Calculating the mean path length of a core
Let's say you hand made a core from finely ground iron powder and used some kind of epoxy to bond those particles into the correct shaped core.

What you have is a core that will be good for many tens of kHz working because the individual grains of powder are insulated. This prevents induced eddy currents in the core due to the vast majority of grains not contacting each other.

This is sometimes also referred to as a distributed air gap and behaves pretty much like a physical air gap but,  would you have a problem with calculating the mean length of the magnetic field now?