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Origami Paper Folding Geometry:     more detail
1. Mathematical Origami: Geometrical Shapes by Paper Folding by David Mitchell, 1997-07
2. Fun with figures, by Mae Blacker Freeman, 1946
3. Origamics: Mathematical Explorations Through Paper Folding by Kazuo Haga, Josefina C. Fonacier, et all 2008-09-11
4. Amazing Origami by Kunihiko Kasahara, 2002-03-28
5. Ornamental Origami: Exploring 3D Geometric Designs by Meenakshi Mukerji, 2008-12-01
6. Marvelous Modular Origami by Meenakshi Mukerji, 2007-04-24
7. Explore Folding of the Circle: Series Book 3 (Explore Folding of the Circle, Book 3) by Bradford Hansen-Smith, 2007
8. Geometric Origami by Robert Geretschlager, 2008-10-14

lists with details

1. About "Origami (The Geometry Junkyard)"
origami (The geometry Junkyard). material on the Japanese art of paper folding, obviouslygeometrical Some origami masters have looked at constructing geometric
http://mathforum.org/library/view/7970.html

Extractions: Visit this site: http://www.ics.uci.edu/~eppstein/junkyard/origami.html Author: David Eppstein, Theory Group, ICS, UC Irvine Description: An extensive annotated list of links to material on the Japanese art of paper folding, obviously geometrical in nature. Some origami masters have looked at constructing geometric figures such as regular polyhedra from paper. In the other direction, some people have begun using computers to help fold more traditional origami designs. This idea works best for tree-like structures, which can be formed by laying out the tree onto a paper square so that the vertices are well separated from each other, allowing room to fold up the remaining paper away from the tree... Related theoretical questions include how many different ways a given pattern of creases can be folded, whether folding a flat polygon from a square always decreases the perimeter, and whether it is always possible to fold a square piece of paper so that it forms (a small copy of) a given flat polygon. Levels: High School (9-12) College Research Languages: English Resource Types: Link Listings Math Topics: Polyhedra Triangles and Other Polygons

paperfolding origami AND TESSELLATIONS origami MATH THOMAS HULL http//www.math.uri.edu/~hull/origamiMath.htmlWhen paper is folded, an origami geometry is

Extractions: http://www.math.uri.edu/~hull/OrigamiMath.html When paper is folded, an origami geometry is at work. Tom Hull provides information on investigations into the mathematics of origami as carried out by mathematicians, scientists, and artists. Contents include: - a tutorial on origami geometric constructions that presents Humiaki Huzita's origami axiom list and compares it to traditional straightedge and compass constructions, with instructions for trisecting angles and doubling cubes - a model: five intersecting tetrahedra - an origami math bibliography - a listing of upcoming origami math events Hull's bibliography on origami geometry and education includes articles from such widely available publications as "Mathematics Teacher" and "Mathematical Intelligencer." http://www.math.uri.edu/~hull/Geombib.html http://www.sanger.ac.uk/~agb/Origami/origami.html Directions for folding Alex Bateman's "square dance," "honeycomb," and "linked circles," with postscript files to be downloaded. Other models by Dino Andreozzi, Nick Robinson, and Edwin Corrie are also provided. HELENA'S ORIGAMI - H. A. VERRILL http://www.mast.queensu.ca/~helena/origami/

3. Origami (reflection)
To learn more about Buckminster Fuller's geometry, check out the Design Science Consortium,which was Since origami is the art of paper folding, I created
http://www.scottkim.com/inversions/gallery/origami.html

Extractions: S TORY. In April 1988 I attended the 25th anniversary reunion of the Design Science program at Harvard University's Carpenter Center for the Visual Arts . Although I hadn't actually attended the program, let alone Harvard, I felt such kinship with this merry band of artist-mathematicians that I showed up anyway. The program, founded by Harvard professor Arthur Loeb, is a uniquely interdisciplinary of 3d polyhedral geometry and sculpture. Equal parts art, mathematics and engineering, the program has produced one of the most interesting collection of alumnae I've ever seen. Talks at the event included: Peggy Weil talking about her vision of the Weatherium: a multi-story inverted polyhedral globe that you view from a platform floating on the inside, with a live projected image of earth's surface as seen from weather satellites. Amy Edmundson, who wrote a most illuminating book about Buckminster Fuller's geometry called A Fuller Explanation, giving a hands-on workshop on building structures out of toothpicks and marshmallows. You quickly learn that in order to build anything stable you have to use triangulated structures like tetrahedra.

