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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
  3. Amazing Origami by Kunihiko Kasahara, 2002-03-28
  4. Explore Folding of the Circle: Series Book 3 (Explore Folding of the Circle, Book 3) by Bradford Hansen-Smith, 2007

1. The Geometry Junkyard: Origami
Burczyk. origami polyhedra. Jim Plank makes geometric constructions by folding paper squares. origami tessellations, Alex Bateman.
http://www.ics.uci.edu/~eppstein/junkyard/origami.html
Origami

2. Ma Baker's Origami And Paper Folding Web Quest Page
of this page is to introduce students to the art of origami and to the various methods of folding paper. paper folding activities related to geometry help to
http://education.nmsu.edu/webquest/wq/origami/
Ma Baker's Origami and Paper Folding Web Quest Page
INTRODUCTION
Origami is the art of folding paper into decorative objects. The term origami is the Japanese word for folded paper . There are about 100 traditional origami figures, most depicting such natural forms as birds, flowers, and fish. An abstract, ceremonial form of origami called noshi, is a pleated paper ornament attache to gifts. Most origami is folded from an uncut square of paper.The most common sizes of square are 6-inches and 10-inches. The preferred paper is thin Japanese paper called washi , but foil-backed wrapping paper, heavy art paper, and typing paper can be used. Origami, like paper, originated in China but flourished in Japan. The purpose of this page is to introduce students to the art of origami and to the various methods of folding paper. Paper folding activities related to geometry help to motivate student interest in mathematics. The process of producing a paper figure allows students to learn to follow directions, to become motivated, to use a visual aide for better understanding of mathematical concepts, and to complete a project through their own perseverance.
THE TASK
(*Before you begin add this site to your bookmark list.) To initiate the exploration of paper folding find out some basic facts about the history of origami at

3. Origami & Math
more ideas from this presentation on origami In Creasing geometry in the Classroom about crease patterns, origami itself is the act of folding the paper, which mathematically can
http://www.paperfolding.com/math
So, you're interested in origami and mathematics...perhaps you are a high school or K-8 math teacher, or a math student doing a report on the subject, or maybe you've always been interested in both and never made the connection, or maybe you're just curious. Origami really does have many educational benefits . Whether you are a student, a teacher, or just a casual surfer, I have tried my best to answer your questions, so please read on. So exactly how do origami and math relate to each other? The connection with geometry is clear and yet multifaceted; a folded model is both a piece of art and a geometric figure. Just unfold it and take a look! You will see a complex geometric pattern, even if the model you folded was a simple one. A beginning geometry student might want to figure out the types of triangles on the paper. What angles can be seen? What shapes? How did those angles and shapes get there? Did you know that you were folding those angles or shapes during the folding itself? For instance, when you fold the traditional waterbomb base, you have created a crease pattern with eight congruent right triangles. The traditional bird base produces a crease pattern with many more triangles, and every reverse fold (such as the one to create the bird's neck or tail) creates four more! Any basic fold has an associated geometric pattern. Take a squash fold - when you do this fold and look at the crease pattern, you will see that you have bisected an angle, twice! Can you come up with similar relationships between a fold and something you know in geometry? You can get even more ideas from this presentation on

4. Folding And Unfolding (Erik Demaine)
folding and unfolding is an exciting area of geometry. It is attractive in the way paper folding origami Mathematics and Computational origami. origami (paper folding) has lead to
http://theory.lcs.mit.edu/~edemaine/folding
Erik Demaine 's Folding and Unfolding Page
Introduction
Folding and unfolding is an exciting area of geometry. It is attractive in the way that problems and even results can be easily understood, with little knowledge of mathematics or computer science, yet the solutions are difficult and involve many sophisticated techniques. The general sort of problem considered is how a particular object (e.g., linkage, piece of paper, polyhedron, or protein) can be reconfigured or folded according to a few constraints, which depend on the object being folded and the problem of interest. In particular, we are interested in efficient algorithms for characterizing foldability, and finding efficient folding processes, or in proving that such algorithms are impossible. There is a wide range of folding and unfolding problems, some going back several centuries and still unsolved, like unfolding convex polyhedra, while others are more recent like protein folding. In the last few years, there has been tremendous progress on many of the fundamental problems in folding and unfolding, yet some of the most important questions still remain open. This leaves the area in an exciting state. Many results in folding and unfolding can be characterized in the following way. My favorite type of results are

