Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs

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Joshua Holden and Lana Holden: Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs. In: Bridges 2014. Pages 405–408



Until now, most methods for making a hyperbolic plane from crochet or similar fabrics have fallen into one of two categories. In one type, the work has constant negative curvature but does not naturally lend itself to a polygonal tiling. In the other, polygonal tiles are attached in such a way that the final product approximates a hyperbolic plane on the large scale but does not have truly constant curvature. We show how crochet can be used to create polygonal tiles that have constant negative curvature in themselves and can therefore be joined into a large region of a hyperbolic plane without significant stretching. Formulas from hyperbolic trigonometry are used to show how, in theory, any regular tiling of the hyperbolic plane can be produced in this way.

Extended Abstract


Used References

[1] Robyn Chachula, Crochet Stitches Visual Encyclopedia, John Wiley & Sons, Hoboken, NJ, 2011.

[2] Helaman Ferguson, helaman ferguson sculpture: Hyperbolic Quilt, 2003. https://web.archive. org/web/20120929025831/http://www.helasculpt.com/gallery/hyperbolicquilt/ (as of Mar. 15, 2014).

[3] Helaman Ferguson and Claire Ferguson, Celebrating Mathematics in Stone and Bronze, Notices of the AMS 57 (2010), 840–850.

[4] David W. Henderson and Daina Taimina, Experiencing Geometry: Euclidean and Non-Euclidean with History, Pearson Prentice Hall, Upper Saddle River, NJ, 2005.

[5] D.M.Y. Sommerville, The Elements of Non-Euclidean Geometry, Dover, New York, NY, 1958.

[6] Daina Taimina, Crocheting Adventures with Hyperbolic Planes, AK Peters, Wellesley, MA, 2009.

[7] Jeff Weeks, How to Sew a Hyperbolic Blanket. HyperbolicBlanket/index.html (as of Mar. 15, 2014). http://www.geometrygames.org/


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