Origamics
Subtitle: Mathematical Explorations through Paper Folding
Contributors: Josefina C. Fonacier and Masami Isoda, editors and translators
Publisher: World Scientific
Published: 2008
Number of pages: 134
First sentence: Whenever an origami activity is brought up in the classroom the students show great interest and enthusiasm.
Table of contents: value: Introduction, v; value: Until the Publication of the English Edition, vii; value: Acknowledgements, ix; value: Preface for the English Edition, xi; value: . 1 A point Opens the Door to Origamics, 1; value: 1.1 Simple Questions About Origami, 1; value: 1.2 Constructing a Pythagorean Triangle, 2; value: 1.3 Dividing a Line Segment into Three Equal Parts Using no Tools, 5; value: 1.4 Extending Toward a Generalization, 8; value: . 2 New Folds Bring Out New Theorems, 11; value: 2.1 Trisecting a Line Segment Using Haga's Second Theorem Fold, 11; value: 2.2 The Position of Point F is Interesting, 14; value: 2.3 Some Findings Related to haga's Third Theorem Fold, 17; value: . 3 Extension of the Haga's Theorem to Silver Ratio Triangles, 21; value: 3.1 Mathematical Adventure by Folding a Copy Paper, 21; value: 3.2 Mysteries Revealed from Horizontal Folding of Copy Paper, 25; value: 3.3 Using Standard Copy Paper with Haga's Third Theorem, 30; value: . 4 X-Lines with Lots of Surprises, 33; value: 4.1 We Begin with an Arbitrary Point, 33; value: 4.2 Revelations Concerning the Points of Intersection, 35; value: 4.3 The Center of the Circumcircle!, 37; value: 4.4 How Does the Vertical Position of the Point of Intersection Vary?, 38; value: 4.5 Wonders Still Continue, 41; value: 4.6 Solving the Riddle of "1/2", 42; value: 4.7 Another Wonder, 43; value: . 5 "Intrasquares" and "Extrasquares", 45; value: 5.1 Do not Fold Exactly into Halves, 46; value: 5.2 What Kind of Polygons Can You Get?; value: 5.3 How do You Get a Triange or a Quadrilateral?, 48; value: 5.4 Now Making a Map, 49; value: 5.5 This is the "Scientific Method", 53; value: 5.6 Completing the Map, 53; value: 5.7 We Must Also Make the Map of the Outer Subdivision, 55; value: 5.8 Let Us Calculate Areas, 57; value: . 6 A Petal Pattern From Hexagons?, 59; value: 6.1 The Origamics Logo, 59; value: 6.2 Folding a Piece of Paper by Concentrating the Four Vertices at One Point, 60; value: 6.3 Remarks on Polygonal Figures of Type <i>n</i>, 63; value: 6.4 An Approach to the Problem Using Group Study, 64; value: 6.5 Reducing the Work of Paper Folding; One Eighth of the Square Will Do, 65; value: 6.6 Why Does the Petal pattern Appear?, 66; value: 6.7 What Are the Areas of the Regions?, 70; value: . 7 Heptagon Regions Exist?, 71; value: 7.1 Review of the Folding Procedure, 71; value: 7.2 A Heptagon Appears!, 73; value: 7.3 Experimenting with Rectangles with Different Ratios of Sides, 74; value: 7.4 Try a Rhombus, 76; value: . 8 A Wonder of Eleven Stars, 77; value: 8.1 Experimenting with Paper Folding, 77; value: 8.2 Discovering, 80; value: 8.3 Proof, 82; value: 8.4 More Revelations Regarding the Intersections of the Extensions of the Creases, 85; value: 8.5 Proof of the Observation on the Intersection Points of Extended Edge-to-Line Cdreases, 89; value: 8.6 The Joy of Discovering and the Excitement of Further Searching, 91; value: . 9 Where to Go and Whome to Meet, 93; value: 9.1 An Origamics Activity as a Game, 93; value: 9.2 A Scenario: A Princess and Three Knights?, 93; value: 9.3 The Rule: One Guest at a Time, 94; value: 9.4 Cases Where no Interview is Possible, 97; value: 9.5 Mapping the Neighborhood, 97; value: 9.6 A Flower Pattern of an Insect Pattern, 99; value: 9.7 A Different Rule: Group Meetings, 99; value: 9.8 Are There Areas Where a Particular Male can have Exclusive Meetings with the Female?, 101; value: 9.9 More Meetings through a "Hidden Door", 103; value: . 10 Inspiraration of Rectangular Paper, 107; value: 10.1 A Scenario: The Stern King of Origami Land, 107; value: 10.2 Begin with a Simpler Problem: How do Divide the Rectangle Horizontally and Vertically into 3 Equal Parts, 108; value: 10.3 A 5-parts Division Point; the Pendulum Idea Helps, 111; value: 10.4 A Method for Finding a 7-parts Division Point, 115; value: 10.5 The Investigation Continues: Try the Pendulum Idea on the 7-parts Division Method, 117; value: 10.6 The Search for 11-parts and 13-parts Division Points, 120; value: 10.7 Another Method for Finding 11-parts and 13-parts Division Points, 122; value: 10.8 Continue the Trend of Throught: 15-parts and 17-parts Division Points, 125; value: 10.9 Some Ideas related to the Rations for Equal-parts Division based on Similar Triangles, 130; value: 10.10 Toward More Division Parts, 134; value: 10.11 Generalizing to all Rectangles, 134