cubic curve

A cubic curve is an algebraic curve described by a polynomial equation of the general form:


ax3 + bx2y + cxy2 + dy3 + ex2 + fxy + gy2 + hx + iy + j = 0,


where a, b, c, d, e, f, g, h, i, and j are constants, such that at least one of a, b, c, and d is non-zero, and x and y are variables.


One of Isaac Newton's many accomplishments was the classification of the cubic curves. Newton found 72 different species of curve. Later investigators found six more, and it is now known that there are precisely 78 different types of cubic curves. Interesting examples include the folium of Decartes and the Witch of Agnesi (see Agnesi, Maria).