# Origami.

## Presentation on theme: "Origami."— Presentation transcript:

Origami

Dragon

Swan

Spider

Unicorn

TRANSFORMERS

YODA

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 + a a2n-1 = 180 and a2 + a4 + a a2n = 180

Origami Axioms 1. Given two points p1 and p2 , we can fold a line connecting them. 2. Given two points p1 and p2 , we can fold p1 onto p2. 3. Given two lines l1 and l2, we can fold line l1 onto l Given a point p1 and a line l1 , we can make a fold perpendicular to l1 passing through the point p1.

5. 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.

6. 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. 7. Given a point p1 and two lines l1 and l2, we can make a fold perpendicular to l2 that places p1 onto 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.

Origami Axioms with Pictures

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.