41. Math On The Street: Using Origami To Teach Math Links uses simple paper folding to develop concepts relating to fractions. Dave Love and Bill Haneberg give a lesson plan that brings geometry, origami, and geology http://math.serenevy.net/?page=Origami-TeachingLinks&layout=framed

42. Slashdot | The World's First Origami Folding Robot origami, the geometry of paper folding, looks simple when you re a kid. origami, the geometry of paper folding, looks simple when you re a kid. http://slashdot.org/articles/04/05/14/1434257.shtml?tid=137&tid=146&tid=216&tid=

43. Projects several Sketchpad versions of origami quilts. See MASU for folding applets. See Kim s Crane for origami paper purchases. 6. Modern applications of geometry, http://www.mtholyoke.edu/courses/jmorrow/projects.html

HOME ASSIGNMENTS Project List Below is a list of topics from which you may choose projects for the seminar. Each item on the list is really an umbrella topic that allows for lots of choices under the umbrella. You aren't restricted to using topics from the list, but you need to consult with me prior to doing the project. If nothing on the list so far looks interesting, please think about alternatives! I'm working on a resource list to go along with the project list. 1. Tilings of the plane (Tessellations) See Tessellations: The Secrets of Interlocking Patterns , Ginny Byer, Contemporary Books, 1999 and this web site, Science U: See also: Click above for an interactive example. 2. Tilings of 3-space Try http://spacebrick.com/geometry/index.html 3. Proofs of the Pythagorean Theorem: Thomas Jefferson did one - how about you? 4. Symmetry Below is a black and white photo of an origami quilt (interlocking folded squares of paper - no glue, no tape) made by Char Morrow. What are its symmetries? See Visions of Symmetry , Doris Schattschneider, Freeman, 1990;

44. Origami- Japanese Paper Folding Star Origami Crane Folding Rose Origami Paper The geometry Junkyard Tilings rose folding diagram, crane folding papers, star origami folding instruction, rose origami folding paper, swan origami folding paper, http://orientalpharmacy.com/opane/origami.php

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45. Origami The aim of COS is to propagate art of paper folding in Czech Republic, to study folding geometry, to arrange origami seminars and exhibitons and to coact with http://www.origami.cz/english.html

Allow me to introduce myself... My name is Franti¹ek Grebeníèek. I was born in 1973 in Uherské Hradi¹tì Czech Republic After finishing studies at Secondary technical school in Uherské Hradi¹tì I graduated from Brno University of Technology Faculty of Electrical Engineering and Computer Science with a master's degree in Computer Science and Engineering . Then, I have finished my PhD studies at this place. Nowadays I work in CLN as a developer. I am interested in Java programming I am an intermediate paperfolder :-) My e-mail: frantiseg@centrum.cz I have started to interest in origami in about 1997. In Czech Republic, there was no origami society and no origami web pages. Information about true origami art was very fragmentary, therefore I started to collect the information (and diagrams) from the Internet. Then I made this origami pages - the first origami pages in czech language - which are still under construction. The pages should prompt czech people to interest in origami and help them to start folding. This web is powered by free webhosting. I have no profit from it, except my pleasure (and - sometimes - a complimentary e-mail).

46. Origami students to the Art of origami as a history of the art of paper folding through storytelling teaching and learning tool, mathmatics, geometry and construction http://www.whimsical-workshop.mb.ca/origami.html

