81. Origami Paper Background By a sequence of folds, a flat piece of paper is turned into In recent times unit or modular origami, in which geometric constructions are built up from so http://rachel.ns.purchase.edu/~Jeanine/origami/oriback.htm

Background Origami is the art of paper folding. By a sequence of folds, a flat piece of paper is turned into a stylized animal, flower, box, or other recognizable object, generally 3-dimensional and often with moving parts or serving a utilitarian purpose. The final object is called a 'model'. Origami is associated with Japan, but it is practiced all over the world. The classical models include the water bomb, crane, and flapping bird. In recent times unit or modular origami, in which geometric constructions are built up from so-called modules, has become popular. Origami is both a craft and an art. Origami as practiced in the United States and elsewhere, has developed a certain culture, largely influenced by Lillian Oppenheimer, Alice Gray, and Michael Shall who over time established Origami USA . In this culture, everyone is potentially a teacher as well as a student; a high value is placed on sharing. Similarly, care is taken to giving credit to creators, people who add variations to models, teachers, collectors, and people who write down directions and diagrams. It is to be noted that the recommended practice in origami circles goes beyond the letter of the law concerning intellectual property. Certain attributes of the nature of origami and this culture provide the potential for its use in teaching (and doing) mathematics. Creating an origami model involves following a procedure.

82. Origami KinderCrafts - EnchantedLearning.com origami WHALE A simpleto-make folded paper whale. These are not exactly origami, but they are fun! done The hexaflexagon is a folded geometric figure that http://www.enchantedlearning.com/crafts/origami/

Become a member of Enchanted Learning. Click here for more information on site membership. $20.00/year or other amount (directly by Credit Card $20.00/year (transaction via PayPal Other Amount (transaction via PayPal As a thank-you bonus, site members have access to a banner-ad-free version of the site, with print-friendly pages. (Already a member? Click here. Main KinderCrafts Page EnchantedLearning.com's Origami KinderCrafts Japanese Crafts These origami crafts projects are for preschool, kindergarten and elementary school children. Origami is an ancient Japanese paper-folding technique. The word origami means "fold (oru) paper (kami)" in Japanese. Click on any of the crafts to go to the instructions. Have fun! FORTUNE TELLER Make a fortune teller (or cootie-catcher) from a piece of paper. ORIGAMI JUMPING FROG Make a frog that really jumps! Then you can have a frog jumping contest. ORIGAMI BUTTERFLY A simple-to-make origami butterfly made by folding a piece of paper. ORIGAMI DOLL Very simple dolls to make and play with. ORIGAMI SAMURAI HAT A wearable Samurai warrior hat.

83. ThinkQuest : Library : Pieces And Creases - A Fun Guide To Origami To origami What gentle art to confine By plane of paper folded line. Shape on shape and fold on fold Creates a world from simple mould. http://library.thinkquest.org/5402/poems.html

Index Crafts Pieces and Creases - A Fun Guide To Origami Visit Site 1999 ThinkQuest USA Awards Best of Contest Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

84. Aaron Walden's Geometric Modular Folds I folded this one from Japanese origami paper. wrapping paper, to use as Christmas ornaments, and even made a giant one of doublesized construction paper. http://s89015200.onlinehome.us/thepaperfold/modular.htm

Aaron Walden's Paper Folding Geometric Modular Folds I always had an interest in folding the paper geometric models found in mathematic textbooks.  The cut and fold method was not to my liking, however.  When I was a teenager, I bought the book Lifestyle Origami , by Jay Ansill.  It introduced me to a form of origami known as modular origami, which uses more than one piece of paper to construct a complete model. Dodecahedron This dodecahedron was my favorite of those that I learned from this book.  It was designed by the Rev. Dr. Robert Neale.  It is constructed of thirty identical units, folded from squares.  The units are simple, and can be constructed of most kinds of paper.  I folded this one from Japanese origami paper.  I have made small ones from wrapping paper, to use as Christmas ornaments, and even made a giant one of double-sized construction paper.  This model, called the penultimate dodecahedron, not only serves as a good tool for teaching geometry, it makes a great decorative piece, especially when origami flowers are placed in the open pentagon shaped spaces. Magic Rose Cube This popular geometric modular design, developed by Valerie Vann opens out to form a rose.  This is a before-and-after shot.  The photographic lights washed the rose cube pictures out a little bit.  This same rose cube, and the yellow one below, are pictured in the photo at the top of this page, in their actual colors.