5. Origami & Paper Folding Resources
Cyberfolks Friendly Guided Web Site Tours. 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. on using origami in the classroom to teach such things as geometry and Oriental culture flavor of origami is modular origami, or the art of folding paper to create complex
http://www.folksonline.com/folks/hh/tours/1999/origami.htm
Cyberfolks Friendly Guided Web Site Tours
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.

6. Origami Mathematics Page
Mathematics of paper folding; includes a bibliography of articles and journals, Combinatorial geometry syllabus, and a tutorial on geometric constructions. Photo gallery of completed modular, geometric, and tessellation models.
http://web.merrimack.edu/~thull/OrigamiMath.html
Origami Mathematics
These pages are an attempt to begin collecting information on the mathematics of paper folding. Anyone who has practiced origami has probably, at one time or another, unfolded an origami model and marveled at the intricate crease pattern which forms the "blueprint" of the fold. Clearly there are some rules at play in these collection of creases. Clearly there is an origami geometry at work when paper is folded. Unfortunately, much of the above-mentioned work is new, and at the time of this writing there are few good references for this type of information. These pages will try to help solve this problem by providing an extensive bibliography for origami-math, list upcoming lectures and events, and offer instructions and tutorials for select topics. However, this is an on-going project! These pages are still in their infancy, and any comments or suggestions (or offers to help!) would be greatly appreciated! In March of 2001 the 3rd International Meeting of Origami Science and Technology (3OSME) was held. See the above link for the program listing, pictures, and information on the proceedings book
Origami Math Menu:

7. Paper Folding Geometry
knot page from a page called geometry Junkyard. I have an origami page where I have instructions for In the geometry of paper folding, a straight line becomes a crease
http://www.cut-the-knot.com/pythagoras/PaperFolding
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Paper Folding
The impetus for this page came from a visitor's letter Hi, I got to your knot page from a page called Geometry Junkyard . I have an Origami page where I have instructions for making a star from a paper strip knot. I used a link to your page for the proof. Let me know if you have any objections and I'll remove it. Thanks, Meenakshi As I never mentioned the word Origami on my pages (i.e., until now), my interest was somewhat piqued. Origami is an ancient Chinese and Japanese art of paper folding. From the Brief History of the Ancient Art of Paperfolding I gather that Origami gained acceptance in the West in the early 1950s. Very comprehensive bibliographies are available online. A search of the online bookstore has resulted in several dozen books and albums. In my own library, I discovered several books wholly or in part devoted to the mathematics of paper folding (see bibliography below.) Unexpectedly, information available online proved to be scarce. (This may explain a reference to my logo page .) Following is my attempt to catch up with the development of the last 50 years of which, regretfully, I knew so little. My main source of information was a

8. Paper Folding Geometry
paper folding. The impetus for this page came from a visitor s letter. Hi,. I got to your knot page from a page called geometry Junkyard. I have an origami page
http://www.cut-the-knot.org/pythagoras/PaperFolding/index.shtml
CTK Exchange Front Page
Movie shortcuts

Personal info
...
Recommend this site
Paper Folding
The impetus for this page came from a visitor's letter Hi, I got to your knot page from a page called Geometry Junkyard . I have an Origami page where I have instructions for making a star from a paper strip knot. I used a link to your page for the proof. Let me know if you have any objections and I'll remove it. Thanks, Meenakshi As I never mentioned the word Origami on my pages (i.e., until now), my interest was somewhat piqued. Origami is an ancient Chinese and Japanese art of paper folding. From the Brief History of the Ancient Art of Paperfolding I gather that Origami gained acceptance in the West in the early 1950s. Very comprehensive bibliographies are available online. A search of the online bookstore has resulted in several dozen books and albums. In my own library, I discovered several books wholly or in part devoted to the mathematics of paper folding (see bibliography below.) Unexpectedly, information available online proved to be scarce. (This may explain a reference to my logo page .) Following is my attempt to catch up with the development of the last 50 years of which, regretfully, I knew so little. My main source of information was a

