9780806974200

This intriguing mixture of art and geometry will excite both your creativity and your curiosity. Out from under your fingers will come strikingly exquisite forms: wish on your own handmade shooting star, all silvery, golden, or fiery red; "grow" pretty pink paper cherry blossoms (symbol of Japan, home of origami), and build pyramids, cubic modules, and other dimensional figures.

Preface

5

(1)

What is origami?

5

(1)

Origami symbols

6

(1)

Paper

7

(1)

The link between esthetics and geometry

8

(1)

Dividing Areas

9

(22)

Dividing areas in half

10

(3)

Spiral shape

11

(2)

A monument to Froebel

13

(1)

Dividing angles in half

14

(2)

Roulette

14

(1)

Grass

15

(1)

Crow

15

(1)

Dividing angles in thirds

16

(6)

Star of David

16

(2)

Regular hexagon

18

(1)

Vase

19

(1)

Regular 12-sided polygon

20

(1)

Twelve-winged spinning top

21

(1)

Dividing segments into parts

22

(4)

Division by iteration

22

(2)

Shooting Star

24

(2)

Regular Octagon

26

(2)

UFO

26

(2)

Regular Pentagon

28

(2)

American Method

28

(1)

Japanese method

28

(1)

Monkiri

29

(1)

Characteristics of the regular pentagon

30

(1)

Drawing template for the regular pentagon

30

(1)

Fun with Geometry

31

(19)

The golden rectangle

31

(1)

The impossible becomes possible

32

(2)

Another way to fold a regular pentagon

32

(2)

Compass folding

34

(2)

Equilateral triangle and square

35

(1)

Regular pentagon

35

(1)

Going farther

36

(2)

Regular hexagon

36

(1)

Regular octagon

36

(1)

Regular heptagonal (7-sided) pyramid

37

(1)

Regular heptagon

37

(1)

The answer lies in between

38

(2)

More ``nonconstructible'' shapes

40

(2)

Regular 16-sided polygon

40

(1)

Regular 17-sided polygon

40

(1)

Regular 18-sided polygon

41

(1)

Regular 24-sided to n-sided polygon

41

(1)

Two theorems and their proofs

42

(2)

Dividing a square in half: 20 shapes

44

(2)

The Super Tangram

46

(2)

Origami and tangrams

48

(2)

Original tangram

48

(1)

Row's tangram

48

(2)

Three-Dimensional Objects

50

(14)

Boxes

50

(2)

Nesting boxes

51

(1)

The cube and some variations

52

(2)

Regular polyhedrons

54

(2)

Cube made of surface modules

54

(1)

The five Platonic solids (regular polyhedrons)

55

(1)

Three basic elements of polyhedrons

56

(5)

Cube made of corner modules

56

(2)

Cube made of edge modules

58

(1)

Cube (hexahedron)

58

(1)

Tetrahedron, octahedron, and icosahedron from 30° modules

59

(1)

Dodecahedron from 54° modules

60

(1)

The Platonic solids: Five good friends

61

(3)

More edge modules

62

(1)

The octahedron: Five variations

63

(1)

Afterword

64

(1)

Index

64

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Amazing Origami

Amazing Origami

0806974206

Summary

Table of Contents

Supplemental Materials