4. Kayee Kwok
folding geometry Kayee Kwok (2000). Abstract origami, originated from Japan, isan art of paper folding in which something as simple as a box or something as

Extractions: 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

5. Amy's Geometry 5-6 Web Links
comments from parents, educators, and students on using tessllations to teach geometry. Findsome nice examples of origami tessellations A paper folding Project.
http://teams.lacoe.edu/documentation/classrooms/amy/geometry/5-6/web/web.html

Extractions: California Mathematics Standards Links to adopted core academic content standards in the areas of English-language arts, mathematics, history-social studies and science. Tangrams Escher Polyhedra Tessellations ... Just For Fun This math unit on tangrams was created by Tom Scavo for the Math Forum at Swarthmore University. Have some fun with tangrams. Tangrams Tangrams are an ancient Chinese puzzle, consisting of 7 geometric shapes. This site includes some history as well as patterns and directions for making a set. Return to the top Read the comments from parents, educators, and students on using tessllations to teach geometry. Instructions for making a tesselation and resource list of information on M.C.Escher. Advanced students may enjoy this page on tesselations of the hyperbolic plane by David E. Joyce. This activity using pattern blocks is provided by Suzanne Alejandre for the Math Forum at Swarthmore University.

6. From The Origami-l Archives - David Lister On Why A Paper Square?
wits against the paper and its inherent geometry. become the classical shape of paperfor folding. accepted shape for what we ordinarily call origami paper .
http://www.worthhall.demon.co.uk/theory/lister/wysquare.htm

Extractions: Brunno Jammes asks (25th May), why we mostly use square paper for origami. He says there has been a discussion on our sister list, Origami-francais. Here is what I wrote, slightly edited for clarification. 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 entitled to adopt whatever rules for folding he or she chooses. A folder can use, or not use square or any other shape of paper at his or her absolute discretion. 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 ribbon or string 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.

7. Ask Jeeves: Search Results For "Folded Paper Cube"
thisname.com/origami.htm 6. The geometry Junkyard origami The geometry Junkyardorigami The Japanese art of paper folding is obviously geometrical in nature.
http://webster.directhit.com/webster/search.aspx?qry=Folded Paper Cube

8. Lazy Geometry
We see that some sets of axioms result in nonEuclidean geometry while some areplain Kunihiko Kasahara, origami Omnibus paper-folding for Everybody
http://puremass.com/yp/geometry2.html

Extractions: Euclid's Elements is a complete reference on Euclidean geometry, both on the plane and in space. The first two volumes are very readable to high school students. The third volume is about solid geometry. It might be more challenging to some teenagers. In any case, Euclid's Elements is a classic and should be on every shelf. These Dover books are very affordable and long-lasting. David Hilbert and Leo Unger (translator)

9. Media Center - Math Projects
paper folding Helena's Mathematical origami Index Page origami geometry DesignThe geometry Junkyard origami paper folding Jim Plank's origami Page (Modular
http://www.anderson2.k12.sc.us/schools/bhp/math_proj.htm

10. Crafts/Origami/Geometry And Modulars - Fractured Atlas Links Directory
origami Mathematics Mathematics of paper folding; includes a bibliography ofarticles and journals, Combinatorial geometry syllabus, and a tutorial on

11. Crafts: Origami: Geometry And Modulars: Paper Folding - Fractured Atlas Links Di
Details of a book which teaches math through origami. Visit Crafts origami Geometryand Modulars paper folding. Be the first to review this link! Bad link?

12. Origami Theme Page
geometry Junkyard origami A site for only the advanced mathematician! These pagesand links will lead you to explore the relationships between folding paper
http://www.cln.org/themes/origami.html

13. Firefly Books - Advanced Origami
As paper became a more accessible commodity, origami became something We know thatLeonardo da Vinci used folding to study geometry and aerodynamics
http://www.fireflybooks.com/books/5274B.html

14. Projects
See Kim's Crane for origami paper purchases. 7. folding geometry, Click HERE togo to the geometry seminar link to folding geometry. (Later in the course).
http://www.mtholyoke.edu/courses/jmorrow/projects.html

Extractions: 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;

15. ActiveMath Workshop Schedule
137 paper folding, origami, and geometry. 138 Using Computers in the MathematicsClassroom in Grades 6 9 Workshop 137 paper folding, origami, and geometry.
http://www.activemath.com/workshop_sched.htm

Extractions: Active Math Workshop Schedule Want to PRINT this schedule? Click here for a printer-friendly version REGISTRATION FEE: for one workshop; each when two or more registrations are received at the same time. Registration fee includes extensive coursebook with blacklines, complimentary snacks, and more. Lunch is included where indicated. Click on a workshop for more information Spring 2003 Summer 2003 Mathematical Literacy through the Standards, Grades 6-10 Mathematical literacy is the capacity to deal effectively and confidently with the quantitative aspects of life. Participants will learn how to apply mathematical methods to the solution of life-skill problems across the strands of mathematics and across other disciplines. This workshop stresses the importance of being able to understand and clearly communicate analytical information.