9. Origami -- From MathWorld
Huzita, H. Understanding geometry through origami Axioms. In Proceedings of the First Kasahara, K. origami Omnibus paperfolding for Everyone.
http://mathworld.wolfram.com/Origami.html
INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index
ABOUT THIS SITE About MathWorld About the Author
DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics
CONTACT Email Comments Contribute! Sign the Guestbook
MATHWORLD - IN PRINT Order book from Amazon Geometry Geometric Construction
Geometry
... Herrstrom, Emily
Origami The Japanese art of paper folding. In traditional origami, constructions are done using a single sheet of colored paper that is often, though not always, square. In modular origami, a number of individual "units," each folded from a single sheet of paper, are combined to form a compound structure. Origami is an extremely rich art form, and constructions for thousands of objects, from dragons to buildings to vegetables have been devised. Many mathematical shapes can also be constructed, especially using modular origami. The images above show a number of modular polyhedral origami constructed by E. K. Herrstrom, together with an animated crane constructed in Mathematica by L. Zamiatina.

10. Folding -- From MathWorld
R. and Arnstein, B. Multimodular origami Polyhedra Archimedeans D.; and Pedersen, J. paperfolding and Number Problems of Elementary geometry The Duplication
http://mathworld.wolfram.com/Folding.html
INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index
ABOUT THIS SITE About MathWorld About the Author
DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics
CONTACT Email Comments Contribute! Sign the Guestbook
MATHWORLD - IN PRINT Order book from Amazon Recreational Mathematics Folding General Folding
Folding The points accessible from c by a single fold which leaves fixed are exactly those points interior to or on the boundary of the intersection of the circles through c with centers at for i n . Given any three points in the plane a b , and c , there is an equilateral triangle with polygon vertices x y , and z for which a b , and c are the images of x y , and z under a single fold. Given any four points in the plane a b c , and d , there is some square with polygon vertices x y z , and w for which a b c , and d are the images of x y z , and w under a sequence of at most three folds. In addition, any four collinear points are the images of the polygon vertices of a suitable square under at most two folds. Every five (six) points are the images of the polygon vertices of suitable regular pentagon hexagon ) under at most five (six) folds.

11. Origami
Because of this, the practice of paper folding was originally origami appealed to the same aesthetic which created as life it is moral geometry, inasmuch as
http://www.tuvy.com/resource/origami.htm
Home About Books Authors ... Household Special thanks to Origami Garden for this info. In the East The art of paper folding is thought to have had its beginnings in China during the first or second century A.D. By the sixth century, it was being practiced in Japan. In this small island country, paper was a scarce and treasured material. Because of this, the practice of paper folding was originally confined to the wealthy nobility. Origami appealed to the same aesthetic which created the tea ceremony, which one scholar has described as "essentially a worship of the Imperfect, as it is a tender attempt to accomplish something possible in this impossible thing we know as life...it is moral geometry, inasmuch as it defines our sense of proportion to the universe." (Kakuzo Okakura, The Book of Tea)
Increasing trade eventually led to the widespread availability of affordable paper, and origami grew into a popular pastime among rich and poor alike. Because of their culture which emphasizes respect for the economy of nature, however, Asian practitioners of this art have never lost the impulse to save even the tiniest scraps of paper to fold into miniature origami models. Hiden Senbazuru Orikata ("How to Fold One Thousand Cranes") was published in 1797, and is the oldest origami publication which survives. Kan no modo ("Window on Midwinter"), the first published collection of origami models, appeared in 1845.
In the West The Moors, who were Muslims from West Africa, brought paper folding with them to Spain when they invaded in the eighth century. Although Islam proscribed the making of representational figures, Islamic mathematicians and astronomers were fascinated with pattern, symmetry, and space. Their explorations included studies on the geometry of tessellation and on the folding patterns hidden within the square. These investigations of pattern were often given form in architecture.

