Both are beyond my math, but I have found several more elementary cases where calculus shows simple relationships between related formulas.
And I recall a sci-fi short story long ago, technological civilization on a single continent with a permanently clouded sky. They had not figured out they were living on a sphere, they were having trouble with train tracks mysteriously being the wrong distance and train passengers feeling light on the high speed trains. I didn't check the guy's math but it sure seemed right when the answers looked exactly like Einstein's equations even though the units were very different. (Limiting velocity = orbital velocity, the discontinuity being weightlessness.)
And I recall a sci-fi short story long ago, technological civilization on a single continent with a permanently clouded sky. They had not figured out they were living on a sphere, they were having trouble with train tracks mysteriously being the wrong distance and train passengers feeling light on the high speed trains. I didn't check the guy's math but it sure seemed right when the answers looked exactly like Einstein's equations even though the units were very different. (Limiting velocity = orbital velocity, the discontinuity being weightlessness.)