I vaguely recall that if a circular disc with a circumference of pi (3.14 ...) is held at an angle of 22.7 degrees relative to a flat surface, it projects an ellipse that has a circumference of 3.000 Coincidence? Eh, probably. Might've also been 26.8 degrees.
One common association of those digits with PI is the handy approximation of 22/7 accurate to three digits, off by just over .0004.
I stress that this is an approximation only! I had to explain about PI being irrational rather than exactly equal to the shortcut approximation to a couple co-workers, explaining some poor behaviors in their rotation function.
