MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

6. OBTENTION OF PARALLELOGRAMS

6.1 SQUARE FROM A RECTANGLE
Solution 1
Rectangle with sides in any given proportion. Square side results to be equal to the smaller
side of rectangle.

Solution 2

Square centered in rectangle. If the latter has b as base and a as height, the condition

2

b

a≥

must be fulfilled to enable construction.

6.2 SQUARE FROM ANOTHER SQUARE.

6.3 RHOMB FROM A RECTANGLE. Rhomb diagonals are equal to the sides of the rectangle.

6.4 RHOMB FROM A SQUARE, the rhomb being the sum of two equilateral triangles.
Observe that ∆(ABC) is a real equilateral triangle. To trisect an angle of 45º, see Point 8.2.2.2
hereinafter.

==

= = = =

=

=

1 2

3

4

5

6

1 2

3

4

1 2 B discard 3

12

discard

3

1

(^3) B 4
2
discard