Where did you go to school? I'm from the UK. > Our teacher said it felt like pulling a rabbit out of the hat. This is something you do when you prove somethin

Where did you go to school? I'm from the UK. > Our teacher said it felt like pulling a rabbit out of the hat. This is something you do when you prove something. It's the shortest way but it's also totally lacking in motivation. It's a Deus Ex Machina, which is a terrible way of explaining mathematics to people. When I was taught "completing the square", it was presented as another method for solving a quadratic equation, and not just a proof of the quadratic formula. If people in the US are taught this way, that's not good for US-ians. And this whole discussion is weirdly US-centric.