How to formally prove this?
What do the xi's represent?
Is there a different way to think about it or any clarifying comments? I'm still confused on why closer points are more likely, it seems like you are literally choosing a radius from all the potential radii equally.
I don't really understand why points further from the circle are less likely to be chosen. I was thinking it might depend on how precise our theta values get, where the closer ones would round to the same thing?
Why points further from the center are less likely to be chosen? Is there a reason behind this?