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Origami

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History of Origami Origami comes from the Japanese words “oru”, which means to fold and “kami” which means paper. Originated in China in the 1 st or 2 nd century. Moved to Japan in the 5 th century. Originally only used by the wealthy since paper was so rare. The crane (one of the most popular shapes) was the first to have written instructions. There is a legend that if you fold 1000 cranes, you are granted one wish.

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There is a theorem called Kawasaki's Theorem, which says that if the angles surrounding a single vertex in a flat origami crease pattern are a 1, a 2, a 3,..., a 2n, then: a 1 + a 3 + a a 2n-1 = 180 and a 2 + a 4 + a a 2n = 180

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Origami Axioms 1. Given two points p 1 and p 2, we can fold a line connecting them. 2. Given two points p 1 and p 2, we can fold p 1 onto p Given two lines l 1 and l 2, we can fold line l 1 onto l Given a point p 1 and a line l 1, we can make a fold perpendicular to l 1 passing through the point p 1.

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5. Given two points p 1 and p 2 and a line l 1, we can make a fold that places p 1 onto l 1 and passes through the point p 2.

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6. Given two points p 1 and p 2 and two lines l 1 and l 2, we can make a fold that places p 1 onto line l 1 and places p 2 onto line l Given a point p 1 and two lines l 1 and l 2, we can make a fold perpendicular to l 2 that places p 1 onto line l 1.

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Compass and Straight Edge (S.E. & C.) Axioms Given two points we can draw a line connecting them. Given two (nonparallel) lines we can locate their point of intersection. Given a point p and a length r we can draw a circle with radius r centered at the point p. Given a circle we can locate its points of intersection with another circle or line.

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Origami Axioms with Pictures

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Given two points p1 and p2 we can fold a line connecting them. Given two points p1 and p2 we can fold p1 onto p2. Given two lines l1 and l2 we can fold line l1 onto l2.

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Given a point p1 and a line l1 we can make a fold perpendicular to l1 passing through the point p1. Given two points p1 and p2 and a line l1 we can make a fold that places p1 onto l1 and passes through the point p2. Given two points p1 and p2 and two lines l1 and l2 we can make a fold that places p1 onto line l1 and places p2 onto line l2.

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