Hello all. This is just a question I've been having while learning about parameterization of curves in my Calc III class. Now, I've never taken parameterization lessons (?) which apparently are supposed to be covered in Calc II (which includes heavy integrals, series, and other stuff). But now that we are revisiting paramerization, I've got a question. Why is it defined in the way that it is? I mean, for some HW questions I had to draw the resultant curve of something. But I didn't paramterize or anything. I just fit in values of t into a function of t and I got points. I connected the points. I checked my answer, and the graph looked really good compared to what the book says the answer is. My teacher, on the other hand, said something along the lines of "try saying that (_1,_2) can be redefined by something easier, for example, let's set _1 as 'x' and then redefine _2 in terms of our new x." What I'm saying, then, is, why do we parameterize? If given a function r(t), and I'm asked to graph it, can't I just plug in values of t and then plot those points and connect them? If anyone also has any good reference websites about parameterization, that would be great too.