1. Paper Folding OVERVIEW INTRODUCTION BASIC FOLDS GEOMETRY CONIC SECTIONS ISOMETRIES FRACTIONS STUDENT WORKBOOK. Paper Folding Supplies PATTY PAPERS http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Ma Baker's Origami And Paper Folding Web Quest Page 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://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. The Geometry Junkyard Origami Folding geometry. Wheaton college course project on modular origami. Geometric paper folding. David Huffman. Rona Gurkewitz' Modular Origami http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Origami Mathematics Page paper folding. Anyone who has practiced origami has probably, at one time or another, unfolded an origami origami geometry at work when http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Sy's Paper Folding Page Function. Geometry. Heart. Human Figure This page is all about my paper folding related works. It does not contain any general origami http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Paper Folding Geometry Geometry Junkyard. I have an Origami The paper folding geometry may be expected to justify this construction. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Marc Kirschenbaum's Origami Page Paper in Harmony. A Collection of Origami Instrumentalists. interesting nonsymmetrical folding going on. Geometry in Motion - a great http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Folding And Unfolding (Erik Demaine) Paper Folding Origami Mathematics and Computational Origami. Origami (paper folding) has lead to an intriguing s Geometry Junkyard page on http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Orihouse Knotology, The Art Of Creating Spheres From Strips Of Welcome to my house, full with origami rooms. This room contains Knotology the art of creating spheres from tickertape, by folding the paper only. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Origami Web Resources For Students The Geometry Junkyard Origami Origami does all that in an enjoyable way. Educational Benefits of Paper Folding This section is designed to http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. 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://www.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: Browse our Origami Math Bibliography Tutorial: Origami Geometric Constructions recently updated!

12. The Geometry Junkyard: Origami Mostly modular origami. Valerie Vann makes polyhedra out of folded paper. paper folding a 3060-90 triangle. From the geometry.puzzles archives. http://www.ics.uci.edu/~eppstein/junkyard/origami.html

Origami Krystyna Burczyk's Origami Gallery - regular polyhedra The business card Menger sponge project . Jeannine Mosely wants to build a fractal cube out of 66048 business cards. The MIT Origami Club has already made a smaller version of the same shape. Cardahedra . Business card polyhedral origami. Cranes, planes, and cuckoo clocks . Announcement for a talk on mathematical origami by Robert Lang. Crumpling paper: states of an inextensible sheet Cut-the-knot logo . With a proof of the origami-folklore that this folded-flat overhand knot forms a regular pentagon. Folding geometry . Wheaton college course project on modular origami. Geometric paper folding . David Huffman. Rona Gurkewitz' Modular Origami Polyhedra Systems Page . With many nice images from two modular origami books by Gurkewitz, Simon, and Arnstein. How to fold a piece of paper in half twelve times . Britney Gallivan took on this previously-thought-impossible task as a high school science project, worked out an accurate mathematical model of the requirements, and used that model to complete the task. Knotology . How to form regular polyhedra from folded strips of paper?

13. Paper Folding Geometry origami is an ancient Chinese and Japanese art of paper folding. The paper folding geometry may be expected to justify this construction. http://www.cut-the-knot.org/pythagoras/PaperFolding/index.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents 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

14. Origami & Math These puzzles involve folding a piece of paper so that certain color patterns origami, geometry, and the Kawasaki Theorem. A more advanced geometry 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

15. Tom's Combinatorial Geometry Class by looking at 3D polyhedral geometry and the mathematics of paperfolding (origami). Axiomatic and Analytic Modelling of paper folding The classic http://www.merrimack.edu/~thull/combgeom/combgeom.html

(Jun Maekawa's Devil, folded from one square of paper, no cutting) Here are some assignments: ASSIGNMENT 1 Due Jan. 31 ASSIGNMENT 2 Due Feb. 14 ... Due April 25 Here are some handouts: (all are in PDF format) Handout 1 Handout 2 Handout 3 Handout 4 MA 323A Combinatorial Geometry! Class Notes: Notes on Planar Graph Theory Notes on how to do Proofs! Notes on spherical Buckyballs Part 1 and Part 2 Notes on Graph Colorings Notes on Spherical and Convex Polyhedral Geometry Notes on Axiomatic Origami Constructions ... Notes on Reflections are Foldings, Part 2 Hi! This page was developed in the Spring of 2000 for the course Combinatorial Geometry at Merrimack College. It is currently being revised and updated for the Spring 2002 offering of this course. Below is a draft of the syllabus. Combinatorics (the mathematics of counting) and geometry have many strong connections. We will explore these connections by looking at 3D polyhedral geometry and the mathematics of paperfolding (origami). In particular, we'll cover... Convex Polyhedral Geometry: construction of paper models, Euler's Formula, planar duality, coloring theorems, Hamilton cycles, Buckyball classification and edge coloring, spherical geometry, solid angles, Descartes' Theorem, surfaces of higher genus, convex polytopes, simplices, the Generalized Euler's Formula.

16. Ma Baker's Origami And Paper Folding Web Quest Page origami is the art of folding paper into decorative objects. paper folding activities related to geometry help to motivate student interest in 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

17. Paper Folding - Models Patty paper geometry contains dozens of activities that motivate kids to read, write, and talk about 24 7 x 7 sheets of origami paper in 12 colors. http://www.mathartfun.com/shopsite_sc/store/html/OrigamiManips.html

Paper Folding - Models Captured Worlds Captured Worlds is a set of five pop-out, glue, and fold-up polyhedra. The five used in Captured Worlds are known as the Platonic Solids. They are decorated with fanciful scenes rendered in six-point perspective by internationally-known artist Dick Termes. This unique perspective system allows an entire three-dimensional surrounding to be projected onto the polyhedra. [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. [Add to Cart] [View Cart] Patty Paper Geometry Student Workbook This companion student workbook contains all of the open investigations plus some exercise sets. 88 pages, paperback. [Add to Cart] [View Cart] Patty Paper 1000 sheets of patty paper.

18. Paper Folding Each of them will have experience of paperfolding activity by going though origami is a fun way to be used in teaching geometry; for many of the folds, http://worldroom.tamu.edu/CL_LitoProject/

Circle and Whale Origami in Geometry By Litao Wang Grade: 3rd Venue: Geometry Instructional Goal: This project is designed to effective student learning with the aid of technology (digitalized video and interactive video). Students will be able to identify and distinguish the five basic definitions (circle, circumference, origin, radius and diameter) of a circle. Each of them will have experience of paper-folding activity by going though self-paced interactive video. Transforming a flat piece of paper into a three dimensional figure is a unique exercise in spatial reasoning. Origami is a fun way to be used in teaching geometry; for many of the folds, whatever is done to one side, is likewise done to the other side. In addition, paper-folding allows students to create and manipulate basic geometric shapes such as squares, rectangles, and triangles. Duration of Instruction: 45 minutes Delivery System: A traditional classroom with computers Draw attention: Content Presentation Give non-example and example for diameter. (lines pass through the origin and not pass through the origin.)

19. Origami Links With Visual Arts Standards origami paper folding for fun At this site is another easy direction sheet to The geometry Junkyard - origami Projects and questions that revolve 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.

20. Kayee Kwok 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 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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