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<p>Die Seite wurde neu angelegt: „ == Reference == Helena Verrill: <a href="/index.php?title=Origami_Tessellations" title="Origami Tessellations">Origami Tessellations</a>. In: <a href="/index.php?title=Bridges_1998" title="Bridges 1998">Bridges 1998</a>. Pages 55–68 == DOI == == Abstract == Origami tessellations are made from…“</p> <p><b>Neue Seite</b></p><div><br /> == Reference ==<br /> Helena Verrill: [[Origami Tessellations]]. In: [[Bridges 1998]]. Pages 55–68 <br /> <br /> == DOI ==<br /> <br /> == Abstract ==<br /> Origami tessellations are made from a single piece of paper, which is folded in a repeating<br /> pattern. Figure l.a shows an example of a crease pattern for an origami tessellation. This pattern<br /> was created with the aim of producing a finished pattern of repeating &quot;heart&quot; shapes.<br /> <br /> The problem of finding tessellations which can be folded is difficult because the paper must not<br /> be stretched or cut, and must end up as a flat sheet, so this imposes many conditions on the pattern<br /> to be folded. An understanding of the geometry of tessellations and of paper folding is required.<br /> However, the study of paper folding is still in its infancy, and many questions which have been an-<br /> swered for Euclidean constructions remain unanswered for origami methods; for instance, although<br /> impossible with Euclidean geometry, it is simple to trisect an angle using folding techniques, (see<br /> [HU2I]). However a satisfactory list of axioms, and a list of exactly what is possible, and what is<br /> not possible, for origami-geometry constructions has not been found conclusively, though several<br /> attempts have been made (See [H4)). On the other hand, though some geometric constructions<br /> may be easier with origami, the problem of determining whether a crease pattern can be collapsed<br /> to give a flat origami, or even folded at all, is generally very difficult (see [BH] and [K]). ...<br /> <br /> == Extended Abstract ==<br /> <br /> == Bibtex == <br /> <br /> == Used References ==<br /> [BP] Barreto, P. and C. K. Palmer, Explo and Anto presentation, Bay Area Rapid Folders Newsletter, Spring 1997.<br /> <br /> [B] A. Bateman, http://www.sanger.ac.uk/..-.agb/Origami/origami.html<br /> <br /> [BH] M. Bern, and B. Heyes, The complexity of fiat origami, Proceedings of the Seventh Annual ACM-SIAM Sym-<br /> posium on Discrete Algorithms, 175-183, ACM, New York, 1996.<br /> <br /> [F] S. Fujimoto, Invitation to creative origami playing (in Japanese), Asahi Culture Center, 1982.<br /> <br /> [GS] B. Griinbaum, and G. C. Sheppard, Tilings and patterns, W. H. Freeman and Co., New York, 1987.<br /> <br /> [Huz] H. Huzita, The trisection of a given angle solved by the geometry of origami, Proceedings of the First Interna-<br /> tional Meeting of Origami Science and Technology, Ferrara, Itally, December 1989.<br /> <br /> [HI] T. Hull, Origametry, 1994. (Unpublished manuscript).<br /> <br /> [H2] T. Hull, Origami Tessellations, Part 2, &quot;Tom Hull&#039;s Thing&quot;, Vol. 2.2, February 1995.<br /> <br /> [H3] T. Hull, Origami Tessellations, Part 3, &quot;Tom Hull&#039;s Thing&quot;, Vol. 2.3, April 1995.<br /> <br /> [H4] T. Hull, On the mathematics of fiat origamis, Congressus Numerantium, Vol. 100 (1994), 215-224.<br /> <br /> [H5] T. Hull, http://www.math.uri.edu/hull/Dragonbib.html<br /> <br /> [Ka] T. Kawasaki, On the relation between mountain-creases and valley-creases of a fiat origami (in Japanese),<br /> Sasebo College of Technology Report, Vol. 27 (1990), 55-80.<br /> <br /> <br /> [KY] T. Kawasaki, and M. Yoshida, Crystallographic flat origamis, Memoirs of the Faculty of Science, Kyushu<br /> University, Ser. A, Vol. 42, No.2, 1988, pp. 153-157.<br /> <br /> [KI] D. H. Kling, Doubly periodic flat surfaces in three-space, Ph.D. thesis, Rutgers, New Brunswick, New Jersey,<br /> October 1997.<br /> <br /> [L] D. Lister, Tessellations&quot; af/-d &quot;Tessellations again e-mails to origami-I, July 1997. See http://www.the-<br /> village.com/origami/listserv~search.html<br /> <br /> [M] K. M. Montesinos, Classical tessellations and three manifolds, Springer Verlag, 1987.<br /> <br /> [PI] C. K. Palmer, http!/www.cea.edu/sarah/chris/<br /> <br /> [P2] C. K. Palmer, Extruding and tessellating polygons from a plane, Proceedings of the Second International Meeting<br /> of Origami Science and Technology, Otsu, Japan, December 1994.<br /> <br /> [P3] C. K. Palmer, Periotych tile system, The Paper, Summer 1996, published by Origami USA.<br /> <br /> [Sh] J. Shafer, The mathematics of flashers, Bay Area Rapid Folders Newsletter, Spring 1995, page 13. (See<br /> http//www.krmusic.com/barf/bakissu.htm)<br /> <br /> [Sm] J. Smith, Half a square, e-mail to origami-I, November 1997.<br /> <br /> [VI] H. Verrill, http:/ fmast.queensu.ca/&quot;,helena/origami/tessellations/<br /> <br /> [V2] H. Verrill, Some origami tessellation problems, preprint, January 1998.<br /> <br /> [V3) H. Verrill, Some parameterizing of some origami tessellations, preprint, February 1998.<br /> <br /> [V4] H. Verrill, Origami weave patterns and star patterns, preprint, May 1998.<br /> <br /> [W] D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, Penguin, 1991, ISBN: 0140118136<br /> <br /> <br /> == Links ==<br /> === Full Text === <br /> http://archive.bridgesmathart.org/1998/bridges1998-55.pdf<br /> <br /> [[intern file]]<br /> <br /> === Sonstige Links ===<br /> http://archive.bridgesmathart.org/1998/bridges1998-55.html</div>

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