages 195-211.
  
  
• Dragana Martinovic and Agida G. Manizade, Technology as a partner in geometry classrooms, Electronic Journal of Mathematics & Technology, vol. 8, issue 2 (Feb. 2014), pages 69-87.
  
  
• Yi-Jheng Huang, Shu-Yuan Chan, Wen-Chieh Lin, and Shan-Yu Chuang, Making and animating transformable 3D models, Computers & Graphics, vol. 54, February 2016, pages 127-134.
  
  

Citations to "Geometric dissections now swing and twist":

• Francisco Pérez Arribas, "Juegos Matemáos Triángulos cuadrados y cruces cuadradas: algunos puzzles geométricos de H. E. Dudeney," Revista de Investigación, 1 de abril de 2012.