I think somewhere around the top of page 3 I warned that this was getting pedantic. Well, we definitely crossed that line! What threw me was when we started talking about an "elliptical track". There are at least two possible definitions of this. As an example was given using a calculator to find the circumferences of two ellipses, I assumed that we were talking about a track in which all lanes were ellipses, and in such a case the formula doesn't hold (as shown). Of course, to make such a track you'd have gaps between the lanes at certain spots in order to keep the actual lane width constant (imagine the lane stripe getting wider and thinner). Amazingly impractical. OTOH, if the definition of an "elliptical track" is "first lane is an ellipse and all other lanes simply wrap around it keeping the distance between lanes constant" then the formula does hold. That makes perfect sense because by a simple extension in this manner, you are basing the new lane on circular subsections of the first.
My point was always that if all the lanes follow some curve other than a circle, the result will be different than 2pi*diff. BUT, I never meant to imply that drawing an arbitrary simple closed path and then wrapping the other lanes on it wouldn't work. If each lane is described by the same general equation (such as an ellipse, or even something weird like a couple of 3rd order polynomials) then in general, it won't work. Why would it? Each lane wouldn't be related to the other via 2pi. I think most of the argument here has been over misinterpretation. That, and a perverse desire to "prove the other guy wrong".
As long as we're talking about impractical tracks, I think we should consider over-and-under style tracks, bridged figure-8 being the most simple. We can then extend the idea into the third dimension by adding hills, ramps, and up/down spirals.
Here's where it gets interesting for the mathematically inclined. Flip the problem backward: We can, of course, create a track whereby each lane has the same circumference by adding appropriate twists and hills! In perhaps the most simple case, we insert a hill in lane 1, a somewhat smaller hill in lane 2, and so on until the outside lane is perfectly flat. Although the distance is constant, the effort won't be because you never get out of a hill what you had to put into it. Thus, the better question is how do we make a flat track where all lanes are the same length? I'm thinking in terms of an infield "bulge" that gradually disappears toward the outside lane (think kidney bean). A flat figure-8 track would work too, but collisions might be a problem.
Imagine a track where all lanes are the exact same length and include the same number of turns of identical radius and also hills and twists, each lane intertwined with the others. Everything is equal. Everybody runs in their own lane, always. Yet nobody would have any clue as to positioning until the finish line. Yeow!