MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

9.4 A SQUARE IN THREE EQUAL PARTS (five exact solutions)
Solution 1

Solution 2

Solution 3

Square with side one unit.

∆ABC and ∆DEC, are similar.

AB BC

4

3

=

A

E C

B

D

2

1

=

=

=

=

=

=

A

EC

H

G

1

2

3

4

F

1- Divide ang A in three equal parts to Point 9.3.

We get point E.

2- Fold A over E. Valleyfold FG is the symmetry

axle.

• ∆AFG = ∆EFG because of symmetry.


• Being ang FAG = 30º, the three angles in G
  (HGF, FGE, EGC) measure 60º.


• ∆EGC is “half an equilateral triangle”, hence

GC EG AG

2

1

2

1

= =

3- AC → AC; G → G

4- G → A: AH HG GC AC

3

1

= = =

(^12)
3
4
= A = B
C
D
P
1/ 3
2 / 3
Let a square with side one unit.
∆ABD and PCD are similar.
As AB BD
2
1
= , it will be PC CB CD
2
1
= =
As BC+CD= 1 , it is
3
1
BC= and
3
2
CD=