A THEORY OF ORIGAMI WORLD 28 1 a 0 FIG5. This paper presents the fundamentals of Origami engineering and its application in nowadays as well as future industry.

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### We have established a labeling procedure for this Origami world which can find the 3-D.

Origami theory. Other interpretations of Fig. However Kawasakis Theorem and Hagas Theorem are still valid in real material folding 7. It is a craft that is fun mindfulness and therapeutic for all ages.

Examples are the crimp fold and the fold at a. Origami Catastrophe Theory In flat folding the folds of a model and the model itself are collapsible onto a flat surface. Origami Theory and its ApplicationsA Literature Review L.

Several main cores of mathematical approaches such as Huzita-Hatori axioms Maekawa and Kawasakis theorems are introduced briefly. Origami crease pattern the difference between the number of mountain creases M and valley creases V must always be 2 as shown in 1. 5 are imaginableThis paper will demonstrate how basic geometric con- straints can be exploited to recover such possible shapes of the object that a given drawing may depict.

Folding papers will involve both our hands and mind to be active. In 1970 an astrophysicist named Koryo Miura conceived what would become one of the most well-known and well-studied folds in origami. Meanwhile flaps and circle packing by Robert Lang is explained to make understood the underlying.

Tomohiro Tachi mentioned in his research that Rigid origami consists of rigid panels connected by hinges constrained around vertices 8. However some folds normally formed towards the end cannot be collapsed onto a plane without having to create additional folds. Less obvious is the fact that constructions in origami can be treated using field and Galois theory 1 2 that curved crease origami requires differential geometry for its analysis and that.

The Origami world is a model for understanding line drawings in terms of surfaces and for finding their 3-D configurations. Moreover some innovative applications of origami such as eyeglass origami stent and high tech origami based on mentioned theories and principles are showcased in section III. An application of tessellation is made possible by Origami theory.

Origami crease patterns can be characterized with tools from knot theory potentially leading to a classi cation of origami models in terms of folding complexity Moreover from a geometric standpoint it turns out that if the an-cient Greeks had thrown away their compasses and straightedges and merely. In addition this can be a mindfulness therapy when folding familiar models. A a concave comer b folded paper roof covering another paper.

The origami configuration is. However the art form has a history that spans back even further than the term origami itself. Sujan O World Academy of Science Engineering and Technology International Journal of Humanities and Social Sciences Vol7 No1 2013.

The pattern of creases forms a tessellation of parallelograms and the whole structure collapses and unfolds in a single motion providing an elegant way to fold a map. It assumes that surfaces themselves can be stand-alone objects unlike the conventional trihedral world which assumes solid objects. Stephen Sells and Megan Neumann teach Robert J Langs TreeMaker Mathematics for Belmonts Graph Theory Class.

Origami within the context of an art therapy session can have many uses includingbut not limited to helping people deal with trauma practicing mindfulness and even promoting sensorimotor skills or frustration tolerance. Fundamentals of origami in Rigid Origami such as Huzita-Hatori axioms. While some updated origami technology such as Vacuumatics self-folding of polymer sheets and programmable matter folding which could greatlyenhance origami structureare demonstrated in Section IV to offer more.

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