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Origami. Dragon. Swan. Spider. Unicorn. TRANSFORMERS. YODA. Lord o f the Rings. Praying Mantis. History of Origami. Origami comes from the Japanese words “ oru ”, which means to fold and “ kami ” which means paper.
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Lord of the Rings
Praying Mantis
History of Origami • Origami comes from the Japanese words “oru”, which means to fold and “kami” which means paper. • Originated in China in the 1st or 2nd century. Moved to Japan in the 5th 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.
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 a1, a2, a3, ..., a2n, then: a1 + a3 + a5 + ... + a2n-1 = 180anda2 + a4 + a6 + ... + a2n = 180
Origami Axioms 1. Given two points p1 and p2, we can fold a line connecting them. 2. Given two points p1and p2, we can fold p1 onto p2. 3. Given two lines l1 and l2, we can fold line l1 onto l2 . 4. Given a point p1and a line l1, we can make a fold perpendicular to l1 passing through the point p1.
5. Given two points p1 and p2and a line l1, we can make a fold that places p1 onto l1 and passes through the point p2.
6. Given two points p1and p2 and two lines l1 and l2, we can make a fold that places p1 onto line l1 and places p2onto line l2. 7. Given a point p1 and two lines l1 and l2, we can make a fold perpendicular to l2 that places p1onto line l1.
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.
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.
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.
