I would argue that this explanation still requires a working knowledge of the Pythagoras theorem, even if you don’t employ the formula directly. Specifically the knowledge that the hypotenuse must be longer than either of the sides unless the angle of the non-90 degree sides are 180 and 0, essentially making it a line.
You deducted the hypotenuse must be longer than 30 since they weren’t aiming directly at the ground. Believe it or not, that’s not common sense.
I watched (some) of a History of Mathmatics documentary, and what struck me was how many of the theorems ancient people came up with were just common sense. But they wrote it down: that’s what made it noteable.
There were some theorems/axioms that i had trouble getting my brain to accept, but generally it came down to me not “getting” their number/tally system or simply having no context for why they needed that math in the first place (ie: it wasn’t common sense to me). For example. I’m not an ancient accountant who needs to be able to calculate grain taxes and – at the same time – be able to assure a farmer (who can’t read my number system) that i’m taking the correct amount of his food, so their method of long division using different colored stones seemed needlessly convoluted to me.
Note, too, that there is value in being rigorous about “common sense” assertions.
Some of the most exciting discoveries happen when something everybody assumed they knew turns out to be wrong.
Very true! I wish I could upvote you more than once, so i’ll write a long-winded comment instead…
Quantum mechanics is the least common-sensical realm of science and math, and yet it is excedingly useful and has expanded our understanding of the universe tremendously. But to get here, many someones had to keep asking “why” without stopping at common-sense answers.
