My brother had a strong dislike for math that wasn't immediately practical. He ended up understanding integrals (at least numerical approximation) after building a small boat and needing to calculate how much air it would hold: obviously less than the containing rectangle, more than the contained rectangle; and then he figured out you can split the boat into sections and get a good guess of each section's volume, move from rectangles to trapezoids, etc.
I'm a bit like that. I scored surprisingly high on the math portion of the SAT, but couldn't remember which thing was sin and which was cosine. In coding for 2D game platforms I think I've needed to reinvent parts of trigonometry and spatial geometry every time I encounter a new version of the problem. What your brother did makes perfect sense to me; not that I dislike math per se, but his way is probably how I would approach that problem too. I need to be able to visualize it in space. By breaking it up into discreet buckets if necessary. Once I do, I can figure out an iterative logic function that approximately describes it... although it may take me much longer if I'm trying to figure out an actual equation.
