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Mathematics of Origami
Mathematics of Origami Angela Kohlhaas Loras College February 17, 2012 Introduction Origami ori + kami, “folding paper” Tools: one uncut square of paper, mountain and valley folds Goal: create art with elegance, balance, detail Outline History Applications Foldability Design History of Origami 105 A.D.: Invention of paper in China Paper-folding begins shortly after in China, Korea, Japan 800s: Japanese develop basic models for ceremonial folding 1200s: Origami globalized throughout Japan 1682: Earliest book to describe origami 1797: How to fold 1,000 cranes published 1954: Yoshizawa’s book formalizes a notational system 1940s-1960s: Origami popularized in the U.S. and throughout the world History of Origami Mathematics 1893: Geometric exercises in paper folding by Row 1936: Origami first analyzed according to axioms by Beloch 1989-present: Huzita-Hatori axioms Flat-folding theorems: Maekawa, Kawasaki, Justin, Hull TreeMaker designed by Lang Origami sekkei – “technical origami” Rigid origami Applications from the large to very small Miura-Ori Japanese solar sail “Eyeglass” space telescope Lawrence Livermore National Laboratory Science of the small Heart stents Titanium hydride printing DNA origami Protein-folding Two broad categories Foldability (discrete, computational complexity) Given a pattern of creases, when does the folded model lie flat? Design (geometry, optimization) How much detail can added to an origami model, and how efficiently can this be done? Flat-Foldability of Crease Patterns 훗 Three criteria for 훗: Continuity, Piecewise isometry, Noncrossing 2-Colorable Under the mapping 훗, some faces are flipped while others are only translated and rotated. Maekawa-Justin Theorem At any interior vertex, the number of mountain and valley folds differ by two. -
Paper Quilling Purpose: in These Difficult Times, Simple Activities Can Help Keep Children Occupied and Distract Them from What Is Happening in the World
History at Home Activity: Paper Quilling Purpose: In these difficult times, simple activities can help keep children occupied and distract them from what is happening in the world. This activity gives children the opportunity to learn about a creative craft that dates back to Colonial times and have a little fun. Quilled artwork made out of canvas strips, produced by artists, Stephen Stum and Jason Hallman Info for Parents or Guardians: You could share a little or a lot of the historical information that follows with children depending on their ages before you start the activity. This activity is geared towards children ages 8 and up. If the children are younger, speak in more general terms and provide a greater amount of help with the activity. These activities are designed to allow you to utilize materials that you probably already have at home. Feel free to substitute other materials. For example, almost any kind of paper, including wrapping paper, would work for this activity. Vocabulary: 1. paper quilling: a decorative art that involves curling and/or shaping strips of paper into coils or other shapes that are then arranged on a flat background to form a picture or design. History of Paper Quilling: Paper quilling is an old decorative art form that involves curling or shaping strips of paper into coils or other shapes and arranging the shapes on a flat background to form a design or picture. The background can be a sheet of paper. Glue is then used to secure the paper strips into place on the background paper. -
Mar.-Apr.2020 Highlites
Prospect Senior Center 6 Center Street Prospect, CT 06712 (203)758-5300 (203)758-3837 Fax Lucy Smegielski Mar.-Apr.2020 Director - Editor Municipal Agent Highlites Town of Prospect STAFF Lorraine Lori Susan Lirene Melody Matt Maglaris Anderson DaSilva Lorensen Heitz Kalitta From the Director… Dear Members… I believe in being upfront and addressing things head-on. Therefore, I am using this plat- form to address some issues that have come to my attention. Since the cost for out-of-town memberships to our Senior Center went up in January 2020, there have been a few miscon- ceptions that have come to my attention. First and foremost, the one rumor that I would definitely like to address is the story going around that the Prospect Town Council raised the dues of our out-of-town members because they are trying to “get rid” of the non-residents that come here. The story goes that the Town Council is trying to keep our Senior Center strictly for Prospect residents only. Nothing could be further from the truth. I value the out-of-town members who come here. I feel they have contributed significantly to the growth of our Senior Center. Many of these members run programs here and volun- teer in a number of different capacities. They are my lifeline and help me in ways that I could never repay them for. I and the Town Council members would never want to “get rid” of them. I will tell you point blank why the Town Council decided to raise membership dues for out- of-town members. -
Wenwu Chang, Exploring Space Filling Origami
