MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

Piece E (five units)

Therefore, the five pieces obtained are:

The square A6; the isosceles right triangles B7 and C10; D13 and E12.

In the following figure also appear those pieces to justify the Pythagorean theorem.

Algebraically we can also see:

JP^2 =JI^2 +IP^2 ; ()JW+WP^2 =JI +IP

2 2

2 2

1

1

2

1

2 2

1













 = +











+ ;

8

1

1

8

1

1 + = +

5 C 67 8

10 9

12 11

A

A

B

B

C

C

D

D

E

E

F G H

IM

P N

J

W

K O

L

It can be seen in it that the

square over the hypotenuse has the

same area than the sum of those built

over the legs

It may be noted also that the

square over the great leg (one unit side)

is equal to the initial Fig.1. The rhom-

boid of the basic unit and the four fig-

ures B, C, D, E are shown now over-

lapped.

These, besides piece A are

shown after with their dimensions.