Origami Creating A Balance Inspired by the book "Sadako and The Thousand Paper Cranes" Author: Eleanor Coerr In the Japanese Culture, The Crane is symbolic of health, hapiness, and peace. Legend has it that if you fold 1000 cranes your wish or prayer will be granted. In the times we live, every day human conflict spreads and grows more severe, the environment grows more threatened. There is an overwhelming need to establish harmony in our world. We have to "Create a Balance". The White, Yellow, Red and Black cranes were adapted from a different 1000 crane mobile created in 1992, as 1 of 10, for the Winnipeg International Children's Festival 10th anniversary by Children of the Earth School. They represent the North, East, West and South. The many-coloured cranes were chosen to represent all the people of the earth, the three levels of the mobile to represent, the air, land and water. The mobile to represent "Creating A Balance". With our world and environment in ever increasing chaos and conflict, we have folded these cranes as a symbol of our prayer, that though events such as these, that all the peoples of the world will try to "Create A Balance" so we may all enjoy "Peace, Good Health and Happiness". Here flies 1000 cranes as a gentle reminder for all to do their part in "Creating A Balance" Program "Creating A Balance" is a 1 or 2 week long workshop that introduces students to the Art of Origami as a means of making a creative statement. Brian presents a history of the art of paper folding through storytelling and demonstrations. The students, through their creative efforts create a mobile sculpture. This brings the whole school together for a presentation focusing on the idea of "Creating A Balance" with nature, the environment and with each other.

47. 4 Your Info Online, 5/10/1999, Origami The name origami was coined in 1880 from the words oru (to fold) and kami Instead, their paper folding was a study of the paper s inherent geometry. http://www.4yi.com/1999/0510origami/

var prop5="4YI" var prop6="specialty" HOME MU SPORTS CLASSIFIEDS JOBS ... ABOUT US NEWS Tri-State News Tri-State Sports Marshall Sports National News ... newspapers in education MARKETPLACE Classifieds Jobs Homes Cars ... Apartments H-D INFO About Us Customer Service Subscribe Where to Buy ... Contact List LINKS The ancient art of folding paper remains popular with adults and children By ERIC FOSSELL - The Herald-Dispatch Simple yet complex, the ancient art of origami remains a favorite of children and adults everywhere. Anyone who's tried origami, the folding of paper into various shapes, knows it's not nearly as easy as it looks. That's why it is so rewarding when, say, that swan or dragon finally emerges from your hands. "It's hard," said Alex Durand, a sixth-grader at Cammack Middle School in Huntington. "I don't know how they come up with some of those things." Alex and his classmate, Brandon Samples, learned about origami in preparation for a Japanese festival last week at their school. They admitted that a lot of patience was required to teach the art form to other students.

48. Recycled Paper Crafts Other paper Subjects Geometric paper folding Dr. David Huffman; Oriland origami Studio Diagrams; The geometry Junkyard origami; New balls please; origami Math. http://www.recycledpapercraft.com/

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49. History they propiciated a revolution in the art of paper folding. The geometers saw in origami many pedagogic possibilities. is a wide handle of geometry with origami http://www.oriworld.joi.com.br/espanol/history.php

By Carlos Gênova In the year 105 AD, T'sai Lao, an administrator in the palace of the chinese emperor, started to mix tree bark, fabric and fishing nets to substitute the sofisticated silk that was used for writting. He certainly couldn't imagine the use that the world would make of this material called paper. The chinese empire kept a secret about the techniques of paper production for centuries, because it exported the material for high prices. In the seventh century the technique arrived in Japan by korean monks as a "chinese business", and one century later, the arabians got the secret of this technique. In Europe, it was only discovered around the twelth century and two centuries later it had already spread for all the chirstian kingdoms. Paper hasn't always had a good quality. Except in China and Japan, where since the beginning it was possible to be folded, in the rest of the world, specially in Europe, it was thick and fragile dificulting the paper folding. Only after the fourteenth century, a more thin and flexible paper was produced in Europe. But the high costs for its production were also an barrier for origami to get popular. It's correct that this art has origined in China. But, as we know, it didn't become much popular in this country. In Japan

50. Paper Folding paper folding paper folding is a such as paper folding, the student paper folding. Overhead transparency masters set. OVERVIEW. INTRODUCTION. INTENDED AUDIENCE. BASIC FOLDS. geometry http://www.lwcd.com/paper-folding

"Math needs to be made more visual - this helps to do that! This is the most comprehensive collection of 'hands-on' paper math that I have ever seen under one cover." -Gwen Terwillinger Chair, Technical Science and Mathematics Department The University of Toledo Community College Make mathematics fun and interesting with paper folding... Paper folding is a simple, novel, hands-on approach to mathematics. Today too many students are beginning to identify mathematics with technology use. By stressing low tech ideas such as paper folding, the student may come to recognize that all technology is a tool to supplement not supplant the thought patterns necessary for successful learning. Good for all ages... Paper folding is useable from grade school through college. Because the material is meant to be a resource for the teacher, the information could be readily used at all levels. In grade school the fraction and tessellation units would be great. In later grades the geometry would be introduced. At the college level the material would be useful for developmental mathematics and as a component to teacher education classes. Activities covered...

