The Zone theorem says that if we stab an arrangement of n lines with another line, the total complexity of its zone, the set of all 0-, 1-, and 2-faces adjacent to it, is O(n). The actual constant is something like 6n at least as stated in various textbooks, and the proof is by induction with a reasonably careful charging argument.
I was asked this question in class, and don't have an answer:
Is there an alternate, more intuitive proof of the Zone theorem ?
Now I realize that many people find induction quite intuitive and would be offended by my implication, and am willing to amend the above to merely "alternate" for them. But is there any such proof ? Or even a proof from the book ?