MATHEMATICS AND ORIGAMI

Mathematics and Origami

8.3 VARIOUS

8.3.1 HOMOTOMIC FIGURES

Din A Pseudo Din A right-angled isosceles ∆

If we divide successively by 2 their respective areas, the original proportion of figures is kept.

The ratio of similarity is 2 and therefore, the ratio of areas is 2. Of course, these divisions

may be made with conventional instruments, but also by folding.

8.3.2 AREA OF A TRIANGLE

Two areas like DEFG are equivalent to ABC, so:

area ABC = ×DEFG= DE×EF= × BC× AH= BC×AH

2

1

2

1

2

1

2 2 2

8.3.3 PYTHAGOREAN THEOREM

1 Isosceles right triangle.

The Tangram structure was already seen in solution 1 of Point 8.1.2. Let ́s take now two equal

tangram sets, one for the hypotenuse and the other to share by the two legs; it is evident that the

square built over the hypotenuse has equal area than the sum of the squares over the two legs. It

is also clear that this explanation is valid only for an isosceles right triangle.

1 1/ 2

2

2 2

(^11)
A
B HCDE
G F
D H E