>Let's see if I can still do elemental math: figure a normal modern track has 4-foot lanes,<
Well, a standard international track certainly has four foot lanes, but go out to your local high schoo, college, or community track and measure the lanes. Betcha they're not 4 feet.
>so if you're in lane 8 you're 28ft from the curb.
6.25x28=175ft (53 metres) more per lap.<
Not quite. Lane one is measured 30cm (about 12 in.) from the curb while the other lanes are measured 20cm (8 in,) from the lane line. Thus, lane 8 is 27'8" further out than lane 1. The difference in terms of the circumference is 4"x6,25 or 25", so over a mile, that would be more than an 8 foot mismeasurement if you used 28' instead of 27'8".
If you really want to be precise, the whole exercise should be in meters, starging with the lane width (which is 1.22 on a standard international track), and getting 2 times pi right too (it's not 6.25, it's more than 6.28).
>So to run a mile in lane 8 all the way, I make it that you need to run a little more than 3.5 laps.<
Depends on what you call a "little more." 3.5 laps is 1400m. Add your 53m and you're still more than 110m short of a mile.
Am I being too picky? Nah, Euclid is supposed to be precise about such things.