Mathematics of origami By Kathy Doan and Lisa

Mathematics of origami By Kathy Doan and Lisa Tran

What is origami? Origami is the Japanese word for paper folding. “Ori” means to fold and “Kami” means paper. Together they form “origami”. Origami involves the creation of paper forms usually entirely by folding.

who discovered origami? ➢Chinese invented paper and origami toys such as the “waterbomb” ➢Buddhist monks introduced paper to Japanese and they evolved origami as a traditional art

When was origami discovered? ➢Evidence point towards Ancient Egyptians and folding of their map (more than 2, 000 years old) ➢Papermaking reached the Arabs in the eighth century; the Arabs brought it to Spain in the twelfth century ○ Papiroflexia: origami of animals ➢Mass production of paper expose origami (1603 -1868)

how is origami related to math? ➢Origami involves geometry ○ Ex. folding a waterbomb base creates a crease pattern with eight congruent right triangles ➢Kawasaki’s Theorem: angles surrounding a single vertex in a flat origami crease pattern will add up to the sum 180

Cont. how is origami related to math? ➢Maekawa’s Theorem: at every vertex where creases intersect in a flat origami crease pattern, the difference between the number of mountain and valley creases is always two ○ Ex. at a vertex you could have 5 mountains and 3 valleys, but never 6 mountains and 2 valleys

Cont. How is origami related to math? ➢ Italian-Jap. Mathematician Humiaki Huzita published a list of possible operations when folding paper

Interesting facts ➢If you make one thousand origami cranes, you will be granted a wish ➢The smallest crane is made by Mr. Naito of Japan (0. 1 x 0. 1 mm) ➢Origami can also be three dimensional or modular

Cont. interesting facts ➢An origami airplane championship is held every two years in Japan ➢There are more than a dozen origami associations in the world ○ Origami Usa sponsors a yearly convention in New York

Origami application in our lives ➢Decorate home or environment ➢Designing satellites ➢Designing airbags ➢Mirrors and solar panels in space ➢DNA nanorobot

Origami models

Are there any careers that involve origami? ➢Engineering ○ Space engineering ➢Architecture ○ Construction ➢Art

What is interesting about origami and why did we choose it? is a form of art ➢Origami ➢Ancient and international ➢Origami is engaging and can relieve stress ➢Can apply to science and math ➢Anyone can do it!

What did we personally learn from researching this topic? ➢Geometry and trig. Applies to origami ○ Ex. Sine, cosine, tangent ➢Origami could be complex or simple ➢Origami is frequently applied in space engineering ➢Practice makes perfect!

Bibliography Bond, Sue. "Simple Origami. " Ezine Articles. N. p. , 10 Sept. 2008. Web. 7 June 2016. <http: //ezinearticles. com/? Simple-Origami---8 -Fun-Facts-About-Paper-Folding&id=1485462>. Hull, Thomas. "Origami: Mathematics in Creasing. " The Conversation. N. p. , 6 Jan. 2015. Web. 7 June 2016. <http: //www. origamiwithrachelkatz. com/origami. php#history>. Katz, Rachel. "What Is Origami. " Origami with Rachel Katz. N. p. , n. d. Web. 7 June 2016. <http: //www. origamiwithrachelkatz. com/origami. php#history>. Main, Douglas. "From Robots to Retinas: 9 Amazing Origami Applications. " Popular Science. N. p. , 7 Aug. 2014. Web. 7 June 2016. <http: //www. popsci. com/article/science/robots-retinas-9 -amazingorigami-applications>. "Origami. " New World Encyclopedia. N. p. , 3 Mar. 2015. Web. 7 June 2016. <http: //www. newworldencyclopedia. org/entry/Origami>. Wu, Joseph. "Origami: A Brief History on the Ancient Art of Paperfolding. " Joseph Wu Origami. N. p. , 15 July 2006. Web. 7 June 2016. <http: //www. origami. as/Info/history. php>.