By Robert J. Lang

The connections among origami, arithmetic, technology, expertise, and schooling were a subject of substantial curiosity now for numerous a long time. whereas lots of individuals have occurred upon discrete connections between those fields in the course of the 20th century, the sector relatively took off whilst formerly remoted participants started to reinforce connections with one another via a chain of meetings exploring the hyperlinks among origami and «the open air world.» The Fourth overseas assembly on Origami in technology, arithmetic, and schooling (4OSME), held in September, 2006, on the California Institute of expertise in Pasadena, California, introduced jointly an unheard of variety of researchers proposing on themes starting from arithmetic, to expertise, to academic makes use of of origami, to high quality paintings, and to desktop courses for the layout of origami. chosen papers in line with talks awarded at that convention make up the booklet you carry on your fingers.

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**Extra resources for Origami 4 (Origami (AK Peters))**

**Example text**

Since α = π2 ((n − 2)/n) we have 1 π − 2α = . n+1 3π − 2α Thus, (π − 2α) tan(α) (π − 2α) sin(α) = lim . (3π − 2α) α→π/2 α→π/2 (3π − 2α) cos(α) lim h = lim n→∞ ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ 48 I. Origami in Design and Art Seventeen-Sided Twist Box Top not for the faint of heart (Warning! ) Box Top: use 1 x 1/2 paper (start with 12") 1 Mark 3/5 along the edge of the paper. 2 Crease into 18ths. Suggestion: Do thirds, then thirds again, then halves. Next, crease along the 3/5 line. Turn over. 3 Crease the diagonals of the lower rectangles.

The accumulation points of the crease pattern form the same Pyramid curve as the accumulation points of the branch pattern. Furthermore, the curve overlaps the area that becomes the surface of the pyramid (Figure 4). The inﬁnitely folded limit region cannot be made from a smooth surface. Thus, the Maekawa Pyramid itself cannot grow further; there is not enough paper. The crease pattern must be modiﬁed. Thus, the Pyramid curve and the smooth surface must be separated within the crease pattern. And the individual contraction of generators shown in Figure 5 separates the curve and the surface because the contraction keeps the accumulation point ﬁxed while the generators become smaller and smaller.

4] Miyuki Kawamura. ” In Origami Tanteidan Convention Book, Vol. 9, pp. 22–25. Tokyo: Japan Origami Academic Society, 2003. ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ Fractal Crease Patterns Ushio Ikegami 1 Redesigning the Maekawa Pyramid Maekawa’s pyramid model (Figure 1) is one of the inﬁnite folding models he presented in [4]. By inﬁnite folding, we mean that in the limit of inﬁnite iterations, it produces an inﬁnite number of branches in four directions from a ﬁnite square. Its crease pattern for any nth iteration consists of two kinds of generators.