The example problem they give is pretty neat, but they don&#x27;t mention the (IMO) interesting part of it. After sketching out the answer, I was suprised that the height you gain is <i>independent of the size of the underlying circle</i>. That certainly suprised me, as my intuition was that the height you would gain would shrink as the underlying circle grew -- after all, you&#x27;d be adding a constant length to an ever growing value. But the answer only depends on the amount of length you add, so the problem has the same answer whether it&#x27;s the earth, the sun, or a proton. Neat!