Titlebook: An Introduction to Computational Origami; Tetsuo Ida Book 2020 Springer Nature Switzerland AG 2020 paper fold.Euclid and Origami geometry.

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https://doi.org/10.1007/978-94-015-0602-1n adequate length, we can construct the simplest knot by three folds. We can make the shape of the knot a regular pentagon if we fasten the knot rigidly. We analyze the knot fold formally so that we can construct it rigorously and verify the correctness of the construction by algebraic methods. In p

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,Vierzehntes und Fünfzehntes Jahrhundert,ewriting system (O, ?), where O is the set of abstract origamis and ? is a binary relation on O, that models a fold. An abstract origami is a structure (∏,?～?,??), where ∏ is a set of faces constituting an origami, and?～?and???are binary relations on ∏, each denoting adjacency and superposition rela

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Book 2020. Focusing on how classical and modern geometrical problems are solved by means of origami, the book explains the methods not only with mathematical rigor but also by appealing to our scientific intuition, combining mathematical formulas and graphical images to do so. In turn, it discusses the verif

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Verification of Origami Geometry, our verification method. One is a simple geometric shape to explain the principle of verification using algebraic methods. The other two are the proofs of a regular pentagon construction and the generalized Morley’s theorem. Through the three examples, we see the computationally streamlined geometric construction and verification.

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,Vierzehntes und Fünfzehntes Jahrhundert,tions between the faces. This view is one step forward towards our more profound understanding of 3D and semi-3D origami folds, where we have overlapping faces. We take a classical origami crane as an example of our discussion and show how the theories discussed in this chapter formally analyze it.

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0943-853X led explanations how classical and modern geometrical proble.In this book, origami is treated as a set of basic geometrical?objects?that are represented and manipulated symbolically and graphically by computers. Focusing on how classical and modern geometrical problems are solved by means of origami