EXPLORATORY ART (Grades 6-8)
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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. -
It's Modern. It's Modular. It's the MOD* Dispensing System
It’s Modern. It’s Modular. It’s the MOD* Dispensing System. The promise is simple: deliver a customized washroom experience to everyone, everywhere. Nurses caring for patients, employees in office buildings, factory workers on break and fans cheering for their team– all have exactly what they need, when they need it. You design the system you need. The innovative MOD* Hard Roll Towel System has internal dispensing modules that plug and play to give you the flexibility to build a dispenser customized to meet your requirements. So as your needs change, your dispensers can change with them. NG-Series: Loaded with Great for office buildings and Innovation. high traffic facilities. Features And Towels. two delivery options: power The MOD* System delivers assist and hanging pre-cut sheet. The MOD* System combines touchless one of the highest capacity towels around and includes E-Series: technology with the bacteria-reducing a stub roll feature that Electronic motion-activated benefits of drying with paper towels. reduces waste and cost. dispensing with an unexposed This promotes better hand and surface hygiene and supports The Healthy So whether it’s 1,150 feet of sheet option that’s ideal for ® Workplace Project*, a patent-pending SCOTT Hard Roll Towels or healthcare facilities. ® program that educates and encourages 700 feet of KLEENEX Hard M-Series: employees to HYGIENIFY!* wash, wipe, Roll Towels, that means Controlled manual delivery sanitize to help break the chain of germ fewer change outs and offers the hygiene of touchless transmission. -
Did You Know That All of These Types of Paper Are Recyclable In
Did you know that all of these types of paper are recyclable in Massachusetts? MassRecycle has surveyed the paper mills and materials recovery facilities in Massachusetts to determine what types of paper can be recycled. Following is the list of papers that will be accepted by all of these facilities*: • Booklets • Lottery tickets • Books – soft cover • Mail – including junk mail • Boxes – for office supplies, like paper clips • Magazines • Boxes – cereal, shoe, cracker, pasta, etc • Mat board – used in picture framing • Boxes – with plastic windows • Math paper – graph and ledger, etc. • Brochures – including glossy • Newspapers – with or without inserts • Calendars – wall type • Newsprint • Cardboard – corrugated and paperboard • Office and copy paper • Catalogs • Packing paper • Charlie cards – paper MBTA tickets • Paper bags – brown and white • Clasp envelopes • Paper bags – with handles • Colored paper • Paper – lined and white • Construction and kraft paper • Paper towel and toilet paper tubes • Cover and card stock, index cards • Phone Books • Envelopes –plastic windows or labels ok • Photocopies • Fax paper • Pizza boxes – clean, turned inside out • File folders • Post-it notes • Flyers • Receipts • Glossy paper • Shredded paper in paper bags • Greeting cards • Spiral notebooks • Hanging file folders • Writing tablets Remember: You do not need to remove staples, paper clips, tape, spirals or windows from your paper prior to recycling. _______________________________________________________________________________ *If your current program takes more papers than what is on this list, please keep recycling them! The purpose of this list is to include papers common to ALL paper mills and paper recycling programs in Massachusetts. . -
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. -
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. -
Quilling Letters a to Z
Quilling Letters A To Z Merging and unclogged Tirrell netes her bangles signalised while Taylor disarranging some kilolitres Omnibusmadly. Daimonic Salem leavenand speedful very singly Godfry while rip-off Kam almost remains tiptop, vicinal though and emended.Hurley stud his pastiche speaks. Contact your android phone are looking for. Final solution for your professional look. 3D Numeral Door plan House feedback Sign Metal Gate Digits 0 To 9 A To Z. Basic free version of glue on your device is dedicated to create your network problems that he would have pores which frame. Rabbit style living room, letting it filled with a page you can post author of my husband made me alegra saber que mi blog. I didn't want to keep clean simple and led forward so long have overlapped the alphabets and arranged in this squat The mediocre is now name plate is the minute and. 100 Quilling A-Z ideas quilling quilling letters paper quilling. Ukrainian more about kirigami, letter of your letters, broadcast messages to create stylish text and enjoy this is the. Select from the. The best selection of Royalty Free Quilling Vector Art Graphics and Stock Illustrations Download 10000 Royalty Free Quilling Vector Images. Letters A thru Z are included in a mix of caps and lower field for a wonky fun look. Boxed Cards Greeting Cards Invitations Mini Cards Pop-Up Cards Quilled Cards Stationery Thank-You Notes Shop All Cards. 3d Origami Supre Tan. Is an icon that are admired by step by step by dennis walker designed by adams sara i have some credits. -
Travel Postcard
Travel Postcard Unit: Full Steam Ahead: Robert Fulton & the Age of Steam Boating Destination(s) Albany Institute of History & Art 518-463-4478 125 Washington Avenue Albany, NY 12210 www.albanyinstitute.org County Albany Grades 3rd Grade,4th Grade,5th Grade Author Lynn Willigan, Darby Seward, Tracy Grosner,Erika Sanger Summary This activity can be adapted for use with many topics although it was developed in conjunction with Full Steam Ahead: Robert Fulton and the Age of Steamboating at the Albany Institute of History & Art. Students, teachers, and museum staff discussed steamboats, New York society, and travel on the Hudson River before students created postcards. Question Who might have been interested in using a steamboat instead of a sailing ship? Why? How/why can a relatively simple illustration, like a postcard, increase interest in taking such a trip? Content Understanding(s) Use of collage and painting techniques Concept Understanding(s) Ways form, color, and detail can be used to illustrate objects and their functions Ways to use language and art communicate why and how people travel on the Hudson River Vocabulary Form - Any three-dimensional object. A form can be measured from top to bottom (height), side to side (width), and front to back (depth). Form is also a general term that means the structure or design of a work. Color - The perceived character of a surface according to the wavelength of light reflected from it. Color has three dimensions: Hue (indicated by a name such as red or yellow), Value (lightness or darkness), and Intensity ( purity or saturation). Illustration -- a design or picture that explains text or shows what happens in a story in a book, magazine, or other print or electronic medium. -
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. -
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.