Todd B. sent me this pie chart, with a note: "Do the areas in the pie chart represent the numbers?"
The short answer is NO.
It's also not so simple to figure out the areas of crescents. The purple area looks tiny compared to the dark green region. If shown this chart, we get the impression that Microsoft's intention to absorb Yahoo! will not vastly expand the number of unique visitors to its properties because so many of their current users overlap.
The following is a bar chart representation of the same data. The combined entity will have 31% more users than what Microsoft has right now. Not a bad growth rate for a mature business! The author of the original post calculated that Microsoft would in effect be paying about $1000 each to acquire these new users.
Perhaps the most important question is how one values a "unique visitor". Have anyone seen any sophisticated analysis on this topic?