51. Paper-Folding Ideas To Help Students Understand High School Geometry paperfolding Ideas to Help StudentsUnderstand High School geometry Concepts9-12 WorkshopNCTM Annual MeetingSession 988San Antonio, TXApril 12, 2003James R. http://www.jamesrahn.com/workshops/paperfolding.pdf

52. Origami Web Resources For Students literally meaning to fold (oru) paper (kami the ancient art of papar folding origami paperfolding fun Jopephy Wu s Origmai Page origami Sociteit Nederland http://www.stemnet.nf.ca/CITE/origami.htm

Gander Academy Origami What is Origami? Paperfolding Instructions Paper Airplanes Search Index ... Teaching Resources What is Origami The East and West of Origami Most of us will remember folding paper cups, salt cellars (we called them 'cootie' catchers or 'fortune tellers') and paper balloons as children in elementary school. There is more to origami than these simple models would lead us to believe. Origami comes from the Japanese words for folding, ori, and the Japanese word for paper, kami. History of Origami Since about the first century AD, the time when it is believed that paper was first invented in China, people have been folding paper into various shapes. The Chinese developed some simple forms, some of which survive down to this day. When the secret of paper was carried to Japan in the sixth century AD by Buddhist monks, it was quickly integrated into their culture. Origami: Fold art, geography and cultural studies into one lesson Origami, the ancient Japanese art of paper folding, can be an interesting way to combine art lessons with units on social studies, culture and even history and geography. The Ten Commandments of Origami 1.Choose suitable paper and cut to required form and size.

53. Origami origami arts. paper folding was also being made in Spain during the 12th century by the Arabs. After the Arabs left Spain, paper folding became more geometric http://everyschool.org/u/logan/culturalmath/origami.htm

Origami What is origami? Origami is the Japanese name for the art of paper folding. In the word origami, oru means to fold and kami means paper. An origami figure that is completed is called a model. The only tool needed in order to do origami is the paper. The paper is usually cut into 15 cm squares. The most common technique in origami is the folding. The folds have different names. In the valley fold, a flat piece of paper is folded towards the paper folder. In the mountain fold, the paper is folded away from the paper folder. After a person makes these folds, there are a series of basic folds that follow. The four most common bases are the kite base, the fish base, the bird base, and the frog base. These show that origami artists like to use animals as their models in this art, Origami can be used to make almost anything such as animals, faces, plants, vehicles and buildings. Many people fold abstract or mathematical shapes, others specialize in modular origami . In modular origami many copies of a simple folded shape are assembled to form larger structures. The paper artists have different occupations like artists, scientists, and therapists. The scientists, architects, and mathematicians love the geometry of origami. Many people just do it because it is fun.

54. David Mitchell's Origami Heaven - Modular Origami Design Encyclopaedia - Useful from all papershapes, the optimum folding solution for a be found by starting from the paper-shape that In modular origami rectangular paper shapes are often http://www.mizushobai.freeserve.co.uk/rectangles.htm

David Mitchell's Origami Heaven Useful Rectangles and Folding Geometries This page introduces various rectangles that are of proven (or potential) use as starting shapes in modular origami and briefly discusses their folding geometry. Folding geometries are of two quite distinct kinds, natural and embedded. The difference between these two types of folding geometry is discussed in Notes on Folding Geometries. Whilst all folding geometries can be obtained from all paper-shapes, the optimum folding solution for a particular module will usually be found by starting from the paper-shape that most naturally yields the angles required. In modular origami rectangular paper shapes are often used in double or double-strip form. A double rectangle is made by joining two rectangles along their longer edges, a double-strip rectangle by joining two rectangles along their shorter edges. Designs made from triple and triple-strip rectangles etc are also occasionally found. The Square The square is undoubtedly the most versatile starting shape in modular origami, to the extent that some modular paperfolders use no other (with the unfortunate result that it is quite often possible to improve the elegance of their designs by the simple expedient of switching paper shapes).