12. Origami
origami the ancient art of papar folding origami - paper folding for fun Jopephy Wu s Origmai Page origami Sociteit Nederland The geometry Junkyard - origami
http://www.tooter4kids.com/Japan/origami.htm
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.

13. Origami Mathematics
origami Page. Even more tessellations! LWCD Inc. This features their book paper folding which provides methods to teach geometry to me!) A paper folding Project. Paul Haeberli has put
http://www.merrimack.edu/~thull/omfiles/mathlinks.html
Other Origami Math Pages
The following are web pages that are related to the origami-math mission. Further our cause and visit these sites!
  • Information on Stamp Foldings
    This is the Combinatorial Object Server's (COS) tutorial on the stamp folding problem, which is related to 1-dimensional folding as well as single vertex flat folds (in 2D). This is a great intro, with descriptions of equivalent problems (like counting mazes and meanders).
    Erik Demaine's Web Page

    Erik has devoted a lot of time towards convincing people that there are interesting computation questions to ask in the field of origami. (Actually, if you take a glance at his web page, you'll see that he spends a lot of time on zillions of other things too. Some people seem to have more time that other people. No fair!) Thus, if you're interested in the field of computational origami then give Erik's page a look. You'll find preprints/reprints of many interesting papers. Erik recently was made an assistant professor at MIT in their Electrical Engineering and Computer Science Department
    Business Card Menger Sponge Project

    Dr. Jeannine Mosely's awesome project of constructing a level 3 Menger Sponge out of folded business cards. A monument of mathematical recycling!

14. Erik Demaine
19th Annual Symposium on Computational geometry, San Diego Hobbies Improv comedy/theater; Glassblowing; origami (paper folding); Juggling ( intermediate );
http://theory.lcs.mit.edu/~edemaine/
Erik Demaine
Assistant Professor in Electrical Engineering and Computer Science and Computer Science and Artificial Intelligence Lab at the Massachusetts Institute of Technology Theory of Computation group, specifically Algorithms
Academics
  • Papers
  • Videos
  • Puzzles
  • Software
  • CV in PostScript or PDF , last updated on May 4, 2004.
  • I co-edit The Open Problem Project with Joseph Mitchell and Joseph O'Rourke
  • I am interested in most areas of research in mathematics and computer science broadly connected to algorithms. Particular interests include
    • Discrete and computational geometry: Folding and unfolding linkages , robotics, motion planning, dissections, simple polygonizations
    • Data structures: Dynamic data structures, succinct encodings of data structures, memory management, cache-efficient and disk-efficient data structures, average-case data structures, text indexing
    • Algorithms and their analysis: Adaptive computation, graph algorithms, string matching, randomized algorithms, approximation algorithms, fixed-parameter algorithms, streaming algorithms
    • Complexity theory: Hardness (NP, PSPACE, EXPTIME, EXPSPACE, ...), parameterized complexity

