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I remember being forced to memorize all kinds of stuff about the quadratic formula until one day the lesson was taught by the headmaster who used to teach maths
by mhh__ 5y ago
I remember being forced to memorize all kinds of stuff about the quadratic formula until one day the lesson was taught by the headmaster who used to teach maths but didn't anymore, and he said to try derive it, so I did.
That was a big step in simultaneously realizing that mathematics could be beautiful but also that mathematics could be ruined by schools.
- impossiblefork 5y agoI myself never learned the quadratic formula, I always just used completing the square, i.e. just using the fact that x^2+ax, and that you can split the ax in two put the resulting rectangles on sides of the square, to make a square with side x+a/2, by only adding an a^2/4 which is independent of x. Then you know that you can just remove the little a/2 square from the big square to relate it to x^2+ax. I think that was the first case where I showed good taste in how to do mathematics.
- xigoi 5y agoIf you complete the square with generic coefficient, you get the quadratic formula.
- impossiblefork 5y agoYes, and that's why I've never had to actually learn the formula, and can make do by understand squares.