55. Origami-Math Bibliography D. and Demaine, Martin L., Planar drawings of origami polyhedra, Proceedings Demaine, Martin L., and Lubiw, Anna, folding and cutting paper, Revised papers http://www.merrimack.edu/~thull/omfiles/comporibib.html

Computational Origami This category deals with problems in trying to figure out when certain questions about paper folding can be answered, as well as if they can be answered in linear time, polynomial time, or what-have-you. There is a lot of overlap here with mathematical modeling of paper folding, but more and more papers are being written on this topic, so it seemed to me that it deserved its own section. Note that I've included Robert Lang's work on origami design (also listed in the modeling and design bibliography section) in this list. I did this because, as Erik Demaine says, Lang's work is, "...in some sense the beginning of computational origami." Arkin, Esther M.; Bender, Michael A.; Demaine, Erik D.; Demaine, Martin L; Mitchell, Joseph S. B.; Sethia, Saurabh, and Skiena, Steven S., When can you fold a map?, Proceedings of the 7th Workshop on Algorithms and Data Structures , edited by F. Dehne, J.-R. Sack, and R. Tamassia, Lecture Notes in Computer Science , volume 2125, Providence, Rhode Island, August 2001, pages 401-413. Shorter version in

56. Edward Crankshaw's 'The East And West Of Origami' Paper origami had it beginnings in the west when the Moors forms in art, the Moors used paperfolding to create tessellations and other geometric forms (see http://fly.hiwaay.net/~ejcranks/arth193b.html

You're at Home About Us Origami / East and West of Origami Paper The East And West of Origami Most of us will remember folding paper cups, salt cellars (we called them 'cootie' catchers or 'fortune tellers') and paper balloons as children in elementary school. There is more to origami than these simple models would lead us to believe. Origami comes from the Japanese words for folding, ori , and the Japanese word for paper, kami . When combined, kami becomes gami and the word is origami. It shares the same origin but has taken two distinct avenues of development since its creation. Those two avenues of origami have merged together in the twentieth century. There is more to origami today than just paper-folding. Origami has a long history in the east and west and a sophistication which is more artistic than a mere craft. The following is the story of the east and west in origami. The Basic Materials The Japanese learned about paper-making in the early seventh century. They gained their knowledge of paper from a Buddhist monks who came to Japan from China through Korea and the books that they brought. This started about 538 A.D. The Japanese began making paper of their own by about 610 A.D. It is believed that Dokyo, a Buddhist monk, brought knowledge of paper-making as well as painting and ink-making. He was even a doctor and became the chief physician to Empress Shotoku. The Eastern Avenue Figure 1: Flower wrapping resembling noshi wrapping The Muromachi period in Japan lasted from 1338 to 1573. The folding style of this period represented a persons place in society. Paper was now inexpensive enough to be used by everyone and origami became a means of social stratification. It was a period of military rule and two schools of origami existed. The samurai followed the Ise school while peasants and farmers followed the Ogasawara school. There has been 400 years of mothers teaching their children how to fold paper.

57. Fuentes De Información, V.Larios Totally real origami and impossible paper folding de David Auckly y John http://www.uaq.mx/matematicas/origami/ligas.html

Regresar a: Doblando la Geometría Fuentes de información sobre Origami y Matemáticas Material preparado por M.D. Víctor Larios Osorio Departamento de Matemáticas (Facultad de Ingeniería). Licenciado en Educación Media (Matemáticas) por la Escuela Normal del Estado de Querétaro, Maestro en Docencia de las Matemáticas por la Universidad Autónoma de Querétaro. Profesor/investigador de bachillerato, licenciatura y maestría. Correo-e: vil@sunserver.uaq.mx Sitio web: http://www.uaq.mx/matematicas/vlarios/. Fuentes impresas sobre construcciones con origami: La siguiente es una lista de fuentes bibliográficas impresas. A algunas de las obras listadas se le han añadido ligas que llevan a librerías o bibliotecas virtuales (o en-línea) para poder ser adquiridas o consultadas. "Lifestyle origami" de Jay Ansill (1992, EEUU: HarperCollins). "Unit origami" de Tomoko Fusè (2000, EEUU: Japan Publications). "3-D geometric origami: Modular Polyhedra" de Rona Gurkewitz y Bennett Arnstein (1995, EEUU: Dover Publications). "Amazing origami" de Kunihito Kasahara (2000, EEUU: Sterling P.).