16. Origami & Paper Folding Resources
origami in the classroom to teach such things as geometry and Oriental Another flavorof origami is modular origami, or the art of folding paper to create
http://www.folksonline.com/folks/hh/tours/1999/origami.htm

Extractions: Origami Sites for Beginners to Enthusiasts Host Rich Gray It is the old meeting the new, the cultured elegance of origami running smack up against the electronic ripple of the Internet. While it may seem odd to some that this delicate art of paper-folding would thrive in the world's largest paperless medium, that's exactly what it's doing. There are numerous sites on the World Wide Web dedicated to origami. They range from simple "look-what-I-did" photo collections to intricate galleries built upon reams of information. So if you're ready to move beyond the crumpled paper-ball stage (makes a mean projectile though, doesn't it?), follow me as we head into the fold. Paper fold, that is. Joseph Wu's Origami Page For sheer beauty and complexity of design, you just can't beat this site. The photo gallery with its Creatures of Myth should give you a pretty clear idea of what can be achieved with origami and a lot of experience. Joseph also provides links to numerous other origami sites, as well as pointing to folding diagrams in several different formats (GIF, PDF, Postscript). A real source of inspiration! The Garden of Origami The Garden of Origami is another great site to start with. A strong Oriental feel runs through this site, from the simple-yet-elegant design to the recurrent theme of origami as philosophy. There are extensive links to folding patterns on the Internet, as well as a great section on using origami in the classroom to teach such things as geometry and Oriental culture. This is a great resource for teachers.

17. Mathematics Of Origami: Paper Square Geomtry
Using origami in the Class; Paperfolding in Schools. Design Choose one lesson fromPaper Square geometry and of students in the process of folding and assembling
http://www.aimsedu.org/spss/origami.html

Extractions: Patty Paper You must have access to a classroom in which to implement selected experiences. Rationale and Purpose Top This course meets the needs of those teachers who are looking for an engaging and innovative way to teach a variety of geometry concepts using origami. It provides guided opportunity for implementation and sustained use of hands-on experiences in a classroom setting. It also serves to enable teachers to reflect upon their teaching practices and to engage in dialogue with an experienced practitioner in the field. This results in better classroom applications and increased benefits for students. Furthermore, earned units may be applied for advancement on the salary scale. Course Content/Description Top This course seeks to empower teachers to provide for their students a hands-on discovery-based approach to teaching geometry through origami. The geometry focus of the origami experiences provided can be modified to suit a wide range of grades from elementary through high school. Topics which can be studied include properties of two- and three-dimensional shapes, symmetry, surface area, problem solving, pattern development and recognition, geometric vocabulary, and geometric notation, to name a few. The course is supported by classroom lessons found in the AIMS publication

18. Geometry Unit Study Resources - Eclectic Homeschool Online
Get an origami book and origami paper and make paper folding creations. How doyou fold your paper to get a sixsided or an eight-sided snowflake?
http://www.eho.org/geometry_unit.htm

Extractions: (Books suggested in this study are available in our online Bookstore in association with Amazon.com.) Math topics are not often considered fodder for unit studies. Most people have a figure or number oriented view of mathematics. They think in terms of number sentences, problems and formulas. From that point of view it can be difficult to see all the possibilities for language, history and science study that can be found in a mathematical topic. Naturally visual, geometry works well as a first mathematical unit study. Geometry is often offered piecemeal throughout most curriculums. In the early grades it is usually given a chapter in math texts. Saxon math books sprinkle it all the way through their upper elementary, junior high and high school level books. Eventually in high school, geometry is given an entire year in most curriculums. Key Curriculum Press is unique in offering a geometry curriculum for the upper elementary years called

19. Ch.5
Connecting geometry©. Chapter 5. Have you ever heard of origami, the Japanese artof paperfolding? There are some fascinating web sites on this topic.
http://www.k12.hi.us/~csanders/ch_05TriangleProp.html

Extractions: 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:

20. Computational Origami At The MIT
He works on computational origami the geometry of paper folding which interestsnot only hobbyists or MIT professors, but also the manufacturing