Origamics : Mathematical Expolorations Through Paper Folding
by Haga, Kazuo; Fonacier, Josefina C.; Isoda, MasamiFormat: Hardcover
Pub. Date: 2008-09-11
Publisher(s): World Scientific Pub Co Inc
Other versions by this Author
List Price: $73.00
Rent Textbook
Select for Price
Rent Digital
$40.80
New Textbook
We're Sorry
Sold Out
Used Textbook
We're Sorry
Sold Out
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
"The art of origami, or paper folding, is carried out using a square piece of paper to obtain attractive figures of animals, flowers or other familiar figures. It is easy to see that origami has links with geometry. Creases and edges represent lines, intersecting creases and edges make angles, while the intersections themselves represent points. Because of its manipulative and experiential nature, origami could become an effective context for the learning and teaching of geometry." "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." "This book is written for mathematics educators and mathematics teachers; general readers."--BOOK JACKET.
Table of Contents
| Introduction | p. v |
| Until the Publication of the English Edition | p. vii |
| Acknowledgments | p. ix |
| Preface for the English Edition | p. xi |
| A Point Opens the Door to Origamics | p. 1 |
| Simple Questions About Origami | p. 1 |
| Constructing a Pythagorean Triangle | p. 2 |
| Dividing a Line Segment into Three Equal Parts Using no Tools | p. 5 |
| Extending Toward a Generalization | p. 8 |
| New Folds Bring Out New Theorems | p. 11 |
| Trisecting a Line Segment Using Haga's Second Theorem Fold | p. 11 |
| The Position of Point F is Interesting | p. 14 |
| Some Findings Related to Haga's Third Theorem Fold | p. 17 |
| Extension of the Haga's Theorems to Silver Ratio Rectangles | p. 21 |
| Mathematical Adventure by Folding a Copy Paper | p. 21 |
| Mysteries Revealed from Horizontal Folding of Copy Paper | p. 25 |
| Using Standard Copy Paper with Haga's Third Theorem | p. 30 |
| X-Lines with Lots of Surprises | p. 33 |
| We Begin with an Arbitrary Point | p. 33 |
| Revelations Concerning the Points of Intersection | p. 35 |
| The Center of the Circumcircle! | p. 37 |
| How Does the Vertical Position of the Point of Intersection Vary? | p. 38 |
| Wonders Still Continue | p. 41 |
| Solving the Riddle of "1/2" | p. 42 |
| Another Wonder | p. 43 |
| "Intrasquares" and "Extrasquares" | p. 45 |
| Do Not Fold Exactly into Halves | p. 46 |
| What Kind of Polygons Can You Get? | p. 46 |
| How do You Get a Triangle or a Quadrilateral? | p. 48 |
| Now to Making a Map | p. 49 |
| This is the "Scientific Method" | p. 53 |
| Completing the Map | p. 53 |
| We Must Also Make the Map of the Outer Subdivision | p. 55 |
| Let Us Calculate Areas | p. 57 |
| A Petal Pattern from Hexagons? | p. 59 |
| The Origamics Logo | p. 59 |
| Folding a Piece of Paper by Concentrating the Four Vertices at One Point | p. 60 |
| Remarks on Polygonal Figures of Type n | p. 63 |
| An Approach to the Problem Using Group Study | p. 64 |
| Reducing the Work of Paper Folding; One Eighth of the Square Will Do | p. 65 |
| Why Does the Petal Pattern Appear? | p. 66 |
| What Are the Areas of the Regions? | p. 70 |
| Heptagon Regions Exist? | p. 71 |
| Review of the Folding Procedure | p. 71 |
| A Heptagon Appears! | p. 73 |
| Experimenting with Rectangles with Different Ratios of Sides | p. 74 |
| Try a Rhombus | p. 76 |
| A Wonder of Eleven Stars | p. 77 |
| Experimenting with Paper Folding | p. 77 |
| Discovering | p. 80 |
| Proof | p. 82 |
| More Revelations Regarding the Intersections of the Extensions of the Creases | p. 85 |
| Proof of the Observation on the Intersection Points of Extended Edge-to-Line Creases | p. 89 |
| The Joy of Discovering and the Excitement of Further Searching | p. 91 |
| Where to go and Whom to Meet | p. 93 |
| An Origamics Activity as a Game | p. 93 |
| A Scenario: A Princess and Three Knights? | p. 93 |
| The Rule: One Guest at a Time | p. 94 |
| Cases Where no Interview is Possible | p. 97 |
| Mapping the Neighborhood | p. 97 |
| A Flower Pattern or an Insect Pattern | p. 99 |
| A Different Rule: Group Meetings | p. 99 |
| Are There Areas Where a Particular Male can have Exclusive Meetings with the Female? | p. 101 |
| More Meetings through a "Hidden Door" | p. 103 |
| Inspiraration of Rectangular Paper | p. 107 |
| A Scenario: The Stern King of Origami Land | p. 107 |
| Begin with a Simpler Problem: How to Divide the Rectangle Horizontally and Vertically into 3 Equal Parts | p. 108 |
| A 5-parts Division Point; the Pendulum Idea Helps | p. 111 |
| A Method for Finding a 7-parts Division Point | p. 115 |
| The Investigation Continues: Try the Pendulum Idea on the 7-parts Division Method | p. 117 |
| The Search for 11-parts and 13-parts Division Points | p. 120 |
| Another Method for Finding 11-parts and 13-parts Division Points | p. 122 |
| Continue the Trend of Thought: 15-parts and 17-parts Division Points | p. 125 |
| Some Ideas related to the Ratios for Equal-parts Division based on Similar Triangles | p. 130 |
| Towards More Division Parts | p. 134 |
| Generalizing to all Rectangles | p. 134 |
| Table of Contents provided by Ingram. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.