58. From The Origami-l Archives - David Lister On Folding From Non-square Paper The accepted constraint in origami has always been that the paper should be a To summarise, the square has become the classical shape of paper for folding. http://www.britishorigami.org.uk/theory/lister/nosquare.htm

Folding from non-square paper I thought I would set down a few random thoughts on folding from non-square as opposed to square paper, but I don't intend it to be a reasoned thesis! 1.A few months ago, I wrote in Origami-L about John Smith's ideas on "Origami Profiles" which analyses how each individual's preferences in folding fit into the general scheme of things. The theory accepts that everyone is entitles to adopt whatever rules for folding he or she chooses. 2. Following from this a folder can choose to fold from a square or from a triangle or from A4 or a pentagon or a rectangle or a rhombus or a long ribbon of paper half and inch wide and ten yards long. He may even prefer silk ribbon or even string. Whether other people would include in their own concepts of Origami is another thing. 3. If you accept that cutting is legitimate (and cutting, too, fits into John Smith's Profiles of Origami), your can convert a square of paper into any shape you like. Or you can trim your dollar bill into a square. Or you can chop off any of those surplus bits of paper that get in the way. (No, I accept that most people who like to use scissors don't look at it in this extreme way, but I assert the possibility.) 4. Without even using scissors, you can convert most simple shapes of paper into most other shapes by folding alone. You can fold a square to make a triangle, or a hexagon or a 3 X 7 rectangle, even A4. So having done that, in theory, you can go on to fold anything that can be folded from a square equally from a Dollar bill or anything that can be folded from a Dollar bill from a square. I write "in theory" advisedly, because all the preliminary folding to get the shape makes the model bulky and difficult or even impossible to fold in practice.

59. AIMS Book: Paper Square Geometry paper Square geometry The Mathematics of origami provides a way for Cube The Cube is an origami activity which relationships are represented in the folded cube http://www.aimsedu.org/Activities/origami/origami.html

Free Activities Activities Database Puzzle Corner Workshops ... Contact Us Match ALL words Match ANY word Grades 5-12 Paper Square Geometry: The Mathematics of Origami Paper Square Geometry: The Mathematics of Origami provides a way for students from upper elementary to high school to experience geometry in a meaningful context. The three-dimensional origami models offer a tangible means for understanding and experiencing mathematical concepts such as symmetry, angle, congruence, and similarity. Encouraged throughout the book are the uses of mathematical language and proper geometric notation to record the attributes of the models. In addition to learning geometric content, students improve their spatial skills as they are challenged to assemble three-dimensional models from two-dimensional units. The completed models are works of art which give students a sense of accomplishment and add to the aesthetics of the classroom. Sample Activities: Cube The Cube is an origami activity which addresses the question, "What geometric relationships are represented in the folded cube?". In this activity, students will fold a cube and identify the geometric relationships that are present in the completed model.

60. Kayee Kwok originated from Japan, is an art of paper folding in which fusion of art and mathematics gives us Modular origami. The idea is to build a geometric shape using http://www.wheatoncollege.edu/academic/academicdept/MathCS/Faculty/tratliff/stud

Folding Geometry - Kayee Kwok (2000) Abstract Origami, originated from Japan, is an art of paper folding in which something as simple as a box or something as elaborate as a crane can be created without gluing, or cutting. The fusion of art and mathematics gives us Modular Origami. The idea is to build a geometric shape using many equivalent pieces of folded shapes. One of the shapes which I'll be talking about is the five intersecting tetrahedran. Transparencies

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