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.
By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant.
The Wallace-Bolyai-Gerwien theorem shows that any two polygons with equal area must admit a dissection into finitely many pieces where one is allowed to arbitrarily rotate and translate the pieces to go from one polygon to the other. The problem about whether a hinged dissection exists remained open until 2007. You can read the paper here, which presents a method which always works to find a hinged dissection.”
MY BRAIN CAN’T HANDLE THIS