We Don't Need No Stinking Derivatives
September 13, 2007 5:53 AM Subscribe
Obscure Mathfilter: In the arcane past of mathematics, there is something known as a "Newton Polygon", which theoretically can be used to help sketch functions of two variables, say, x^3 + y^3 =3xy, for instance. But --
posted by wittgenstein to Science & Nature (4 answers total) 3 users marked this as a favorite
exactly HOW you use the polygon information to help sketch the graph has never been clearly explained to me.
Does anyone know how to do this?
Related -- there was a post last May or June in (i think) one of the Math Blogs that may have related to this. It was a shortcut approach to sketching polynomials without using derivatives, that just looked at the exponents of each term of the polynomial, and then connected them together using some rules. At the time, I thought "I'll come back and look at this in detail when I get a chance", but, alas, I cannot find it again. (My google-fu is not strong.) Does anyone know what I am talking about?
Alternatively, how would you sketch f(x, y) by hand, especially if it cannot be explicilty solved for x or y? (I realize all sorts of programs will do this for you; I am interested in by hand techniques.)