Jesús de la Peña Hernández

2 Escalen right triangle

Tangramlike demonstration of Fig.1 is correct when b c

3

4

= (a c

3

5

= ). It shows that the width

of the central strip in square on a has equal area than the square on c.

Fig. 2 (any right triangle) shows the difficulty to divide the square on c in pieces in such a

manner to cover the central strip of square on a. Been CD = b, we can get the strip ́s width h:

2 2

2 2

(^22)
a b h
c

• = ;
  a b
  c
  h


• 
  

  ×

  
  

  2 2
  On the other hand, the value of h in the strip over a is:
  h= 2 ()a−b
  Equalising both values of h we get what we know as the Pythagorean enunciation: c^2 =a^2 −b^2
  To tangram the shaded areas of square on c to fit the other shaded area is theoretically feasible
  but hard to do in practice.
  1
  a
  b
  c
  b
  2
  c
  a
  C
  D