Proving the Kawasaki Theorem

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We chose this project; because we all love making origami and now we will know everything in it. Origami means the art of paper folding. It’s connected to the mathematics called geometry. When we fold origami we also create lots of surfaces. For instance, by folding a square piece of paper in half diagonally or from one tip to the opposite tip, we create two surfaces in the shape of triangles. Mathematicians’ related origami to a theorem called the Kawasaki theorem. The Kawasaki theorem states that if we add up the angle measurements of every angle around a point, the sum will be 180. It is a theorem giving a decision for an origami construction to be flat. Kawasaki theorem also states that a given crease pattern
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Sink Fold

The sink fold is a method of blunting a point that has no open edges. The fold should first be precreased. Then carefully open the model and tuck the point inside. Flatten the model afterwards along existing creases.

Procedure of making a pelican origami:

1. Start with your paper white side up. Fold in half, along the line shown, and then open out again. 2. Fold the outside corners into the centre line, and crease well.

3. Fold the outside edges into the centre once again. 4. Turn model over and fold bottom point up to the top point. Crease very well. 5. Fold in half

6. Rotate model so it is now lying down. 7. Raise the inside triangle upwards slowly, then flatten and crease well. 8. Inside Reverse Fold the head along the crease shown.
9. Fold each wing upward as shown, then fold it back again slightly. The pelican will now rest on its wings and sit up. Finished Pelican!

Classifying some types of origami
There are lots of types of origami:
• Action Origami
• Origami Tessellations
• Pure land Origami
• Toilet Paper Origami
• Wet Folding Origami
• Crease Patterns
• Dollar Bill Origami
• Golden Venture Folding
• Modular Origami

Thus, we conclude that in this project we can use the Kawasaki theorem to construct a pelican or a crane using certain folds of origami.

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