Chapter Fifteen

# How Many Different Rational Parametric Cubic Curves Are There? Part II, The “Same” Game

## November-December 1999

$\text{RCM=}\tilde{\text{C}}$

OK. Here's the deal. I've been playing with the question in the title on and off for over a year now. I'm interested in both the answer to the question and in finding the clearest possible derivation of that answer. My first efforts were very algebra intensive but had an aura of concreteness about them. As I played with the question and went through innumerable drafts of this column, I came up with more and more elegant ways to ward off the brute-force algebra and make the answer more intuitive without reams of calculation. ...