Origami and Math

Presents instructions for folding thirty-nine origami models, from geometrical figures to an elephant--each made from a single sheet of paper--that emphasize the mathematical principles behind each design.

Origami and Math

Author: John Montroll

Publisher: Courier Corporation

ISBN: 0486488861

Page: 120

View: 701

Presents instructions for folding thirty-nine origami models, from geometrical figures to an elephant--each made from a single sheet of paper--that emphasize the mathematical principles behind each design.

Mathematical Origami

Each of the beautiful and fundamental mathematical shapes described in this book is achieved by folding sheets of standard A4 paper. It is remarkable what can been done and David Mitchell gives clear step by step instructions for each.

Mathematical Origami

Author: David Mitchell

Publisher: Tarquin Group

ISBN: 9781911093039

Page: 148

View: 927

This book shows the reader how to make a range of robust polyhedra from ordinary printer paper using a technique known as modular origami. Modular origami designs are made by first folding several, or sometimes many, sheets of paper into simple individual modules and then by putting these modules together, normally without the help of any kind of adhesive, to create a finished polyhedral form. Modular origami design has moved on since the hugely popular first edition which has been expanded and revised to present both a wider range of designs, and to introduce new designs which are more robust and offer more potential for mathematical adventures. Ideal for the classroom and fun for any enthusiast of either origami, or mathematics. David Mitchell gives clear step-by-step instructions.

Origami Design Secrets

Containing step-by-step instructions for 26 models, this book is not just an origami cookbook or list of instructions—it introduces the fundamental building blocks of origami, building up to advanced methods such as the combination of ...

Origami Design Secrets

Author: Robert J. Lang

Publisher: CRC Press

ISBN: 1568814364

Page: 770

View: 455

The magnum opus of one of the world’s leading origami artists, the second edition of Origami Design Secrets reveals the underlying concepts of origami and how to create original origami designs. Containing step-by-step instructions for 26 models, this book is not just an origami cookbook or list of instructions—it introduces the fundamental building blocks of origami, building up to advanced methods such as the combination of uniaxial bases, the circle/river method, and tree theory. With corrections and improved illustrations, this new expanded edition also covers uniaxial box pleating, introduces the new design technique of hex pleating, and describes methods of generalizing polygon packing to arbitrary angles. With coverage spanning the foundations of origami construction and advanced methods using both paper and pencil and custom-built free software, Origami Design Secrets helps readers cultivate the intuition and skills necessary to develop their own designs. It takes them beyond merely following a recipe to crafting a work of art.

Twists Tilings and Tessellations

It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.

Twists  Tilings  and Tessellations

Author: Robert J. Lang

Publisher: CRC Press

ISBN: 148226241X

Page: 756

View: 907

Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.

Project Origami

Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics.

Project Origami

Author: Thomas Hull

Publisher: CRC Press

ISBN: 1466568097

Page: 364

View: 594

Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. With over 100 new pages

Origami 5

This book begins with a section on origami history, art, and design.

Origami 5

Author: Patsy Wang-Iverson

Publisher: CRC Press

ISBN: 1568817142

Page: 660

View: 800

Origami5 continues in the excellent tradition of its four previous incarnations, documenting work presented at an extraordinary series of meetings that explored the connections between origami, mathematics, science, technology, education, and other academic fields. The fifth such meeting, 5OSME (July 13–17, 2010, Singapore Management University) followed the precedent previous meetings to explore the interdisciplinary connections between origami and the real world. This book begins with a section on origami history, art, and design. It is followed by sections on origami in education and origami science, engineering, and technology, and culminates with a section on origami mathematics—the pairing that inspired the original meeting. Within this one volume, you will find a broad selection of historical information, artists’ descriptions of their processes, various perspectives and approaches to the use of origami in education, mathematical tools for origami design, applications of folding in engineering and technology, as well as original and cutting-edge research on the mathematical underpinnings of origami.

More Origami With Explanations Fun With Folding And Math

Today people do origami, create new models, share their work, and discover mathematical principles. This book continues the approach of Origami with Explanations; but is independent, with basic instructions repeated.

More Origami With Explanations  Fun With Folding And Math

Author: Jeanine Meyer

Publisher: World Scientific

ISBN: 9811219486

Page: 276

View: 279

Find out Origami with Explanations: Fun with Folding and MathOrigami, paper folding, originated hundreds of years ago in China and Japan, with independent discovery across the world. Today people do origami, create new models, share their work, and discover mathematical principles. This book continues the approach of Origami with Explanations; but is independent, with basic instructions repeated. Carefully written instructions, using photos and diagrams, will turn you into a successful folder and stimulate your own creativity. The models in this book include action models, money folds, beautiful and useful containers, and modular origami. Mathematics topics touched on include improving estimates, tessellations, mathematical induction, flat-foldability, and fold-and-cut. The Explanations section provide insight into the origami and introduce or re-introduce you to basic and advanced subjects in mathematics.