15. Origami Im Geometrieunterricht
paper folding for the Mathematics Class.
http://www.geometry.at/strobl/strobl2000/vortrag00/hofer/origami.htm
21. Fortbildungstagung des ADG
Strobl / Wolfgangsee
7-10 November 2000
Workshop:
Origami im Geometrieunterricht
Michael Hofer
geometrie.tuwien.ac.at">hofer
geometrie.tuwien.ac.at "I hear and I forget.
I see and I remember.
I do and I understand."
(Chinese Proverb)
Die Geschichte von Origami
Sadako and the Thousand Paper Cranes ( dt., Sadako will leben) von Eleanor Coerr illustriert.
Alice in Wonderland
Modular (Unit) Origami
Geometrie und Origami
Geometric Exercises in Paper Folding von Sundara Row, erschienen in einer revidierten Auflage 1905. Dieses Buch ist als Referenz in Felix Klein’s
Bibliographie
  • Franco, Betsy. Unfolding Mathematics with Unit Origami. Key Curriculum Press, 1999. (ISBN 1-55953-275-0) Gurkewitz, Rona und Arnstein, Bennett. 3-D Geometric Origami – Modular Polyhedra. Dover Publications, 1995. (ISBN 0-486-28863-3) Johnson, Donovan. Paper Folding for the Mathematics Class. National Council of Teachers of Mathematics, 1957. (ISBN 0-87353-412-3) Mitchell, David. Mathematical Origami – Geometrical Shapes by Paper Folding. Tarquin Publications, 1997. (ISBN 1-899618-18-X) Olson, Alton. Mathematics through Paper Folding. National Council of Teachers of Mathematics, 1975. (ISBN 0-87353-076-4)

16. David Mitchell's Origami Heaven - Notes On Folding Geometries
in modular origami is discussed in Useful Rectangles and folding geometry. Embedded folding geometry. A folding geometry that is natural to one particular paper
http://www.mizushobai.freeserve.co.uk/natural.htm
David Mitchell's Origami Heaven Notes on Folding Geometries Folding geometries are of three quite distinct kinds, natural, embedded and non-located. In the first two kinds of folding geometry the folds and/or creases are positioned by the use of location points. In the third kind the position of the folds and/or creases are positioned by eye (though their positions may subsequently be refined by an iterative process). Two or more of these distinct types of folding geometry may be combined within a single design. Natural Folding Geometry The natural folding geometry of a paper-shape is the folding geometry obtained by using just the primary reference points (the original edges and corners of the paper-shape) to determine where the creases will form. In the case of the square the natural folding geometry consists of two creases obtained by folding opposite edges onto each other and two creases obtained by folding opposite corners onto each other. The first set divide the square into four smaller squares. The second set bisect these smaller squares at 45 degrees. This system of natural folding geometry can be called the 90/45 degree system. The resulting crease pattern is familiar as the crease pattern of the waterbomb base and preliminary fold. The natural folding geometry creates secondary reference points (in the case of the square, four internal creases and five points where these creases intersect each other and the edges) which can be used to locate further creases, such as those required for the bird base.

17. Washington Parent Article
In the Western world, origami is mostly practiced by In the United States, paper folding has also been explored who appreciate the art for its simple geometry.
http://www.washingtonparent.com/articles/0203/origami.htm
March 2002 Folding is Fun Creating Origami Architecture at the National Building Museum
Jill Wiley White, M.A.T. and Ayumu Ota, M.A.T. Make your next family experience memorable with a trip to the National Building Museum’s annual Festival of Origami Architecture. On Saturday, March 30, families can explore the Japanese craft of paper folding, known as origami. Why origami at the National Building Museum? Because origami allows people to explore the basic design of all forms, including those found in architecture and the landscape. History of Origami The art of paper folding originated in China but was elevated into an artform by the Japanese after it was brought to that country in the sixth century. The Japanese coined the term origami ( ori means "to fold" and kami means "paper"). In the eighth to twelfth centuries, because paper was such an expensive commodity, origami was practiced and used only by the Japanese nobility. They exchanged origami creations as good luck tokens and used them at wedding ceremonies to wrap sake (rice wine) bottles with paper butterflies representing the bride and groom. By the 1500s when paper became more affordable, origami was practiced by all Japanese and was used as a means of identifying one’s social status. Aristocrats folded differently from farmers and peasants. People knew their position and folded accordingly. In the 1600s-1800s, one of the high periods of Japanese art and culture, origami emerged into a true artform. Japanese publications of this period document the creation of basic origami forms that we know today.

