Heine-Borel is the kind of theorem that is essential for your life. I mean, you can handle doing grocery shopping without Bolzano-Weierstrass, but you would never succeed without Heine-Borel.
An explanation of what radians measure: the angle in terms of the radius curved around the circle.
holy fucking shit, my entire education has just clicked.
I love seeing things click for other people (especially in math). That instant exhilaration is the reason math and science are fun for me.