MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

9.11 A SQUARE IN FIVE EQUAL PARTS

Let ́s begin with a square of one unit side:

α α senα

2

1

x=PBsen =ABsen =

α= 180 − 2 β= 180 − 2 arctg 2

sen() 2 arctg 2 0. 4

2

1

x= = ;

5

1

0. 2

2

1

y= x= = (exact solution)

9.12 OTHER INEXACT FORM OF DIVISION

• Let C at a distance x from D, obtained according to Point 9.11.


• Fold H over C to produce G and F.


• In Point 9.11 it is

2

5

1

5

2

x=CD= 0. 4 = = ; recalling Corollary P, we shall have

7

4

2

7

2

1

2

5

2

= =

+

AF=

• Being similar ∆AFC and ∆DGC, it is:

GD

CD

AC

AF

= ;

GD

5

2

5

2

1

7

4

=

−

;

50

21

5 4 5

2 7 3

=

× ×

× ×

GD=

B

A B

C C

P

P

x x

y

= =

P

(^123)
4
5 6
7