http://de.evo-art.org/index.php?action=history&feed=atom&title=Hyperbolic_Tilings_with_Truly_Hyperbolic_Crochet_Motifs 2026-04-20T15:16:16Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Hyperbolic_Tilings_with_Truly_Hyperbolic_Crochet_Motifs&diff=3849&oldid=prev 2015-01-27T18:58:49Z

<p>Die Seite wurde neu angelegt: „ == Reference == Joshua Holden and Lana Holden: <a href="/index.php?title=Hyperbolic_Tilings_with_Truly_Hyperbolic_Crochet_Motifs" title="Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs">Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs</a>. In: <a href="/index.php?title=Bridges_2014" title="Bridges 2014">Bridges 2014</a>. Pages 405–408 == DOI ==…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Joshua Holden and Lana Holden: [[Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs]]. In: [[Bridges 2014]]. Pages 405–408 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Until now, most methods for making a hyperbolic plane from crochet or similar fabrics have fallen into one of two<br /> categories. In one type, the work has constant negative curvature but does not naturally lend itself to a polygonal<br /> tiling. In the other, polygonal tiles are attached in such a way that the final product approximates a hyperbolic plane<br /> on the large scale but does not have truly constant curvature. We show how crochet can be used to create polygonal<br /> tiles that have constant negative curvature in themselves and can therefore be joined into a large region of a hyperbolic<br /> plane without significant stretching. Formulas from hyperbolic trigonometry are used to show how, in theory, any<br /> regular tiling of the hyperbolic plane can be produced in this way.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] Robyn Chachula, Crochet Stitches Visual Encyclopedia, John Wiley &amp; Sons, Hoboken, NJ, 2011.<br /> <br /> [2] Helaman Ferguson, helaman ferguson sculpture: Hyperbolic Quilt, 2003. https://web.archive.<br /> org/web/20120929025831/http://www.helasculpt.com/gallery/hyperbolicquilt/ (as of Mar. 15, 2014).<br /> <br /> [3] Helaman Ferguson and Claire Ferguson, Celebrating Mathematics in Stone and Bronze, Notices of the<br /> AMS 57 (2010), 840–850.<br /> <br /> [4] David W. Henderson and Daina Taimina, Experiencing Geometry: Euclidean and Non-Euclidean with<br /> History, Pearson Prentice Hall, Upper Saddle River, NJ, 2005.<br /> <br /> [5] D.M.Y. Sommerville, The Elements of Non-Euclidean Geometry, Dover, New York, NY, 1958.<br /> <br /> [6] Daina Taimina, Crocheting Adventures with Hyperbolic Planes, AK Peters, Wellesley, MA, 2009.<br /> <br /> [7] Jeff Weeks, How to Sew a Hyperbolic Blanket. HyperbolicBlanket/index.html (as of Mar. 15, 2014). http://www.geometrygames.org/<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2014/bridges2014-405.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2014/bridges2014-405.html</div>

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