Sometimes with math the proof you read in the textbook is not the first proof someone thought of. It may not be the clearest. It may be the shortest. This is not a new thought, but I can't remotely remember where I read/heard it. The interesting bit
Last time we made a geometric argument that given four complex numbers \(A, B, C, D\) lying on the unit circle, if they satisfy \(A + B + C + D = 0\), then they form a rectangle. Okay, technically, I didn't show the rectangle part. I did show the segments are
I want to return to yesterday's problem from Visual Complex Analysis. Suppose we have four complex numbers \(A, B, C, D\) on the unit circle such that \(A + B + C + D = 0\). We want to show that these points must form a rectangle. How can we do this?
There's an exercise that's bugged me for a while from Tristan Needham's Visual Complex Analysis. It's a proof exercise: Prove that for complex numbers \(A, B, C, D\) lying on the unit circle (so magnitude 1), if \(A + B + C + D = 0\
Thinking out loud about the recursive Cantor function construction again. I realized shortly after the post that the points \(x = k/2^N\) do not become fixed points. On the other hand it seems right to focus on the plateaus where \(y = f_N(x) = k/2^N\)... the difficulty