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