Exploring space-filling origami Wenwu Chang [email protected] Shanghai Putuo Modern Educational Technology Center, China Abstract A new tetrahedra origami model was discussed in this paper. Sommerville in 1922 found four kinds of tetrahedron can fill space. This model starts from a rectangle paper, whose shape ratio is 1:√2, to produce one Sommerville’s main tetrahedron. It is proved that as long as the original paper is big enough, one can produce by this origami method more and more so-called Sommerville-tetrahedrons without cutting or pasting. Furthermore, these tetrahedrons fill three-dimension space in the same time. Just like Peano curve fills two-dimensional space, the original paper (two dimensional manifold) used in producing tetrahedrons fills the three-dimensional space. This article also introduces some interesting models in the lower number cases. Introduction In 1922, D.M.Y Sommerville found Aristotle, a famous philosopher during Ancient Greek Times, made a mistake. Aristotle stated there were two kinds of regular polyhedron, including regular tetrahedra could tile space. In fact, cube is the only regular polyhedron that can fill space. Sommerville in his paper ended this mistake and pointed out that several general tetrahedra could fill space indeed. Resulting from the way of cutting and reassembling a cube, he found 4 kinds of tetrahedra. The most important tetrahedron was the one made up of four triangles whose edge ratios are 2:√3:√3. I will call it Sommerville-tetrahedron within this paper. Another three kinds of tetrahedra were developed by dissection or reassembling of the dissection to this original tetrahedron. -
Origami Heart Box Instructions Step by Step
Origami Heart Box Instructions Step By Step Swift or tasteless, Giovanni never diking any profitableness! Unilobed Forrest gallops her nominals so excursively that Kris spiral very belatedly. Fulgid Ichabod still blazons: pileate and Aztecan Bear barbarises quite volubly but bestir her carpel noiselessly. GO662 Heart Box Diagram Also Origami Box With good On. But i need to origami heart lock box by measuring the citrus shape flower bouquet that it absorbs moisture. Yakomoga origami heart shaped quilled fringed flower by the flowers will then cut, which the dotted lines. First step by. Do the strip around a triangle shapes and includes a quality time! Go through the paper plate ocean craft ideas about origami tree quilled petals together in to learn how to. Diy gift box card that comes in the step by his disposable mask face you just download. Here i wanted to origami heart tabs on making this product designers who. Craft for his friends or tv or follow these folds open the box body friendly gift home you need it would take your. We heart box by step guides are among the hearts on your email. Diy heart origami box from your dollar bill and a clear origami video tutorials without the diagrams to. Step 15 Fold the average corner downwards and eve the squash fold at the square dot line Step 16 Flatten along the dotted line Step 17 The origami heart praise is. Push on the box by email address will be used for the ox and! Suprisingly it by step instructions to make boxes and decorate your box that sits in slightly faster to create various forms usually in. -
Download the Materials List
Book Arts Jerry Bedor Phillips August 15-21, 2021 COURSE DESCRIPTION In this workshop, the objective for students is to learn basic bookbinding techniques and experiment with some easy methods of creating artist books. Open spine binding methods such as the Coptic stitch, strap binding, and Japanese stab binding will be covered. These techniques will translate into creating some artist books structures including but not limited to the accordion fold books, flag books, etc. Students are encouraged to be creative with the contents of their artist books to reflect their interests. Artists books can cover the spectrum of illustrative drawings, collage and watercolor paintings. Students are encouraged to bring any printed paper ephemera with them (old magazines, printed book pages, or old sketches/drawings). Students will also have the opportunity to create content with drawing, watercolor, other paper based media. Examples and reference books will be available to study during the workshop. No prior experience necessary as the course is designed to be suitable for anyone with a casual book binding/artist book interest. MATERIALS LIST *Bone Folder (small Lineco) dickblick.com- item#: 64212-1678-$5.99 *Medium Awl dickblick.com-item #12868-1000 $8.05 *Xacto Knife Decorative Papers and/or scrapbooking paper (High-end and Low-end options) o High end: Talas.com, Hollanders.com, plazaart.com, dickblick.com, jerrysartarama.com o Low end: scrapbooking paper packs at Hobby Lobby, Wal-Mart, Michael’s stores, colored card stock *Glue brush (Lineco) Item: -
Reconstructing David Huffman's Origami Tessellations
