Do the "Rich" Pay Their Fair Share?

As noted by Charles Sizemore, in 2007 the top 1% of taxpayers earned "only" 22.8% of all income while paying 40.42% of all federal income taxes.

By contrast, the bottom half of all taxpayers earn 12.26% of all income, but pay less than 3% of all income taxes.

In short, for every $1 dollar in tax paid by a taxpayer in the bottom 50% of income earners, taxpayers among the top 1% of earners paid $13 dollars.

Fair?