I like to apply mathematics for the long range shot, and the 2 most memorable using math were these--
Was hunting coyotes with a buddy's kid years ago and he was carrying his Marlin 22 RF. We were walking back from a failed coyote stalk when i asked to take a look at his little rig. He had a Simmons 3-9x riflescope on top of it and a Harris bipod--nicely outfitted actually. The plex post tips in the reticle appeared to subtend about 6 MOA from x-hair axis @ 9x. I told this kid that if he cranked the power down to 3x it would be about 18 MOA to PPT's (reticle subtension is ~inversely proportional to magnification), and it oughtta' net him maybe 300 yd. zero at the tip of the post. We were walking thru a PD town and decided to test it. We set up on a PD hole and i'd lasered a couple dogs at ~290-something. Zero wind, and this kid shoots, and just hits low. Next shot knocked the dog off the back of the mound. It crawls back up and hesitates on top for a second. He shoots again and nails it rolling it off the back of the mound once again, this time killing it. His buddy runs up out of the hole to check him out and the next couple shots kills this dog too. rolling it off the back of the mound. On the way up to the hole i still couldn't believe there were gonna' be 2 dead PD's off the back of it, but sure enuf they were there.
Another mathematical shooting experience was at 1 of the prairie dog/sniper matches that are held at the Pueblo West, CO Range every month. They set 10 9" steel PD's out at unknown distances, and u have to engage each one, one at a time with only 1 shot. The tgt. markers are the human silhouette tgts. with numbers on each one to know which tgt. you're shooting at. For some reason one of the tgts. couldn't be ranged with all the lasers there, so i thought to "mil" it with my 4 MOA reticle. The problem was i didn't know the size of the tgts, but i already knew the range to many of them. So i picked one of the closer tgts. to calculate (reverse mil) the tgt. size, then remil the other unknown tgts. range. Can't remember the exact range now (300-something), but i did score a hit on that tgt. using mathematics--loved it.