How To Fold It

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? You can answer these questions and more through the mathematics of folding and unfolding. From this book, you will discover new and old mathematical theorems by folding paper and find out how to reason toward proofs. With the help of 200 color figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's Web site, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.

"The influential artist Hedi Kyle and renowned architecture graduate Ulla Warchol shows you how to create their unique designs using folding techniques. From creating flag books and fishbones, to blizzards and nesting boxes, you'll gain an invaluable insight into the work of two skilled artists with this fun read! With the help of their thorough instructions and simple illustrations, you'll be on your way to becoming a pro paper crafter in no time at all" – Sew magazine "A wonderful insight into the work of a truly skilled artist" – PaperCrafter The renowned and influential book artist Hedi Kyle shows you step–by–step how to create her unique designs using folding techniques in The Art of the Fold. Bookbinding and paper craft projects include flag books, blizzard books, the fishbone fold, and nesting boxes. Written by the doyenne of artists' books, Hedi Kyle, The Art of the Fold is a wonderful insight into the work of a truly skilled artist. Hedi will show you how to bind a book and fold paper to create over 35 of her cut–fold book designs. The book is beautifully illustrated with Hedi's finished works of art. An excerpt from the book: 'I can still remember the thrill I experienced when my first folded book structure emerged from my fingers – how eager I was to explore its possibilities and to share it with whoever was interested. The Flag Book, as I now call it, is a simple accordion and has interlocking pages oriented in opposite directions. Little did I know that this simple structure would have legs and be the catalyst for the next forty–plus years of thinking about and making books. The common perception of the book today is fairly straightforward: a series of pages organized around a spine and protected on either side by two covers. This format allows for easy access, storage and retrieval of information. Yet what happens when the book is stripped away of centuries of preconceptions and is allowed to reveal something else: playfulness, utility, invention? Expanding the notion of the book is what the structures in the following chapters of The Art of the Fold attempt to do. Exploring its tactile, sculptural form, primarily through folding methods, the book as a structural object is celebrated while content is considered in a new and unconventional way. My range in this medium has always been broad. In part this is due to my introduction to the world of bookbinding and some chance encounters. In the 1970s in New York City, the art and craft of hand bookbinding and papermaking were experiencing an unprecedented revival. I was fortunate to arrive in the city at just this moment. With an art–school background and an impulse to make things, I was naturally drawn to pursue this new opportunity. The Center for Book Arts, the famous forerunner of so many centers yet to come, was located in a small storefront just down the street from where I lived on the Lower East Side of Manhattan. Under the direction of founder Richard Minsky, it had a radical mission: to push concept, materials, printing and making of artist books in a new direction. When Richard dared me to teach at the Center one evening a week, I was hooked. My career as a book conservator and a book artist has now spanned over 45 years. As head conservator at the American Philosophical Society in Philadelphia, I've had the opportunity to handle some of the rarest volumes and manuscripts in the world. I have also dealt with decrepit books, torn maps and countless curiosities discovered in stacks and archives. All were endless sources for ideas and provided a springboard for a departure from tradition. Leading book–arts workshops around the world and a 25 year tenure teaching in the graduate program for Book Arts and Printmaking at the University of the Arts in Philadelphia have shown me, in retrospect, that the more I taught, t

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.

Many designers use folding techniques in their work to make three-dimensional forms from two-dimensional sheets of fabric, cardboard, plastic, metal, and many other materials. This unique book explains the key techniques of folding, such as pleated surfaces, curved folding, and crumpling. It has applications for architects, product designers, and jewelry and fashion designers An elegant, practical handbook, Folding for Designers explains over 70 techniques explained with clear step-by-step drawings, crease pattern drawings, and specially commissioned photography. All crease pattern drawings are available to view and download from the Laurence King website.

A boy awakens in the Afterlife, with a pocketful of vague memories, a key, a raven, and a mysterious atlas to guide him as he sets out to piece together what happened, and try to find his way home ... Twig is alone as a newly-made street kid after his dad goes missing. But when he meets Flea, a cheerful pickpocket, the pair become fast friends. Together, Twig and Flea raise themselves on the crime-ridden streets, taking what they need and giving the rest to the even-poorer. Life is good, as long as they have each other. But then Twig wakes up in the Afterlife with just a handful of memories from Earth and one big question ... how did he get there? Loyalty will be tested, and a cruel twist of fate will lead to an act of ultimate betrayal in this epic story that spans a city, a decade, and the divide of life and death itself. From the award-winning author of The Bone Sparrow.

In this funny, uncannily wise portrait of the dynamics of a sixth-grade class and of the greatness that sometimes comes in unlikely packages, Dwight, a loser, talks to his classmates via an origami finger puppet of Yoda. If that weren’t strange enough, the puppet is uncannily wise and prescient. Origami Yoda predicts the date of a pop quiz, guesses who stole the classroom Shakespeare bust, and saves a classmate from popularity-crushing embarrassment with some well-timed advice. Dwight’s classmate Tommy wonders how Yoda can be so smart when Dwight himself is so clueless. With contributions from his puzzled classmates, Tommy assembles this first case file in the blockbuster bestselling Origami Yoda series, written by Tom Angleberger, author of Star Wars: Return of the Jedi: Beware the Power of the Dark Side, and hailed by School Library Journal as “honest, funny, and immensely entertaining.” F&P Level: T F&P Genre: RF

Make decorative, simple do-it-yourself projects with this friendly guide to paper crafting. You and your family will love to spend hours making beautiful paper art, jewelry, and decorations with All Things Paper. This easy paper crafts book comes with simple-to-follow instructions and detailed photos that show you how to create colorful and impressive art objects to display at home—many of which have practical uses. It is a great book for experienced paper craft hobbyists looking for new ideas or for new folders who want to learn paper crafts from experts. Projects in this papercrafting book include: Candle Luminaries Citrus Slice Coasters Mysterious Stationery Box Everyday Tote Bag Silver Orb Pendant Fine Paper Yarn Necklace Wedding Cake Card Perfect Journey Journal And many more… All the projects in this book are designed by noted paper crafters like Benjamin John Coleman, Patricia Zapata, and Richela Fabian Morgan. They have all been creating amazing objects with paper for many years. Whether you're a beginner or have been paper crafting for many years, you're bound to find something you'll love in All Things Paper. Soon you will be on your way to creating your own designs and paper art.