Just cut down every tree that you ever encounter, and the mathematical perfection of your head-to-head layouts will be ensured. While you're at it, insist that all slopes be regraded to near-flat perfection. Because, as has been vigorously expounded, the sprinkler layout is the all-important concern, and no others need apply.
Meanwhile, back in the real world, all those triangular-spacing layouts are still covering their lawns. One can be reminded of all the aeronautical analysis that was done in respect to the flight of a bumblebee, and how the scientists would claim that their calculations insisted the bumblebee could never fly.
Funny thing, if you get your hands on some older manufacturer's catalogs, you will see their technical sections describing system layouts with triangular spacing, and not head-to-head square spacing. Kind of makes you wonder when they figured out that a change in layout philosophy would sell more sprinkler heads.