A History of Folding in Mathematics PDF Download
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Author: Michael Friedman
Publisher: Birkhäuser
ISBN: 3319724878
Category : Mathematics
Languages : en
Pages : 430
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Book Description
While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
Author: Michael Friedman
Publisher: Birkhäuser
ISBN: 3319724878
Category : Mathematics
Languages : en
Pages : 430
Get Book Here
Book Description
While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
Author: Thomas C. Hull
Publisher: Cambridge University Press
ISBN: 1108478727
Category : Art
Languages : en
Pages : 343
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Book Description
Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It is an essential reference for researchers of origami mathematics and applications in physics, engineering, and design. Educators, students, and enthusiasts will also enjoy this fascinating account of the mathematics of folding.
Author: David Mitchell
Publisher: Tarquin Group
ISBN: 9781911093169
Category : Crafts & Hobbies
Languages : en
Pages : 0
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Book Description
Origami is the art of paper folding without the use of either scissors or glue. 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. He has gathered together a most impressive collection which will amaze and interest mathematics teachers and other admirers of pure geometrical forms. This new second edition extends the selection massively and has been split into two volumes - see contents.
Author: Joseph O'Rourke
Publisher: Cambridge University Press
ISBN: 9780521767354
Category : Mathematics
Languages : en
Pages : 192
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Book Description
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.
Author: Alton T. Olson
Publisher: National Council of Teachers of
ISBN: 9780873530767
Category : Education
Languages : en
Pages : 0
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Book Description
Paper folding not only simplifies the learning of mathematics it also builds an experiential base necessary for further learning. The exercises in this publication, appropriate at various grade levels, lead students to discover and demonstrate such mathematical relationships as reflections, transformations and symmetry.
Author: Erik D. Demaine
Publisher: Cambridge University Press
ISBN: 1107394090
Category : Computers
Languages : en
Pages : 388
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Book Description
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.
Author: Karen Latchana Kenney
Publisher: Millbrook Press
ISBN: 1728411556
Category : Young Adult Nonfiction
Languages : en
Pages : 109
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Book Description
Space probes, self-assembling robots, crash-absorbing cars, and designer proteins all have one thing in common: their use of folding technologies. To develop these technologies, engineers are taking inspiration from an unusual source—origami, the ancient art of paper folding. Examine origami's origins, how it intersects with mathematics, and how it became a tool to solve some of the most complicated challenges in engineering, architecture, technology, and medicine today. Plus, get a close-up look at these technologies with two augmented reality images included in the book!
![Geometrical Exercises in Paper Folding. [1893] PDF](https://books.google.com/books/content/images/frontcover/8zxPswEACAAJ?fife=w80-h100)
Author: T. Sundara Rao
Publisher: Trieste Publishing
ISBN: 9780649592555
Category : History
Languages : en
Pages : 138
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Book Description
Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.
Author: Jaime B Weaver
Publisher: Independently Published
ISBN:
Category : Crafts & Hobbies
Languages : en
Pages : 0
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Book Description
Mathematical Origami: The Art and Science of Geometric Folding Unlock the secrets of origami and mathematics with Mathematical Origami: The Art and Science of Geometric Folding. This comprehensive guide takes you on an extraordinary journey through the world of origami, blending the precision of mathematics with the beauty of paper folding. Whether you're a seasoned folder, a math enthusiast, or a curious beginner, this book offers a unique perspective on the art of creating intricate geometric shapes through origami. Discover the Beauty of Mathematical Principles in Origami Mathematical origami goes beyond traditional paper folding by incorporating geometric principles and mathematical concepts. This book delves into the fascinating relationship between origami and mathematics, providing a deep understanding of how mathematical principles can be applied to create stunning and complex models. From basic geometric shapes to intricate polyhedra, each project is designed to enhance your skills and appreciation for the mathematical foundation of origami. What You'll Learn: Fundamental Geometric Concepts: Master the essential geometric principles that form the backbone of mathematical origami, including symmetry, angles, and proportions. Step-by-Step Instructions: Follow detailed, easy-to-understand instructions for creating a variety of geometric shapes, from simple triangles and squares to complex structures like the cuboctahedron and snub cube. Historical Insights: Explore the rich history and origins of origami, tracing its evolution from a traditional Japanese art form to a modern mathematical discipline. Practical Applications: Discover how mathematical origami is used in various fields, such as engineering, architecture, and technology, to solve real-world problems. Innovative Techniques: Learn advanced folding techniques and tips for creating precise, elegant models that showcase the beauty of mathematical design. Features: Illustrated Guides: Hundreds of high-quality illustrations and diagrams to guide you through each step of the folding process. Expert Tips: Insights and tips from renowned origami artists and mathematicians to help you refine your technique and achieve professional results. Inspirational Gallery: A stunning gallery of completed models to inspire your creativity and showcase the possibilities of mathematical origami. Who Should Read This Book? Origami Enthusiasts: Expand your repertoire with new, mathematically inspired models. Math Lovers: Explore the practical application of geometric concepts in a creative and hands-on way. Educators: Use this book as a resource to teach students about the intersection of art and mathematics. Hobbyists: Enjoy a relaxing and intellectually stimulating hobby that combines the precision of mathematics with the art of paper folding. Mathematical Origami: The Art and Science of Geometric Folding is more than just a craft book-it's an exploration of the harmony between mathematics and art. Whether you're folding for fun, education, or artistic expression, this book will guide you through the mesmerizing world of mathematical origami, where paper and geometry come together in perfect symmetry. Grab your copy today and start your journey into the mathematical wonders of origami
Author: Michael Friedman
Publisher: transcript Verlag
ISBN: 3839434041
Category : Philosophy
Languages : en
Pages : 243
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Book Description
It is only recently, with the increasing interest in origami and folding in natural sciences and the humanities, that the fold as a new conception in a whole range of disciplines has begun to be conceived in a broader way. Folding as a material and structural process offers a new methodology to think about the close relationship of matter, form and code. It henceforth crosses out old dichotomies, such as the organic and the inorganic or nature and technology, and blurs the boundaries between experimental, conceptual and historical approaches. This anthology aims to unfold this new interdisciplinary field and its disciplinary impact, ranging from materials science, biology, architecture, and mathematics to literature and philosophy.