Reconstructing David Huffman’s Origami Tessellations Eli Davis Erik D. Demaine Martin L. Demaine Jennifer Ramseyer MIT CSAIL MIT CSAIL MIT CSAIL MIT CSAIL Cambridge, MA 02139 Cambridge, MA 02139 Cambridge, MA 02139 Cambridge, MA 02139 [email protected] [email protected] [email protected] [email protected] David A. Huffman (1925–1999) is best known in com- ing to the symmetries of one of the 17 periodic “wallpaper puter science for his work in information theory, particu- groups”. Origami historian David Lister [4, 5] attributes the larly Huffman codes, and best known in origami as a pio- origin of origami tessellations to Shuzo Fujimoto, a Japanese neer of curved-crease folding. But during his early paper schoolteacher of mathematics who self-published the first folding in the 1970s, he also designed and folded over a origami tessellation book Twist Origami in 1976. In 1966, hundred different straight-crease origami tessellations. Un- however, artist Ronald Resch patented several origami tes- like most origami tessellations designed in the past twenty sellation designs [6]. Huffman met Resch in 1968, and they years, Huffman’s straight-crease tessellations are mostly talked more extensively at University of Utah in 1973, while three-dimensional, rigidly foldable, and have no locking Huffman was on sabbatical and Resch was a professor there. mechanism. In collaboration with Huffman’s family, our Both Huffman and Resch may have been influenced by these goal is to document all of his designs by reverse-engineering discussions, though we have no clear documentation to this his models into the corresponding crease patterns, or in some effect. -
4 Days Workshop Introduction to New Mokume Gane + Silver Quilling Certification 17 to 20 October 2016 Legnano
presents 4 Days Workshop Introduction to New Mokume Gane + Silver Quilling Certification with Astari G. Swatantri 17 to 20 October 2016 Legnano – Milano - Italy Astari G. Swatantri “I’m Astari G. Swatantri, an award winning metal clay artist with more than 10 years experience of working with metal clay. I’m passionate about metal clay and sharing it with others. Metal clay is a versatile material which keeps me exploring the possibilities to combine it with different art, craft and jewelry techniques and materials. I’m always up for the most recent development and I’ve followed metal clay trainings worldwide, the newest was Silver Quilling certification in Japan in 2016. As a metal clay artist I’ve received several awards for my jew- elry, one of the highlights was the Grand Prix of Silver Acces- sories Contest in 2013. I love meeting other metal clay enthu- siasts and share the passions for metal clay!” Awards 2013 Silver Accessories Contest ‘Coral’ Grand Prix Award of Minister’s encouragement at the Japan Ministry of Education, Culture, Sports, Science and Technology 2012 Pearl Contest ‘Between the Sky & the Sea’ Award of Selected Work 2008 Silver Accessories Contest ‘Secret Garden’ Semi Grand Prix Award of The Japan Association for Leisure and Culture Development 2007 Silver Accessories Contest ‘Inner Evolution’ Honorable Mention 2007 Art Clay Silver Photo Contest (Silver door chain decoration) Honorable Mention 2006 Art Clay Silver Photo Contest ‘Chappy’ (Silver name card holder) Honorable Mention 新木目金 NEW MOKUME-GANE Developed and presented by Aida Chemical Industries Co.,Ltd. New Mokume Gane is a totally new application designed for Art Clay Silver and Copper based on tradi- tional Japanese metalsmith techniques back in the 1600s in Japan for sword fittings. -
Exhibition Gallery Guide (PDF)
Dedicated to promoting artists’ books and bringing increased visibility and appreciation to the field, New York non-profit Printed Matter, Inc. Cut, Fold, defines artists’ books as “publications that have been conceived as and Form: artworks in their own right. These ‘projects for the page’ are generally inexpensive, often produced in large or open editions, and are Featuring democratically available…it is this potential to reach a larger audience that lends the books its social qualities and increases Kiff Slemmons its political possibilities.” and Julie For example, mixed media artist JoAnna Poehlmann brings her wit, sensitivity, and love of nature, art, and history to a variety of media, VonDerVellen including watercolor, prints, sculpture, and limited edition books. She pays special attention to the binding and boxes that are created to house the work –– implicitly challenging the line between book and object. Artist and printmaker Jim Lee runs his own press producing limited edition hand-printed letterpress books. While he may use the landscape—and the people who inhabit it—as subject for prints and Even in a culture that seems more and more digitally-oriented, paper is pervasive. Over the illustrations, he ages, artists have included paper in their practice in a variety of ways, such as a surface for also creates books an image, a component of a larger piece, in the form of a book, or as a sculptural medium. that contain poetry and work While there are aspects of paper that are fragile and delicate, it can also be versatile by other writers. and durable. Historically, it has been utilized in a myriad of objects such as jewelry, clothing, Varying book sizes lampshades, and vessels. -
North American Quilling Guild Official Shape Chart
