Gary, wasn't implying anything by my previous response. It's a good question. I can vaguely remember talking about the peculiarities of pi in one of my math classes and this was mentioned.
It's been far too long since I was even remotely tolerable at proofs and number theory. However here's how I broke this down: The distance between the circle circumferences' increase linearly as the circumference increases.
Or try thinking of it this way:
A circle of circumference 1,000,000 relates to a circle of 1,000,100 as a ratio of
1,000,000 / 1,000,100 or approx 0.999 right?
A circle of circumference of 10000 relates to circle of 10100 as a ratio of 10000/10100 or approx. 0.9900
A circle of circumference of 1000 relates to circle of 1100 as a ratio of 1000/1100 or approx. 0.909
The ratio approaches but never exceeds 1. As the circumference increases so does the number of significant digits. Therefore the variance appears to stabilize at 15.xxx at values over three significant digits, ie distances greater than 10,000 units in circumference.