18. Origami Links With Visual Arts Standards
Plus inks to other geometric shapes. The geometry Junkyard origami Projects and questions that revolve around the math of paper folding.
http://www.artteacherconnection.com/pages/origami.html
Math and Art
Origami
The Japanese word "Origami" is now an internationally recognized word and is synonymous with the art and craft of paper folding.Origami is a traditional Japanese pastime where a single square of paper is folded in different ways to create shapes like cute animals and beautiful plants.Since it only takes a sheet of paper, the hobby can easily be enjoyed anywhere; many people in Japan enjoy it at home and at school. The practice of origami began in the early 700s, when paper was first introduced to Japan. At first paper was folded to make decorations for use in religious ceremonies at shrines, but gradually people came to use it in their regular lives as well. During the Heian period(794-1185), it was popular to fold valuable paper and use it to beautifully wrap letters and presents. Later, origami continued to be used in traditional ceremonies, but the women of the imperial court began to fold dolls and other shapes for their amusement. you can find more historical information at Origami - the ancient art of paper folding.

19. Origami-Math Bibliography
by origami (paper folding), Symmetry Culture and Science, Vol. 5, No. 1 (1994), 6984. Huzita, Humiaki, The trisection of a given angle solved by the geometry
http://www.merrimack.edu/~thull/omfiles/geombib.html
Origami Geometry and Education
These articles deal with pure geometrical aspects of folding a piece of paper. Since so many of these articles are also about using origami as an educational tool, I'm listing both of these categories together.
  • Bruckheimer, M. and R. Hershkowitz, Constructing the parabola without calculus, Mathematics Teacher , Vol. 70, No. 8 (Nov. 1997), 658-662.
  • Faulkner, J., Paper folding as a technique in visualizing a certain class of transformations, Mathematics Teacher , Vol. 68. No. 5 (May 1975), 376-377.
  • Fehlen, J., Paper folds and proofs, Mathematics Teacher , Vol. 68, No. 8 (Nov. 1975), 608-611.
  • Frigerio, Emma, New relations in origami geometry proposed by J. Justin, Proceedings of the First International Meeting of Origami Science and Technology , H. Huzita ed. (1989), 125-130.
  • Frigerio, Emma, Origami geometry: old and new, Proceedings of the First International Meeting of Origami Science and Technology , H. Huzita ed. (1989), 379-386.
  • Frigerio, Emma and Humiaki Huzita, A possible example of system expansion in origami geometry, Proceedings of the First International Meeting of Origami Science and Technology , H. Huzita ed. (1989), 53-69.

20. Paper Folding - Books
list of folding symbols, plus stepby-step folding diagrams for origami for Beginners $5.95 By Vincent Palacios. Patty paper geometry $21.95 By Michael Serra.
http://www.mathartfun.com/shopsite_sc/store/html/OrigamiBooks.html
Paper Folding - Books
The Complete Book of Origami
By Robert J. Lang. Includes a brief history of Origami, guide to folding techniques, illustrated list of folding symbols, plus step-by-step folding diagrams for 48 projects ranging from simple to complex. Over 1000 drawings and diagrams.
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Unfolding Mathematics with Unit Origami
By Betsy Franco. A book of blackline activity masters designed for algebra and geometry students in high schoool or middle school. Contains 16 activities arranged in order of increasing difficulty. The book's primary purpose is to teach mathematics, but it also introduces students to the art of origami. 136 pages.
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3-D Geometric Origami
By Rona Gurkewitz and Bennett Arnstein. Contains step-by-step instructions and diagrams for building over 60 different polyhedra-based models from origami units. 80 pages.
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Origami for Beginners
By Vincent Palacios. An easy-to-follow guide book with 57 models. Each is illustrated with step-by-step diagrams and captions that take you through their construction. 80 pages. [Add to Cart] [View Cart] Patty Paper Geometry By Michael Serra. Patty Paper - the stuff that separates hamburger patties - can also be used for geometric investigations! These square of paper can be written on, they hold creases well, and they are semi-transparent like tracing paper. "Patty Paper Geometry" contains dozens of activities that motivate kids to read, write, and talk about geometry. This book is a blackline master book with 12 chapters of guided and open investigations. Grades 6-10. 272 pages, paperback.

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