North American Quilling Guild Official Shape Chart The following is a list of the recognized shapes and techniques the NAQG deems to be the basic shapes used in quillwork. Although each and every shape has numerous variations, these are the ones felt to be most commonly used by quillers. The NAQG official accepted name for each shape is listed under the photo. Alternate names are listed to the right. There seems to be no set standard amongst the various books, kits, self published instructions, or brochures as to the exact name for each quilled shape. The shape names seem to be randomly applied by whoever designs a quilled item or writes about one. Therefore any alternate names used to describe the shape (that the NAQG is aware of) have been included to help identify which shape is being referenced. Literally dozens of variations can be created from these basic shapes and most of them have no specific name. Other shapes have one or more variations that are given an “official” name as in the teardrop or marquise shapes. Both have a recognized variation with a separate name, i.e. shaped teardrop or shaped marquise. The hundreds of other variations are only known as an alteration of the original basic shape from which they were created. Shape Name Other names Shape Name Other names Shape Name Other names LOOSE COILS SOLID ROLLS ball bead coil tight coil closed loose coil solid roll closed loose roll peg SR-4…….Bead loose circle disc roll pom pom LC-6 Loose coil carnation SR-1 Tight roll drop raindrop cup peacock eye domed roll SR-5 Fringed can be very long, flower thin, and pointy or short, fat, and squat SR-2 Grape LC-7 Teardrop roll comma cone curved teardrop cone roll flame dimensional tight petal roll wing LC-8 Shaped SR-3 Teardrop Tapered/Sculpture d roll Copyright North American Quilling Guild (www.naqg.org) Page 1 of 4 These quilling reference materials are for your own personal use; You may print them and distribute them, we only ask that you spread the word about NAQG by leaving our information on the pages intact. -
Origami Animals by Robert Salazar
Robert Salazar’s Artist Statement From a single uncut sheet of paper, all origami arise. Folding alone each sheet into any of an endless diversity of forms. Despite its finite surface area and simplicity, even a single sheet of paper can take on staggering complexity. Since surface area – the resource- is finite, any of an origami’s features can only come about by exchanging surface area with its other features until harmony is found among its many interdependent parts. Each transformation is an elaborate play with intricate geometric relationships that are akin to the evolution of a genome. Cutting geometric relationships with scissors or adding additional resource are impossible. Just as with our relationships with nature and each other, the interdependence that bring us together cannot be cut and resources cannot be created from nothing, everything becomes possible by seeking harmony with what we have. The focus of my work is to show how powerfully harmony can transform a finite resource as simple as a sheet of paper, along with its intrinsic geometric rules, into endless possibilities. I invite everyone to imagine the power of what’s possible when we strive for harmony with our own relationships, with each other and with nature, as they consider my works. www.salazarigami.com The Wildling Museum in Solvang presents Folded Art: Origami Animals by Robert Salazar. On View November 10, 2018 – March 25, 2019 His art shows how harmony can transform something as simple as a sheet of paper into endless possibilities. The exhibit features a collection of origami animals found in Santa Barbara County such as the Steelhead Trout, California Condor, Tarantula, and a few prehistoric species as well. -
EXPLORATORY ART (Grades 6-8)
EXPLORATORY ART (Grades 6-8) Learning in Place Weeks 4, 5, 6 Review Weeks 1- 3: Exploratory Art Packet (March 16th - April 3rd) - found on the NPS website under Learning in Place. If you have not done this packet yet, please work through these things first, then move on to the lessons listed here for weeks 4, 5 and 6. Please refer to the first packet for review of basic art vocabulary and techniques. Pacing Guide: Students should spend approximately 3 hours a week on their fine arts elective. Your assignments will begin with art vocabulary. You will then transition to art analysis. Finally, you will be creating art! Our focus during this packet is on sculpture/3-dimensional art. Page 1- Pacing Guide and Table of Contents Page 2- Sculpture Media Notes (use for pages 3-5) Page 3- Sculpture Types Review Page 4- Analyzing Art Page 5- Sculpture Scenarios Page 6- Compare and Contrast (Paper sculpture) Page 7- Exploring Origami (Creating a paper crane) Page 8-9- Exploring Quilling Page 10- Observational Drawing Practice SCULPTURE MEDIA NOTES SCULPTURE TYPES REVIEW Match the definition to the correct sculpture medium (material). 1. Environmental sculpture _________ S. Sculpture in the Round _______ 3. Ceramic Pottery ______________ 4. Papier Mache ________ 5. Kinetic Sculpture __________ 6. Construction ______ 7. Clay Coil Building _______ 8. Relief Sculpture ________ 9. Clay Slab Building ________ 10. Assemblage/Found object sculpture ______ A. Clay sculptures created by throwing on the potter’s wheel, good for creating vessels B. Sheets of clay created by a rolling pin, good for creating large clay sculptures C.