I was writing a blog post today, and I ended up asking the question of how many layers tall a human pyramid would be if it contained all of the people who use Facebook, approximately 750 million.
First I had to define how the pyramid would work. Basically, I ended up with $n$ being the number of layers from the top, and $n^2$ being the number of people in that layer.
So the top layer would be $n=1$ and would contain $n^2=1$ people. Next layer would be $n=2$ and would contain $n^2=4$ people. I ended up writing a simple python script to answer the question, but now I'm wondering about a more generalized answer.
Given $x$ people, how tall would the pyramid be? There's quite possibly a very simple answer to this, but I don't know what it would be.