Paper Folding (Origami) and Geometry

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“I told them that origami is not just about geometry, it is about science”

How can you prove the Pythagorean Theorem by using only a square paper? Or a simpler question for you, how can you teach one of the most important postulates of Euclid to young minds with a small piece of paper?

I am sure all mathematics teachers have their own solutions. But if you know that paper folding is not just an authentic art, you can give different answers to these questions.

When I tried to teach some basic geometry and mathematics concepts through paper folding activities to my students, some of my parents who were worried about the academic success of their pupils asked me what kind of relationship there was between geometry and origami.

I told them that origami is not just about geometry, it is about science. 

Teaching some basic geometry and mathematics concepts through paper folding activities to students

Arabs taught their children geometry through paper folding for hundreds of years, Moors brought paper folding to Spain in the twelfth century and this art spread to Europe. Nowadays, paper folding art is most popular with Japanese and Chinese origin, but it has very different geographical history, too.

Origamist Scientists and Origami Usage Areas

Today, many important origami artists contribute to the advancement of modern origami and create wonderful works of art, but there are some origami masters, especially with an identity of a scientist. I especially recommend watching Robert J. Lang’s videos. It may be more instructive to hear from a genuine scientist and origami artist “how science, mathematics and origami are interconnected and paper folding is not just an art”.  Robert J. Lang (born May 4, 1961) is an American physicist who is also one of the foremost origami artists and theorists in the world.

Nano origami is a new method that allows objects in the nano scale to be folded into simple three-dimensional objects

Erik D. Demaine (born February 28, 1981) is a professor of Computer Science at the Massachusetts Institute of Technology and a former child prodigy.

Nano Origami Robots and Devices:

George Barbastathis and a group of researchers are developing nano origami, a new method that allows objects in the nano scale to be folded into simple three-dimensional objects. The folded tiny elements can be used as motor and capacitor, allowing for better computer storage memory units, faster microprocessors and the use of new nanophotonic devices. Nano-size foldable robots can easily move though diseased tissues and organs in the human body. Scientists are trying to reveal protein folding and DNA secrets with molecular origami.

Origami miniature

Here some news from NASA ”Researchers at NASA’s Jet Propulsion Laboratory, Pasadena, California, and Brigham Young University, Provo, Utah, collaborated to construct a prototype of a solar panel array that folds up in the origami to make easier deployment and ”NASA’s New Shape-Shifting Radiator Inspired by Origami”

In your opinion, how safe can a randomly folded airbag be? You would probably prefer a folded air bag with the best folding model thought by scientists. Parachutes are examples of the fact that smooth and systematic folding is vital. Nobody wants to invite a wedding or a brochure in the hunt, it is so impressive if you are invited or your brochure is aesthetic and functional. We can list hundreds of fields in which paper folding is used from the construction of heart stents attached to the cardiac vessels to simple tools to meet your everyday.

How you can use paper folding art in mathematics lessons?

If you are beginning to think that the art of paper folding is a good thing, then we can begin discussing how you can use paper folding art in mathematics lessons.

I know it very well; it’s difficult for science teachers to make a subject, such as geometry, interesting for their pupils. Many students, especially lower secondary school pupils, find mathematics boring.

I have experienced that the art of paper folding is a great way to have funny lessons. Actually, teachers can teach many mathematical concepts in fields of geometry via origami.

To measure the angles use protractor or take a photo of your unfold origami model and insert its image into the Geogebra

In this article I will provide you with the examples of my lessons of how simple origami shapes can be used to explain important concepts of geometry. I believe that all students will develop skills and understanding in basic concepts of geometry and the art of paper folding.

I hope origami will be a funny way to understand: Example: Give pupils this homework: ‘’Learn origami model from YouTube and create 3 same origami model in the same size using 3 origami paper (square papers)’’ When your pupils bring their origami models to you, ask them: ‘‘Can you fully open your origami model (unfold your origami) and show us which geometric shapes appeared on the paper? Show us using pencil and ruler, if you need to measure the angles use protractor or take a photo of your unfold origami model and insert its image into the Geogebra‘’

During my lessons, my students developed skills in basic concepts related to geometry and paper folding art. Origami was a fun way for our students to understand the concepts of geometry. Activities have allowed students to have fun while learning many challenging mathematical concepts in geometry.

Students developed skills in basic concepts related to geometry and paper folding art

You can get more detailed examples for using Origami in your geometry lessons from different sources. As a last word, I would like to conclude by summing up the benefits of paper folding art on student development.

Benefits on Origami’s Student Development

First of all we should know that paper folding is a game for students, and students love playing games. While students are trying to make origami figures and trying to sort a set of algorithms in a certain order, they face many geometric shapes at the same time. They see in concrete terms the relationship between different geometric forms in many examples. Especially square, rectangle, triangle, equilateral triangle, similarity, symmetry with the basic geometric concepts are encountered while doing origami. Origami also allows students to develop psychomotor skills, and it helps hand, eye muscles and hand-eye coordination to develop.

Bibliography:

 

Article written by: Tayfun Acar, Mathematics teacher and Scientix Ambassador

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