I don't disagree. I will make the point though that this proof is #29. I'd have run out of proofs at #5, if not earlier. I'm sure David MMR has probably effectively exhausted the easy non-sciency ones.
@flawr Oh sweet. I knew that had a mathematical name, but I couldn't remember what it was. The Bernoulli shape is lot nicer than mine, I night change it to that
@DJMcMayhem The bernoulli lemniscate also has a very simple representation in polar coordinates as well as a nice parametrization in cartesian coordinates.
Although one advantage of what I'm doing right now is that it's very easy to define it as having a certain width (which is important to what I'm doing). If I switched to Bernoulli I'll have to find out a relation between a and the total width of the lemniscate