Mathematical Theory of Origami Constructions and Numbers

"The New York Journal of Mathematics" presents the full text of an article entitled "A Mathematical Theory of Origami Constructions and Numbers," by Roger C. Alperin and published in the journal July 2000.

Mathematical Theory of Origami Constructions and Numbers

Author:

Publisher:

ISBN:

Page:

View: 533

"The New York Journal of Mathematics" presents the full text of an article entitled "A Mathematical Theory of Origami Constructions and Numbers," by Roger C. Alperin and published in the journal July 2000. The article discusses a set of axioms for mathematical origami and numbers. The fields of Thalian, Pythagorean, Euclidean, and origami numbers are obtained using this set of axioms.

Applications Practical Conceptualization Mathematics fruitful Innovation

Mathematical. Origami. and. Origami. Engineering. Sachiko Ishida and Ichiro
Hagiwara Abstract This paper introduces the basics of origami-based foldable
structure designs and gives examples of practical applications using these
structures ...

Applications   Practical Conceptualization   Mathematics   fruitful Innovation

Author: Robert S. Anderssen

Publisher: Springer

ISBN: 4431553428

Page: 278

View: 758

This book is a collection of papers presented at the conference “Forum Math-for-Industry 2014” for which the unifying theme was “Applications + Practical Conceptualization + Mathematics = fruitful Innovation” in October 2014. This epigram encapsulates the dynamics of the process that takes an application through to an innovation. Industrial mathematics can be viewed as the causal engine that implements the epigram by taking an Application such as input and convolving it with a mixture of Practical Conceptualization and Mathematics to generate a fruitful Innovation as output. The book illustrates various aspects of the two-way interaction between applications and their association highlighting how practical conceptualization assists with the linking of the question that encapsulates the current application to the relevant mathematics. The contents of this volume address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

Origami 4

sion possible within origami. But there are absolute limits on the physical
structures foldable with origami. Those limits are defined by the underlying
mathematics of origami. By exploring, elucidating, and describing those
mathematical laws, ...

Origami 4

Author: Robert J. Lang

Publisher: CRC Press

ISBN: 1439871043

Page: 572

View: 474

The connections between origami, mathematics, science, technology, and education have been a topic of considerable interest now for several decades. While many individuals have happened upon discrete connections among these fields during the twentieth century, the field really took off when previously isolated individuals began to make stronger connections with each other through a series of conferences exploring the links between origami and "the outside world." The Fourth International Meeting on Origami in Science, Mathematics, and Education (4OSME), held in September, 2006, at the California Institute of Technology in Pasadena, California, brought together an unprecedented number of researchers presenting on topics ranging from mathematics, to technology, to educational uses of origami, to fine art, and to computer programs for the design of origami. Selected papers based on talks presented at that conference make up the book you hold in your hands.

What s Happening in the Mathematical Sciences Volume 10

Origami engineering uses new materials, breaks size barriers (creating objects
that are scarcely larger than a mote of dust), and places a new emphasis on
functionality rather than aesthetics. It also poses some new mathematical
challenges.

What s Happening in the Mathematical Sciences  Volume 10

Author: Dana Mackenzie

Publisher: American Mathematical Soc.

ISBN: 1470422042

Page: 111

View: 161

What's Happening in the Mathematical Sciences is a collection of articles highlighting some of the most recent developments in mathematics. These include important achievements in pure mathematics, as well as its fascinating applications. On the pure mathematics side, "Prime Clusters and Gaps: Out-Experting the Experts" talks about new insights into the distribution of prime numbers, the perpetual source of new problems, and new results. Recently, several mathematicians (including Yitang Zhang and James Maynard) significantly improved our knowledge of the distribution of prime numbers. Advances in the so-called Kadison-Singer problem and its applications in signal processing algorithms used to analyze and synthesize signals are described in "The Kadison-Singer Problem: A Fine Balance". "Quod Erat Demonstrandum" presents two examples of perseverance in mathematicians' pursuit of truth using, in particular, computers to verify their arguments. And "Following in Sherlock Holmes' Bike Tracks" shows how an episode in one of Sir Arthur Conan Doyle's stories about Sherlock Holmes naturally led to very interesting problems and results in the theory of completely integrable systems. On the applied side, "Climate Past, Present, and Future" shows the importance of mathematics in the study of climate change and global warming phenomena. Mathematical models help researchers to understand the past, present, and future changes of climate, and to analyze their consequences. "The Truth Shall Set Your Fee" talks about algorithms of information exchange in cyberspace. Economists have known for a long time that trust is a cornerstone of commerce, and this becomes even more important nowadays when a lot of transactions, big and small, are done over the Internet. Recent efforts of theoretical computer scientists led to the development of so-called "rational protocols" for information exchange, where the parties in the information exchange process find that lies do not pay off. Over the last 100 years many professional mathematicians and devoted amateurs contributed to the problem of finding polygons that can tile the plane, e.g., used as floor tiles in large rooms and walls. Despite all of these efforts, the search is not yet complete, as the very recent discovery of a new plane-tiling pentagon shows in "A Pentagonal Search Pays Off". Mathematics can benefit coaches and players in some of the most popular team sports as shown in "The Brave New World of Sports Analytics". The increased ability to collect and process statistics, big data, or "analytics" has completely changed the world of sports analytics. The use of modern methods of statistical modeling allows coaches and players to create much more detailed game plans as well as create many new ways of measuring a player's value. Finally, "Origami: Unfolding the Future" talks about the ancient Japanese paper-folding art and origami's unexpected connections to a variety of areas including mathematics, technology, and education.

