A plane algebraic curve is the zero locus in R2 or C2 of a polynomial in two variables f(x,y). (Or more generally in algebraic geometry one can work over any field).

For example the unit circle is the zero locus of the polynomial x2 + y2 -1.

Here are some interesting curves.

I'll slowly work through and node these. If you have one to add to the list /msg me. If you feel competent and you want to node something on the list feel free, but please let me know to avoid duplication of effort. A good writeup should include some historical background and the equation of the curve.