Posted by Ian on Tuesday, June 5, 2012 at 6:36pm.
Each of the sides of a square (S) with an area of 16 is bisected and a smaller square (S2) is constructed using the bisected parts as vertices. The same process is carried out on S2 to construct an even smaller square (S3). What's the area of S3? (Draw a diagram, please?)

calculus  MathMate, Tuesday, June 5, 2012 at 9:44pm
The square S is cut into 5 pieces by S2, namely the square S2, and 4 triangles at each of the four corners.
If you flip each of the four triangles at the four corners about the sides of S2 so they go inside of S2, you will find that the sum of the areas of the four triangles equal to the area of S2.
In other words, the area of S2 is half that of S (16/2=8).
Similarly, S3's area is half that of S2 (8/2=4), and so on.
Draw a diagram, or even better, cut out a square piece of paper and demonstrate the above.