Why should I allow the maximum to be not a triangle - too much for me, right now. So, you want to make me rethink my view? Okay, I still have to work through only the first ten of your lectures. (Which I do slowly.... but I still do.... ).
What is not "simple" or "natural" to me - at least, it does not come naturally to me - is when the hight is outside the triangle. The same difficulty with me, when I look at a spread and make it open more than the perpendicular...
We show how the basic notion of rational trigonometry---quadrance---arises from the geometry of the ancient Greeks. The little-known sister theorem...
Why should I allow the maximum to be not a triangle - too much for me, right now. So, you want to make me rethink my view? Okay, I still have to work through only the first ten of your lectures. (Which I do slowly.... but I still do.... ).