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Emily Gunning

on 25 February 2013

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Transcript of Origami

The Math of Origami By Emily Gunning What is Origami ... Modern Origami... How to make your own Origami... Robert Lang Crease Patterns... References Origami is the Japanese art of folding paper into decorative shapes and figures. In Japanese Ori means folded and kami means paper, creating the name Origami. In the last 20 years origami has transformed into an art form. The use of Mathematical concepts have allowed this transformation to occur. Robert Lang is one of the worlds leading masters of origami. He is known for creating very unique and complex origami designs. He develops these designs by incorporating math, science, and engineering in his work. http://www.origami-fun.com/origami-crane.html a "crease pattern," or CP, is nothing more than a set of lines that is a representation of some subset of folds in an origami shape, real or imagined. http://www.langorigami.com/ Origami began in the first or second century in China and later migrated to Japan in the sixth century. Origami was originally very simple figures but, later transformed into the complex art form it is today. Originally origami was only available to the rich because, of the small supply of paper. When advances in paper making made it less expensive, allowing origami to become a popular art form for everyone. http://library.thinkquest.org/5402/history.html The History of Origami... Origami Mathematics Huzita-Justin Axioms This form of mathematics explains the underlying laws of origami. Origami Mathematics is at most an approximation of real-world folding. Huzita-Justin Axioms are considered to be the simplest set of operations you can use. HJAs provide a realistic and practical tool for origami design. A seventh axiom was later added by Koshiro Hatori in 2002. The Huzita axioms are shown to the right. Through the use of these six axioms, it is possiable to... Solve all quadratic, cubic, and quartic equations with rational coefficients;
Trisect an arbitrary angle;
Construct cube roots, including the famous problem of "doubling the cube";
Construct a regular N-gon for N of the form 2i3j(2k3l+1) when the last term in parentheses is a prime (a so-called Pierpont Prime);
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