If the side length of the first square is 2, then the right-angled side of the first isosceles right triangle is 2/ root number 2 = root number 2.

So the side length of the second square is the root number 2.

The area is 2.

(2) Similarly (1)

The side length of the third square is 1 and the area is 1.

The side length of the fourth square is 2/2 of the root sign and the area is 1/2.

(3) Through the observation of (1)(2), the law is obtained:

The area of the first square is 4.

The second one is 2.

The third is 1.

The fourth is 1/2.

……

The law is divided by 2, that is, the common ratio is a geometric series of 1/2.

The area of the square in 2003 is: 1/(2 2000).