![]() In our proofs, the trisection ofan angle by H.Abe, the duplication of the cube volume and the Cardano'sformula of the cubic equation play essential parts. Those were described by H.Huzita and B.Scimeni in theProceedings of the First Meeting of Origami Science and Technology, butour proofs are different from theirs. Also, a regular polygon of p(p:odd prime) sides can be constructed using origami if and only if p isan origami prime. Then weobtain the necessary and sufficient condition for which a real number isan origami number constructed by origami. In the present paper,we study which shapes are possible to construct using origami. I will illustrate how to use the algebraic information fromfields and curves to construct a solution to the famous optical problemof Alhazen and indicate how this leads to a solution by origami.Ībstract: The art of origami is from Japanese traditional cultureand produces many interesting geometrical shapes. Roger Alperin (San Jose State University)Ībstract: I will give a survey of the axioms of mathematicalorigami and their connections with the theory of fields and constructionswith conics. Mathematical Origami and Alhazen's Problem #4 How to fold a mathematically accurate pentagramstar from a single sheet of square paper. #3 An arbitrarily made mother line bears elevenwonder babies. #2 Haga's theorem enables a standard rectanglepaper to divide its length into an odd number of equal parts. #1 The first step of folding induces an insectface pattern. I will talk about some origamics phenomena belowwhich appear on a simply folded square or rectangle sheet of paper. Please fold paper together with me and experience my origamics world! The term is made of the stem, origami and the suffix,ics which is often used to stand for science or technology, as mathematics. Now I think that the term ORIGAMICS may become a good name to representall scientific origami shown at 3OSME. ORIGAMICS at the 2nd Origami Science Meeting in 1994 for studies uponmy findings. I was motivated in this during the 1980s after finding severalmathematical phenomena in folded square paper. ![]() Regarding above circumstances, I felt the need fora new name to describe the genre of scientific origami other than origamifor children. In Japan, origami usually means a handicrafthobby for children, so almost all books about origami are arranged in thejuvenile section of bookstore even if some of them are for enthusiasts. They have samespelling, but they differ somewhat in sense as well as pronunciation. The accent of the former falls on the third syllable (ga) while the latteron second one (ri). Kazuo Haga (University of Tsukuba, Japan)Ībstract: The subject of our meeting ORIGAMI is an internationalword which is derived from the Japanese word origami. įold Paper and Enjoy Mathematics: ORIGAMICS I will also comment on the insightsthis research gives into the nature of singularities in regular crumpling.įor more information and illustrations, go to. I will discuss whether the two cases converge to the sameconfiguration in the unstretchable limit. In simulations ofvery thin sheets in 3 or 4 spatial dimensions, small deviation of the sheetinto the fourth dimension effectively negated the strain field around ridges- leading to greatly reduced total elastic energy and different energyscaling. Changing the spatial dimensionchanges the geometric coupling between energies. I will then present the results of our studies on crumpling ofthin sheets in four spatial dimensions. In this lectureI will review the energy scaling properties of ridges in thin elasticsheets. The energy condensation is driven by acompetition between bending and stretching energy costs, which are coupledby the geometric relation between curvature and strain. ![]() ![]() This crumpling process can be viewed as acondensation of elastic energy onto the area surrounding ridge lines, anarea fraction of the sheet which becomes arbitrarily small as the thicknessof the sheet goes to zero. Plenary Talks Mathematicsof Origami Origami in Education Science and ApplicationsĪbstract: When a thin sheet of elastic material is confined withina shrinking volume it does not deform uniformly, but instead forms a networkof singular point and ridges.
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