To work with a GSP sketch of the problem click here
NOTE this sketch plots the ratio of the areas!
To watch a Quicktime movie illustrating the problem click here
Using GSP we can illustrate the relationship beween the ratio of the blue area and the ratio of the red area and we get the sketch above. The challenge is to derive this relationship by some other means.
Finally we can show that area triangle AB''B = area triangle BC''C = area triangle CA''A from which it follows that (note the corresponding graph appears on the right):
to look at a GSP animation.
Click here to watch a movie of the animation.
Illustration 2: This is the illustration offered by Steinhauss in his book Mathematical Snapshots.
NOTICE that the principle behind the two illustrations is really