85. Origami, Kirigami, Origamic Archetecture From SpaceStation42.com The Ancient Arts of origami Kirigami Anything but square Your raw material is a simple square of paper, but through A few folds and you have a treasure box, a http://www.spacestation42.com/Shops/origami.html

SPACESTATION42.COM Free Origami Free Origamic Architecture Origami Jewelry Paper Model Shop ... Little Japanese Dolls Kit - For a fun, easy craft choose our exclusive new kit to create five lovable little dolls for play and for display. Use the kit's permanent marker to draw faces and hair, then clothe the miniature wooden dolls in Japanese-style kimonos made from beautiful origami papers, and the finished dolls are ready to keep and to give... The Buck Book - What can you do with a dollar bill - besides spend it? Lots of fun things, as it turns out. It's easy to create a peacock, jumping frog, dime-and-dollar ring and more, using the REAL dollar bill that comes with the book. Illustrated, step-by-step instructions plus tidbits and interesting info about dollars make this kid-friendly book a huge hit with everyone who's seen it. Besides, you get a genuine buck with this book - how can you lose? Great fun for ages 6 and up. Extreme Origami - The cutting edge. Well, more appropriately, the folding edge. Extreme Origami will help you master a variety of spiral designs, many pointed stars, nine sided gift boxes and 12 sided gyroscopic whirligigs. You’ll learn to make flying saucers, nested boxes, running children, swans and much more in this 64 page full color book. Hardcover, 8 1/4" x 10 1?4".

86. Origami Math origami Resources. The art of origami is truly handson learning. As students use their fine motor skills to fold and crease paper into fun shapes and http://teacher.scholastic.com/products/instructor/April04_origami.htm

Scholastic Home About Us Site Map Search ... Customer Service Origami Math "Unfold" math learning with hands-on fun and activities By Karen Baicker Origami Resources The art of origami is truly hands-on learning. As students use their fine motor skills to fold and crease paper into fun shapes and structures, they build skills involving spatial reasoning, following precise directions in sequence, fractions, geometry, and more. Best of all, the results-fantastic frogs, dragonflies, birds-are works of art! Your students can try out their own origami creations with the Whale Reproducible and Frog Reproducible , below. Here are some tips on teaching with origami: Prepare for the Lesson Teach The Lesson Key to Using Origami Symbols Mini-Reproducible Folding Fundamentals Karen Baicker is the author of Instructor . To order a copy of this book, call 1-800-SCHOLASTIC. Download the Key to Using Origami Symbols Reproducible. To open the Reproducible, you will need Adobe Acrobat Reader software. If you do not have this software already installed, click here to download it FREE Download the Wonderful Whale! Origami Reproducible.

87. K's Origami : History Of Origami For example, we cannot fold Catfish, Water Lilly, or Sembazuru with Western paper without tearing Moreover, the point of ceremonial origami is not to make http://www.jade.dti.ne.jp/~hatori/library/historye.html

K's Origami Fractional Library History of Origami Before Origami We know very little about the origin of origami. Some say origami originated in China around 2000 years ago. But it is probably wrong. This opinion is based on the conjecture that origami started right after the invention of paper, for which we have no evidence. The paper of Former Han dynasty shows no trace of origami. The Chinese character for paper, zhi, originally stood for writing material made of silk. The origin of the Japanese word for paper, kami, is said to be birch tree, kaba, or strips of wood or bamboo, kan. Both of them were also writing material. These suggest that paper was primarily writing material, not folding. Others say origami originated from Japan in Heian era. Again, it is probably wrong. They refer to a story of Abe-no Seimei who made a paper bird and turned it to a real one, or another story about Fujiwara-no Kiyosuke who sent his ex-girlfriend a fake frog. There is no reason, however, for believing that they folded paper to make them. In Japan, we use wrapping paper called tatogami or tato. Today we mainly wrap kimono with it. It actually dates back to Heian era. But it is by no means an example of origami, since it is folded just squarely.

