http://de.evo-art.org/index.php?action=history&feed=atom&title=Artfully_Folding_Hexagons%2C_Dodecagons%2C_and_Dodecagrams 2026-04-07T01:27:05Z Versionsgeschichte dieser Seite in de_evolutionary_art_org MediaWiki 1.27.4 http://de.evo-art.org/index.php?title=Artfully_Folding_Hexagons,_Dodecagons,_and_Dodecagrams&diff=3901&oldid=prev 2015-01-28T11:11:48Z

<p>Die Seite wurde neu angelegt: „ == Reference == Greg Frederickson: <a href="/index.php?title=Artfully_Folding_Hexagons,_Dodecagons,_and_Dodecagrams" title="Artfully Folding Hexagons, Dodecagons, and Dodecagrams">Artfully Folding Hexagons, Dodecagons, and Dodecagrams</a>. In: <a href="/index.php?title=Bridges_2013" title="Bridges 2013">Bridges 2013</a>. Pages 135–142 == DOI == == Abstract…“</p> <p><b>Neue Seite</b></p><div><br /> <br /> == Reference ==<br /> Greg Frederickson: [[Artfully Folding Hexagons, Dodecagons, and Dodecagrams]]. In: [[Bridges 2013]]. Pages 135–142 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Folding dissections are introduced for hexagons, dodecagons, and dodecagrams. Each folding dissection transforms<br /> one of these figures to a similar figure but of a different height. The goal is to minimize the number of pieces in<br /> the folding dissection, while at the same time exploiting symmetry to create beautiful objects that fold magically<br /> before our eyes. For regular hexagons, the dissections transform a regular hexagon of height h to a regular hexagon<br /> of height n ∗ h, where n is, in turn, 3 or 4 or 9 or 16 or 25. For regular dodecagons, our dissection transforms one<br /> dodecagon to another twice as high. For the 12-pointed star {12/2}, we give a dissection to a star 3 times as high,<br /> and also one to a star twice as high. The design of these various folding dissections is explored.<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [1] Greg N. Frederickson. Dissections Plane &amp; Fancy. Cambridge University Press, New York, 1997.<br /> <br /> [2] Greg N. Frederickson. Hinged Dissections: Swinging and Twisting. Cambridge University Press, New<br /> York, 2002.<br /> <br /> [3] Greg N. Frederickson. Piano-hinged Dissections: Time to Fold. A K Peters Ltd, Wellesley, Mas-<br /> sachusetts, 2006.<br /> <br /> [4] Greg N. Frederickson. Updates to chapter 17, ‘Manifold Blessings’, in piano-hinged dissections: time<br /> to fold! webpage (http://www.cs.purdue.edu/homes/gnf/book3/Booknews3/ch17.html), 2007.<br /> <br /> [5] Greg N. Frederickson. Four folding puzzles by Greg N. Frederickson that illustrate his talk ‘Unfolding an<br /> 8-high square, and other new wrinkles’. In Scott Hudson, editor, G4G8 Gathering 4 Gardner Exchange<br /> Book, volume 2, pages 42–45. Gathering for Gardner, Inc., 2008.<br /> <br /> [6] Ernest Irving Freese. Geometric transformations. A graphic record of explorations and discoveries in<br /> the diversional domain of Dissective Geometry. Comprising 200 plates of expository examples. Unpub-<br /> lished, 1957.<br /> <br /> [7] Harry Lindgren. Geometric Dissections. D. Van Nostrand Company, Princeton, New Jersey, 1964.<br /> <br /> [8] Lyle Pagnucco and Jim Hirstein. Capturing area and a solution. http://jwilson.coe.uga.edu/Texts.Folder/Pag/HirPag.html, 1996.<br /> <br /> [9] T. Sundara Row. Geometrical Exercises in Paper Folding. Addison, Madras, 1893. See sections 17 and<br /> 18 on page 4.<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/2013/bridges2013-135.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/2013/bridges2013-135.html</div>

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