Ornamental Origami

[Hul02] Thomas Hull, ed., Origami 3: Third International Meeting of Origami
Science, Mathematics, and Education, A K Peters, Ltd., 2002. ◈ [Hul06] Thomas
Hull, Project Origami: Activities for Exploring Mathematics, A K Peters, Ltd., 2006.

Ornamental Origami

Author: Meenakshi Mukerji

Publisher: CRC Press

ISBN: 1000179923

Page: 154

View: 824

This book is a great resource for people who enjoy polyhedra, symmetry, geometry, mathematics and origami. The types of models presented are similar in nature to the models in Mukerji's Marvelous Modular Origami, but some of the chapters are more advanced and all of the designs are new. The reader can learn about polyhedra while making these models and is left with the ability to design one's own models. Step-by-step folding instructions for over 40 models are presented. Although the book is for intermediate folders, beginners are encouraged to try because origami basics are explained. The diagrams are easy to follow and each model is accompanied by breathtaking finished model photographs.

Genuine Japanese Origami

This is the first publicationoutside Japan of these original figures, offering intermediate leveland serious origamists an intriguingblend of art and science.Dover (2012) English translation andnew selection of models from GenuineOrigami ...

Genuine Japanese Origami

Author: Jun Maekawa

Publisher: Courier Corporation

ISBN: 0486483355

Page: 128

View: 150

Unique and wildly creative, this mathematical and geometricapproach to origami contains 40 models of cubes, towers, andgeometric shapes as well as puzzles and models of everyday items— all folded from rectangular paper. This is the first publicationoutside Japan of these original figures, offering intermediate leveland serious origamists an intriguingblend of art and science.Dover (2012) English translation andnew selection of models from GenuineOrigami Ã2, Japan Publications TradingCo. Ltd., Japan, 2009.

How to Fold It

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.

How to Fold It

Author: Joseph O’Rourke

Publisher: Cambridge University Press

ISBN: 1139498541

Page:

View: 259

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.

Geometric Origami

This book contains a collection of geometric origami models made from folding strips of paper using a special technique.

Geometric Origami

Author: Garret Rodick

Publisher: Independently Published

ISBN:

Page: 116

View: 319

The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability, and the use of paper folds to solve up-to cubic mathematical equations. This book contains a collection of geometric origami models made from folding strips of paper using a special technique. You'll learn how to make paper-strip models based on the Platonic solids - polyhedra made of only one shape, as well as the Archimedean solids - polyhedra made of two or more shapes.

Origametry

This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design.

Origametry

Author: Thomas C. Hull

Publisher: Cambridge University Press

ISBN: 1108805159

Page:

View: 543

Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.

Origamics

In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result.

Origamics

Author: Kazuo Haga

Publisher: World Scientific

ISBN: 9812834915

Page: 152

View: 304

In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing.

Mathematical Knowledge Management

What are new in our study are the computational origami construction and
streamlined automated proof . Seemingly different kinds of knowledge in
mathematical sciences , i . e . origami and automated theorem proving , are
integrated in a ...

Mathematical Knowledge Management

Author:

Publisher:

ISBN:

Page:

View: 178

Origami Eleusis and the Soma Cube

The second of fifteen updated editions of the collected Mathematical Games of Martin Gardner, king of recreational mathematics.

Origami  Eleusis  and the Soma Cube

Author: Martin Gardner

Publisher: Cambridge University Press

ISBN: 0521756103

Page: 234

View: 610

Martin Gardner continues to delight. He introduces readers to the Generalized Ham Sandwich Theorem, origami, digital roots, magic squares, the mathematics of cooling coffee, the induction game of Eleusis, Dudeney puzzles, the maze at Hampton Court Palace, and many more mathematical puzzles and principles. Origami, Eleusis, and the Soma Cube is the second volume in Martin Gardner's New Mathematical Library, based on his enormously popular Scientific American columns. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.