88. Ch.5 chapter. Your Project assignment Fold a square piece of colored, good quality paper, to create an interesting origami. It http://www.k12.hi.us/~csanders/ch_05TriangleProp.html

Connecting Geometry Chapter 5 Triangle Properties It may seem surprising to you, but being able to prove two triangles are congruent will now allow us to discover and prove many geometric properties, not only about triangles but about other figures as well! In this chapter, through your explorations on The Geometer's Sketchpad, you will discover many properties of isosceles triangles, equilateral triangles, right triangles, and of triangles in general. Let us begin the discoveries by looking at the symmetries of triangles, and see where this leads us. Let's begin with the most symmetrical triangle of all: the equilateral triangle. If you construct an equilateral triangle on Sketchpad, and print it out, you can do some interesting symmetry experiments by simply folding the triangle. Begin by folding any vertex over onto the other vertex, as in the sequential steps below: If you did this by actually folding an accurately constructed equilateral triangle made of paper, you probably noticed that the triangle is perfectly symmetrical, with reflection symmetry. Unfold the triangle and then fold it again, folding any vertex onto any other vertex. What seems to be true about the equilateral triangle? This symmetry will tell us a number of properties of the equilateral triangle, properties of its sides, its angles, the medians, altitudes and angle bisectors. We will explore these properties using the Geometer's Sketchpad as well as by folding. What would happen if you tried this with an isosceles triangle (one that was definitely not equilateral)? Construct an isosceles triangle on GSP and print it. Then try the folds shown below:

89. Introduction is derived from the words “oru” (to fold) and “kami century AD following the invention of paper (Natajaran, 1 origami also has quite a bit of historical http://cosmos.ucdavis.edu/2003/cluster 6/Daxing Zhen and others/pg4.htm

90. The Zing-Man Origami Gallery Elephants After reading Robert J. Lang s origami Design Secrets, I was developed from a base that makes good use of the paper. Fold pattern for Elephant Base http://www.zingman.com/zingorigami.html

The Zing-Man Origami Gallery Welcome to my origami page. Here you will find photos and instructional diagrams of some original origami models I have designed. The Foldinator Origami Modeler and Document Generator now has its own page, available here Animals, Beasts and Creatures Natural Still Life Subjects Polyhedra Animals, Beasts and Creatures: Dragon - A dragon in the Western (European) tradition rather then the Eastern (Oriental) style, this is the kind of dragon that breathes fire and has wings to fly. This model features detailed body stance, head, tail, wings, claws, and exploits the posibilities of using two-colored paper. I recommend using a large (10" or more) sheet of foil paper or other relatively stiff but thin paper for maximum sculptability. High complexity. Diagrams for the Classic Version of the Dragon Lizard - Features detailed head and claws, and a nice, posable body stance. This model is made from a base of my own invention that employs the geometry of a regular hexagon. High intermediate complexity. Fold pattern for Lizard Base Elephants - After reading Robert J. Lang's

91. NTTI Lesson: Patty Paper And Origami A Tool For All Students Using the other right trapezoid, fold the right angle vertex on the longer base to origami Use the Mathematical Eye Series II Program 4 paper Engineering . http://www.thirteen.org/edonline/nttidb/lessons/kc/paperkc.html

PATTY PAPER AND ORIGAMI: A TOOL FOR ALL STUDENTS Grades 8-10 Tangrams and symmetry will be explored using patty paper. Using a basic building block in origami, polygons and three dimensional figures will be engineered. Landscape of Geometry Program 7 - "Cracking Up" The Riddle of the Wizard's Oak Program 4- "Shapes make shapes" Mathematical Eye Series II Program 4- "Paper Engineering" Tacile experience will be used to demonstrate geometry. These activities are designed to include all students and learning styles. Students will each create a tangram puzzle and use it to discuss topics of form and area. Students will create a building block that can be used to make origami. A piece of patty paper for each student, and a pair of scissors for each pair will be needed for the tangram. For the extention a piece of centimeter graph paper for each student may be used. For the origami, each student will need thirty pieces of square paper. If origami paper is used each student may make one unit and the class complete the stellated icosahedron. Tangram The patty paper and scissors are passed out. Students review the vocabulary of square, isosceles right triangle, rhombus, trapezoid, and parallelogram.

92. Education And Origami will you get if you do not fold the paper in half at 1, 2 and square root of 3 triangle to fold a 60 I would like to quote the Postscript from origami for the http://home.istar.ca/~wko/education_and_origami.html

[Home] [Science Fiction Origami Models] [Origami Writings] [Origami Puzzle] ... [Links] Education and Personal Value of Origami Yes origami is fun and one of the reasons I have a personal interest in it is because of this fun factor. However, just because something is fun does not mean that it has no educational or personal value. In fact, origami has so many facets that it can enrich all disciplines of learning. Origami is not just a childish pastime of making toys from paper. Origami has a long history and is also a reflection of culture and ideals. Many models have significance and meaning. For example, the crane is a symbol of peace. The story of 12 year old Sadako Sasaki and her attempt to fold 1000 cranes in the hopes of recovering from radiation sickness after the atomic blast at Hiroshima puts a real face to the realities of war. It makes history more personal and raises moral issues that would make excellent discussions for history and English. When I was in elementary school, I remembered one event that made science a major fascination in my life. Our school actually had a paper airplane contest - there were categories for longest flight, longest time in air etc. Yes it was a lot of fun and games but I remembered investing a lot of my own personal time learning about lift and the shapes of airplane wings and on and on.... I was actually motivated and inspired to try to produce the best little plane in school. By the way, I didn't win in any category, but I won intellectually because I learned about flight in a real and meaningful manner. As a personal note, this was not what started me in origami - my fascination started much later in my life.

