# World Space Week – Origami and space research

When origami is mentioned, the first associations are paper cranes. In Japan, origami is considered traditional, and crane represents good fortune.

Paper cranes

But did you know that origami, mathematics and science are connected? Origami, the ancient Japanese paper-folding skill is actually such a powerful tool that solves vast range of problems, from medicine to nano-science, and even NASA uses it in its research.

It started with so-called father of modern origami, Akahira Yoshizawa (1911-2005) inventor of about fifty thousand models and diagrams collected in eighteen books. His approach changed traditional origami. The basic modification was making folding diagrams which exhilarate connection of origami and mathematics, and science in general.

Flat origami, such as the above mentioned crane, is full of mathematical problems. In order to fold a flat origami figure, one needs to follow steps that can be mathematically described. There are seven origami axioms, widely known as Huzita-Hatori axioms, that describe creases. They represent the mathematically formal description of origami constructions.

When talking about involving origami and space science, we need to mention Miura folding or so-called Miura-ori (ミウラ折り). This form of origami folding is proposed by Koryo Miura, Japanese astrophysicist. Miura-ori is a way of folding paper or another flat surface into smaller area. Miura-ori paper version of folding pattern is showed in the figure below.

Miura-ori folding pattern (Wikipedia commons, source: www. commons.wikimedia.org/wiki/File%3AMiura-Ori_CP.svg)

This kind of folding makes objects that are collapsible, which makes them transportable and deployable. These features are very useful in designing robots and mini surgical devices. Beside paper or similar materials, rigid materials can be also folded by Miura-ori. That characteristic made this kind folded objects important and influential in technology, particularly in astronautic engineering, space satellites and its solar panels.

The first research vessel equipped with solar array that was folded by the principle of Miura-ori was launched in 1995. It is in the Figure below.

The space satellite with the solar panel that folds (Courtesy: National Science Foundation, source: www.nsf.gov)

Since then, NASA uses principles of origami in its own research to create a folding technology suitable for launching into space. The magic of origami comes from folding, and the component that is needed for travelling to space is simply smaller packing. So far, NASA missions created many hardware inspired by origami, such as Starshade, that would be useful in blocking the distant stars’ light so the exoplanets could be observed by telescopes. Origami inspired pattern of Starshade could be packed down to fit a rocket, but eventually unfurl when in space. Implications of origami could be also found in radiation shielding that could protect astronauts in their space missions.

So, keep folding, to the moon and back!

Author: Natalija Budinski, School Petro Kuzmjak, Ruski Krstur, Serbia

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### 2 Responses to “World Space Week – Origami and space research”

1. Eleftherios Pavlides says:

Koryo Miura is a brilliant engineer for adopting the zig zag fold in 1970s and 1980s to solve engineering problems but Koryo did not invent it. The zigzag fold was invented in Joseph Albers studio at the Bauhaus in 1928. Albers a famous painter taught an introductory design class that asked students to allow the properties of materials shape form. This exercises involved a number of materials wire, wood, screen wire, iron, etc and also included paper. They folded paper for it structural qualities with no idea where the exploration of structure and material will lead to. In that sense the Bauhaus exercises is the opposite of Origami, the elegant exploration though paper folding representing natural or mathematical objects.

2. Eletherios Pavlides says:

I should have added that Koryo may have invented the zigzag fold independently 40 years after it was first invented at the Bauhaus studio, but I doubt it. The paper folding Bauhaus exercises had been published in Japanese in the 1930s by Japanese students who had studied at the Bauhaus. By the 1960’s every design school in Japan and the world over, taught these exercises. I saw a demonstration of how the zigzag fold exhibits Negative Poisson’s Ratio at Yale in the 1960’s. This means if you pull the fold along one axis it will expand laterally along both axes. If you push it in along we one axis it will contact along both axes.

The only way to resolve this is to ask Koryo is he had seen a demonstration of the zigzag fold at an art school. In the 1960’s, this demonstration was in vogue in design schools all over the world.