Claim-III:

Proof: Take a square, and divide it 4 equal pieces. Now take 3 pieces and let the area of this part be A (See the red part in Figure-1a). Now repeat this process on the fourth piece of the orginal square. This time the area of the three pieces is is A/4 (See the light blue area in Figure-1b). Repating this process again and again we may get a sequence of areas,

 

Figure-1a

Figure-1b

Figure-1c

Figure-1d

 

Figure-1e

 

The part

goes to A/3 (See Figure-2a)

 

Thus,



A. Kursat ERBAS © 2000

mail: aerbas@coe.uga.edu