I need help in following things -
There had been 2 problems I had been trying to guess the recurrence relation but have been unsuccessful.
number of different regions formed when \(n\) mutually intersecting planes are drawn in 3-D space such that no four planes intersect at a common point and no two have parallel intersection lines in a 3rd plane.
number of regions into which a convex \(n\)-gon is divided by all its diagonals.
I would love to have a detailed explanation on how to find the recurrence relation - is it all about inspection, in these types of geometry problems?
One more doubt is related to mechanics. I was reading David Morin and he explains about a "slick neat trick" of finding the moment of inertia. The method is about "scaling, using \(I\)'s definition and using parallel axis theorem". It seemed quite helpful, in primarily his fractal triangle problem. But I couldn't understand the first step exactly i.e. scaling. Any help on this will be appreciated.
I was looking up to entropy. I understand that the entropy is first of all the proportionality constant of heat and thermodynamic temperature and it remains conserved in a reversible process and that in irreversible, it should always increase and all that. But the one thing I didn't understand is how this relates t disorder.