I doubt that this was a serious question but there is actually something you can apply in a way so I will go ahead and respond.

A lot of people say that Belmont's sweeping turns favor "sweeping moves" by closers. Ignoring the possibility of dead rails (which seem to exist often at Belmont for some reason), this is probably more of illusion than anything else.

Understanding the geometry of the turn (the "pi" theory as you described it) explains why it is easier for an outside horse to "make up ground" on the turn at Belmont (as compared to smaller tracks). The outside horse does not have to increase his speed as much to make up that lost 10-15 feet per path.

Note that Belmont is probably the only major track in the US in which this would apply because it is so much larger than the rest. The difference in geometry between a track like Churchill nad Pimlico is probably insignificant unless the banking is much different.

Cheers.

Chris