i see the problem in my case anyways i failed to see what was going on in this table i did not realize it was a series of steps as decried in the article but thought it was list of various fractions being computed i did not realize that each row was a series of iterative steps or perhaps gavin green your example i was ready to understand the table i still like how you presented the process it just clicked for me very easy to understand i don't think you could make it any clearer than how you have presented it i especially like that the decimal numbers are shown approaching the final result is the fraction expansion right