Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving

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Gwen L. Fisher: Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving. In: Bridges 2015. Pages 99–106



The impossible triangle and other impossible figures are optical illusions that have inspired much artwork since their discovery by Oscar Reutersvärd in the 1930s. This paper shows how I use the impossible triangle and its variations to create a series of sculptures woven with seed beads and thread, using a bead weaving technique known as “cubic right angle weave” (CRAW). The flexibility of the beadwork eliminates the paradox of the optical illusion by substituting curves for the otherwise straight beams. The resulting “highly unlikely” beaded art objects generate surfaces that twist like Möbius bands around the objects, often making several distinct paths, which make interesting colorings possible. The many beaded examples include triangles, squares and frames. The beading techniques were then applied to tetrahedra and a dodecahedron that generate no corresponding optical illusion.

Extended Abstract


 author      = {Gwen L. Fisher},
 title       = {Highly Unlikely Triangles and Other Impossible Figures in Bead Weaving},
 pages       = {99--106},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{http://archive.bridgesmathart.org/2015/bridges2015-99.html }},
 url         = {http://de.evo-art.org/index.php?title=Highly_Unlikely_Triangles_and_Other_Impossible_Figures_in_Bead_Weaving },

Used References

[1] H. Collin, Cubic Right Angle Weave - how to create shapes, YouTube video, https://www.youtube.com/watch?v=d9jE2dldiVo, Accessed April 22, 2015.

[2] H. Collin, Cubic Right Angle Weave video Tutorial, YouTube video, https://www.youtube.com/watch?v=P1Ib0qsQSy4, Accessed April 22, 2015.

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[6] G. L. Fisher, Highly Unlikely Triangles Beaded with Cubic Right Angle Weave, Self Published on Etsy, https://www.etsy.com/listing/204753180/, pp. 2, 14. 2014.

[7] G. L. Fisher, How to Weave Cubic Right Angle Weave with Beads, YouTube video, https://www.youtube.com/watch?v=BSM9OiO4xjk, Accessed April 22, 2015.

[8] G. K. Francis, A Topological Picture Book, Springer-Verlag, New York, pp.68-75, 1987.

[9] V. Hector, The Art of Beadwork, Watson-Guptill Publications, pp 90-94, 2005.

[10] D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books, Inc., New York, p. 10. 1979.

[11] D. R. Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern, Basic Books, Inc., New York, p. 18. 1985.

[12] L. S. Penrose and R. Penrose, “Impossible Objects: A Special Type of Visual Illusion,” British Journal of Psychology, 49(1), pp. 31–33, February 1958.

[13] A. Seckel, Masters of Deception, Sterling Publishing Co., Ltd., New York, pp. 67-87, 90, 132-136, 179-184. 262. 2004.

[14] A. Seckel, Optical Illusions: The Science of Visual Perception, Firelfy Books Ltd., New York, pp. 309. 2006.

[15] Wikipedia, Penrose Triangle, http://en.wikipedia.org/wiki/Penrose_triangle, Accessed April 21, 2015.


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