93. O'Rourke Papers Retrieve from CoRR get paper cs.CG/9908007. Appl., 9(6) 615618 (1999). Two results in ``computational origami are illustrated. When can a polygon fold to a http://cs.smith.edu/~orourke/papers.html

Organization. My recent papers are listed in two tables, each entry of which links to full bibliographic details in a long list below both. The first table lists regular papers , in reverse chronological order. The second lists my Computational Geometry Columns , again in reverse chronological order. The detailed list into which these two tables links includes buttons to download PDF, and/or compressed Postscript, and perhaps includes a representative figure. If you are looking for a specific paper, you might use Edit/Find in your browser. File Formats. Most of these papers are in gzip'ped postscript form (file.ps.gz); a few older ones are in compressed postscript (file.ps.Z). The newer papers are in PDF format (.pdf), or compressed .pdf.gz. If your browser has the appropriate plugins, it will automatically gunzip (or uncompress) to file.ps, and then invoke a postscript viewer (e.g., GhostView ) to display the paper. Some are linked to Electronic Conference Proceedings, and some are available, in both postscript and PDF, on the e-print arXiv CoRR : Computer Science Research Repository).

94. SuccessLink-Great Ideas (Based on Unit origami, pp. (Later, students will be able to fold paper correctly without 1) Last fold is to crease all triangles in half, resulting in twelve http://www.successlink.org/great/g440.html

Great Teaching Ideas PARTY TIME IN THE MATH ROOM Submitted by: Clarice Nelson Erika Nelson (graphics) 305 East Cole Street California, MO 65108 EMAIL: cndnelson@socket.net PARTY TIME IN THE MATH ROOM Inspired by a visit to the Museum of Science and Industry display of “Christmas Trees Around the World”, 1996, these ornaments are direct applications of mathematical concepts. The ornaments function as manipulative teaching devices whether the instructor displays and describes a finished ornament or the student constructs an ornament. A brief history, description, application, or function is provided for most ornaments as well as suggestions for interdisciplinary connections. In the presentation, overhead transparencies of diagrams and sketches complement these written instructions. Source materials referenced in the instructions are listed in the bibliography. SCANDINAVIAN ORNAMENT TREE The Scandinavian Christmas Tree used to display the scaled manipulative ornaments is similar to the traditional German Feather Tree but translated into a simplified wooden tree. Spacing of branches and graduated length of branches can be altered to individual needs. (Author's scale diagram and materials used listed at end of handout.) FOLDING STRUCTURAL UNITS, NO CUTTING

95. Teknollogy.com origami. http://www.math.umn.edu/~morgan/Eva/projects/crafts.html

Doing with your hands, your arms, your body, and observing the process and the product with the senses and the mind. Traditions, particularly craft traditions, have something fascinating in that we get to see the product of many lifetimes worth of experimenting and refining. And yet despite the saying, there are still infinitely many things to invent since the process is unique to every individual, and no two people will ever invent the same thing in exactly the same way. Here are a few of my experiments and interests. As expected they are more works in progress than final products, and in some cases, I have quoted a reference which eloquently expresses what I am trying to get at. I listed here the topics that have more to do with crafts and art. You can also find my projects more related to 'science' , and to places and people , though it is all intertwined. Tilings and Tesselations 2-D Tilings on the Square Grid 2-D Tilings on the Triangular Grid 2-D Tilings: the Islamic Tradition 3-D Tilings on the Cubic Grid 3-D Tilings on the Tetrahedral-Octahedral Grid 3-D Tilings: Islamic Ceilings Origami The Geometry of Paper Folding Modular Square Origami Single Unit Telescopic Square Origami Multiple Unit Telescopic Square Origami: the Lotus Band Origami Circular Origami 3-D Hilbert's Space-Filling Curve in Origami Others Knots and Interlaces More Fun with Space-filling Curves Mazes and Labyrinths Calendars and Representations of Time Barn Raising an Endo-Pentakis-Icosi-Dodecahedron

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