Mathematics and Origami

9 DIVISION IN EQUAL PARTS

9.1 EVEN PARTS OF A PERIGON

Begin with an irregular piece of paper to divide the 360º of the plane in 2 n equal parts:

n = 1, straight angle.

n = 2, right angles (perpendicular rays)

n = 3, 45º angles.

n = 4, 16 angles measuring 22º 30 ́ each.

9.2 A SQUARE IN TWO PARTS OF EQUAL AREA

9.3 THE RIGHT ANGLE OF A SQUARE IN THREE EQUAL PARTS

The angle A is divided in three equal parts for:

∆ABC is equilateral (B lies on the perpendicular bisector of AC and AB = AC)

hence ang BAC = 60º ; ang DAB = 30º

ang BAE = ang EAC (symmetry) = 30º

(^1234)
5
0º
22º 30 ́
90º 67º 30 ́ 45º
112º 30 ́
157º 30 ́
180º
225º
292º 30 ́
315º
337º 30 ́
360º
135º
202º 30 ́
247º 30 ́
270º
6

=
Any segment AB passing through the center O fulfils
the requirement.
AB determines two right trapeziums having all their
angles, respectively congruent (ang A = ang B as
alternate interior), sides CD = EF, and common side
AB; hence, both areas are equal.
E F
B
C D
A
O