Pythagoras Theorem

There are several proofs for the Pythagorean Theorem.Though the theorem is elementary some of these proofs are quite interesting.

1) Look at Fig 4-A,

Area of the outer square = (a+b)²

Area of the yellow triangles = 4*12(ab)

Area of inner square (white one) = c²

Therefore,

c²=(a+b)²-4*12(ab)=a²+b²

Now lets do it a bit diffently,

2)Consider a white floor on which we are keeping the yellow tiles (as in Fig. 4A).

Now shift those yellow tiles and arrange them as shown in Figure 4-B.(See :"http://www.youtube.com/watch?v=T2K11eFepcs" if you can't visualize this)

Net Area uncovered (i.e the white portion) in both the diagrams is the same.
or, c²=a²+b²

3)The image explains everything.

The best and the most common proof perhaps is using similarity. Watch this:

http://youtu.be/LrS5_l-gk94

Thanx...