Math in Origami

7/31/2019 Math in Origami

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Math in OrigamiPresented by

김경진(30101), 김서현(30102), 노수아(30107), 한영준(30132)



Table of Contents

• What is origami?

• What can it do?

•

Problems• Resources & Mastery



What is Origami?

• Origami, or paper folding is an art developed inancient time by artists.

• Today, through the efforts are being made to connectmathematics with origami.

• Its basis was created when two mathematicians Huzitaand Hatori created 7 axioms of origami.

• In modern science, it is used for preserving solarpanels on satellites by folding it up during itsdeparture from the Earth. It is also used in many otherareas because of its interesting ability to convert 2Dforms into 3D structures.



What Can It Do?(1)

• Here are the Huzita-Hatori axioms;

1. There is a fold that passes through two points at once.

2. You can make a fold that places one point to the other.

3. By folding the paper, you can place a line onto another.

4. There is a fold perpendicular to a line that passes a point.5. Given two points and a line, there is a fold that places onepoint to the line and passes the other.

6. When there are two lines and points, there is a fold that placeseach point onto a line.

7. A specific fold exists that is perpendicular to a line and places apoint onto another line.





Problems

• Let us now solve the following problem;

Construction of a Regular Pentagon(on a square paper)

1. Single side of a pentagon measures (5^(1/2)-1)/2.

2. Fold the paper in half make a fold passing the corner andthe creased corner made by the previous fold.

3. Match one of the divided sides to the previous fold transferthe subtracted length on one side of the paper.

4. Move the length to the center fold the length so that leanother sides to make a regular pentagon.



Resources & Mastery• When you become more familiar with origami, you would realize that

there are a lot applications of paper folding in math, especially in thefields of geometry.

• One example would be proving that area of any internal rectangle ina triangle is smaller than half the area of the triangle. It is a simplematter of dividing the triangle into many pieces of right triangles. If one considers paper folding, it becomes much easier to prove suchthing

• There are also other interesting facts about paper folding, such asrepresenting the topology of a certain 3D structure by showing howa 2D paper can be folded into such shape. For example, thedevelopment drawing of a sphere is a 4-edged paper with a fold oneach 2 pairs of 2 edges each sharing an overlooking corner in thesame direction.

• For more information go to;

-http://www.numeracyworks.com/Site/Paper_Folding.html

-http://en.wikipedia.org/wiki/Mathematics_of_paper_folding

-http://www.paperfolding.com/math/

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Math in Origami