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Discover the fascinating history of origami, from its Chinese roots to Japanese refinement, and how it evolved from a luxury to a beloved art form. Learn about traditional shapes like cranes and the myth of 1000 cranes, along with mathematical theorems like Kawasaki's Theorem. Explore the principles of origami axioms and the intersection of geometry and art in compass and straight edge axioms. Delve into the world of origami with engaging visuals and follow step-by-step instructions to create your own beautiful origami pieces. Unfold the magic of this ancient paper-folding art!
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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.
