Origamics

The following sections are included:

• Introduction

• Until the Publication of the English Edition

• Acknowledgments

• Preface for the English Edition

• Contents

The following sections are included:

• Simple Questions About Origami

• Constructing a Pythagorean Triangle

• Dividing a Line Segment into Three Equal Parts Using no Tools

• Extending Toward a Generalization

The following sections are included:

• Trisecting a Line Segment Using Haga's Second Theorem Fold

• The Position of Point F is Interesting

• Some Findings Related to Haga's Third Theorem Fold

The following sections are included:

• Mathematical Adventure by Folding a Copy Paper

• Mysteries Revealed from Horizontal Folding of Copy Paper

• Using Standard Copy Paper with Haga's Third Theorem

The following sections are included:

• We Begin with an Arbitrary Point

• Revelations Concerning the Points of Intersection .

• The Center of the Circumcircle!

• How Does the Vertical Position of the Point of Intersection Vary

• Wonders Still Continue

• Solving the Riddle of “”

• Another Wonder

The following sections are included:

• Do Not Fold Exactly into Halves

• What Kind of Polygons Can You Get?

• How do You Get a Triangle or a Quadrilateral?

• Now to Making a Map .

• This is the "Scientific Method"

• Completing the Map

• We Must Also Make the Map of the Outer Subdivision

• Let Us Calculate Areas

The following sections are included:

• The Origamics Logo

• Folding a Piece of Paper by Concentrating the Four Vertices at One Point

• Remarks on Polygonal Figures of Type n

• An Approach to the Problem Using Group Study

• Reducing the Work of Paper Folding; One Eighth of the Square Will Do

• Why Does the Petal Pattern Appear?

• What Are the Areas of the Regions?

The following sections are included:

• Review of the Folding Procedure

• A Heptagon Appears!

• Experimenting with Rectangles with Different Ratios of Sides

• Try a Rhombus

The following sections are included:

• Experimenting with Paper Folding

• Discovering

• Proof

• More Revelations Regarding the Intersections of the Extensions of the Creases

• Proof of the Observation on the Intersection Points of Extended Edge-to-Line Creases

• The Joy of Discovering and the Excitement of Further Searching

The following sections are included:

• An Origamics Activity as a Game

• A Scenario: A Princess and Three Knights?

• The Rule: One Guest at a Time

• Cases Where no Interview is Possible

• Mapping the Neighborhood

• A Flower Pattern or an Insect Pattern

• A Different Rule: Group Meetings

• Are There Areas Where a Particular Male can have Exclusive Meetings with the Female?

• More Meetings through a “Hidden Door ”

The following sections are included:

• A Scenario: The Stern King of Origami Land

• Begin with a Simpler Problem: How to Divide the Rectangle Horizontally and Vertically into 3 Equal Parts

• A 5-parts Division Point; the Pendulum Idea Helps

• A Method for Finding a 7-parts Division Point

• The Investigation Continues: Try the Pendulum Idea on the 7-parts Division Method

• The Search for 11-parts and 13-parts Division Points

• Another Method for Finding 11-parts and 13-parts Division Points

• Continue the Trend of Thought: 15-parts and 17-parts Division Points

• Some Ideas related to the Ratios for Equal-parts Division based on Similar Triangles

• Towards More Division Parts

• Generalizing to all Rectangles