# Math and origami

Just as paper folding in the past allowed practitioners to extract the mathematical principles behind the art, the rigorous application of mathematical reasoning has in turn given contemporary paper-folders the ability to create precise, elaborate geometric constructions.

Paper folding was also practiced in China and Europe. For instance paper folding may be used for angle trisection and doubling the cube. Therefore, it is legal to redraw the folding instructions of a model of another author even if the redrawn instructions share similarities to the original ones, as long as those similarities are "functional in nature".

Robert Lang and Alex Bateman are two designers who use computer programs to create origami tessellations. From that moment on, I was the greatest origami master in the world. In Europe, there was a well-developed genre of napkin foldingwhich flourished during the 17th and 18th centuries.

Video displaying the folding and unfolding of a Miura-creased material source: In origami tessellations, pleats are used to connect molecules such as twist folds together in a repeating fashion.

This article was originally published in March If you are a student doing a report on origami and math, you can again impress your teacher by showing that you know what topology is, and how it is related to origami. I had a friend called Kim, who was visiting England for a year from Japan.

Artisan papers such as unryu, lokta, hanji[ citation needed ], gampi, kozo, saa, and abaca have long fibers and are often extremely strong. What is Modular Origami?

You absolutely do not need to be a talented origami artist to pull off these lessons with your students.

During the s, Shuzo Fujimoto was the first to explore twist fold tessellations in any systematic way, coming up with dozens of patterns and establishing the genre in the origami mainstream. Pegasus made by Robert J. Euclid knew that by using a straight-edge and compass a straight-edge is like a ruler without markingsit was possible to perform a large number of geometric operations, like drawing a pentagon, a hexagon and a circle.

Given two points andthere is a unique fold that passes through both of them. Students who caught the modular origami bug will be so motivated after learning the first two projects, that they will likely want to figure out other origami designs.

Origami-derived techniques have been used in the design of solar panels for spacecraft because they allow large structures to be folded up into a compact form for launch; and then, once in space, the structures can unfold in a simple, reliable way with little need for assembly or human intervention.

Chris Palmer is an artist who has extensively explored tessellations after seeing the Zilij patterns in the Alhambraand has found ways to create detailed origami tessellations out of silk.

Modular origami Modular origami consists of putting a number of identical pieces together to form a complete model. Later, the art of paper folding took the form of napkin-folding that was extremely popular in the 17thth cc.The power of origami.

By. Liz Newton. Submitted by plusadmin on December 1, Euclid's book The Elements is the most successful textbook in the history of mathematics, and the earliest known systematic discussion of geometry.

Euclid knew that by using a straight-edge and compass (a straight-edge is like a ruler without. Mathematics of paper folding Jump to The first International Meeting of Origami Science and Technology (now known as the International Conference on Origami in Science, Math, and Education) was held in in Ferrara, Italy.

Pure origami Flat folding. Mountain-valley counting. Origami is the Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square.

In modular origami, a number of individual "units," each folded from a single sheet of paper, are combined to form a compound structure.

Origami is an extremely rich art form. Origami math gives my tactile and spatially gifted students a chance to shine, it helps students with sequencing and direction following, and it’s a fun way to introduce a wide range of geometry terms and concepts.

Watch video · Robert Lang is a pioneer of the newest kind of origami -- using math and engineering principles to fold mind-blowingly intricate designs that are beautiful and, sometimes, very useful.

The ancient art of paper-folding (zhezhi in Chinese and origami in Japanese) can be impressive to viewers of all ages. But no less impressive is the mathematics behind origami.

Math and origami
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