MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

Being n the number of folds, and generalising, we have:

2

3

Limx n nx

2

3

2

1

2

1

= − +

Lim

3

1

2

1

3

2

x= × =

n→∞ as wanted.
9.17.2 DIVISION IN 5 EQUAL PARTS

Exaggerating the position of starting point W, we have placed it at midpoint of AB.

From A we fold, first up to W and then, up to Z1. So we get C:

AB = 1 ; AC = x

Fold B successively over C (getting Z 2 ), and over Z 2 getting D. It will be:

4

1 x

BD

−

=

Similarly we get AC ́:

()x x

BD

AC

16

1

16

1

4

1

1

4

1

1

4

1

4

1

́ = − +











= − −

−

=

Here BD ́ is obtained; its value is:

x x

AC

BD

64

1

64

1

16

1

4

1

16

1

16

1

4

1

1

4

1

4

1 ́

́ = − + −























= − − +

−

=

The two following folds from A give:























AC = −BD = − − + − x

64

1

64

1

16

1

4

1

1

4

1

4

1 ́

́ ́

1

A C Z

W

1 B

2

A C Z D B

2

3

A C ́ Z 3 D B

4

A C ́ Z 4 D ́ B