0
$\begingroup$

I happen to give some private lessons to an IB (International Baccalaureate) student. He asked me for help with writing some kind of a project on a set topic, given some materials (containing the definition and a few clues/overall plan of the paper). (Just in case someone is wondering: please notice that I do understand that "help with writing" is different from "writing it for someone", and I am very careful about only guiding him, but not doing his homework.)

My question is: where can I find some information (just basic things, definitions and maybe fundamental properties) about shadow functions? From the materials he was given (of rather medium quality, I'd say) I know that they can be applied to finding complex roots of some polynomial $P$ (seemingly with real coefficients) by means of associating with it another one (say, $S$), with only real roots (but connected with the complex ones of $P$: if $P(a\pm bi)=0$, then $S(a\pm b)=0$). Also, any kind of intuition would be helpful, but I specifically ask not to give any in the answer to this question; I prefer to find it myself from the definition and properties, please do not spoil my pleasure of finding it myself; if in trouble, I'll ask about it in another question.

As to the form: websites are fine, books too (my faculty has quite a decent library), I have also access to some journals (I imagine that a few of them, like, say, American Mathematical Monthly might contain some info), so please share any sources you know.

  • 0
    what is quartics' shadow function?2012-10-01

1 Answers 1

2

Here, I did this project, and this page gives a little bit of intuition.

http://www.math.hmc.edu/funfacts/ffiles/10005.1.shtml

  • 0
    For cubics, just set the function and shadow function equal to each other and solve for X to find the points of intersection. The two points appear to be random, but there is a formula to it.2012-03-21