I once had a teacher write “I have no idea how you got here, but this correct” on a test.
I’d forgotten some trig identity and derived the cosine law and then solved for all the angles with it to get the answer.
It was like that math joke where a mathematician is asked to boil water. The first time he takes the pot off the shelf, fills it with water, then puts it on the stove and boils it.
The next day he’s asked to boil water again. The pot is on the counter with water in it. He dumps the water out, and puts it back on the shelf, as that is a known solved state for boiling water.
So why memorize the formula we were studying when I could just solve more angles and then get the lengths.
I once had a teacher write “I have no idea how you got here, but this correct” on a test.
I’d forgotten some trig identity and derived the cosine law and then solved for all the angles with it to get the answer.
It was like that math joke where a mathematician is asked to boil water. The first time he takes the pot off the shelf, fills it with water, then puts it on the stove and boils it.
The next day he’s asked to boil water again. The pot is on the counter with water in it. He dumps the water out, and puts it back on the shelf, as that is a known solved state for boiling water.
So why memorize the formula we were studying when I could just solve more angles and then get the lengths.