# Polynomials in nature

What polynomials occur in "nature"? I am interested in polynomials of degree three and higher. I am aware of Stefan Boltzmann Law and Chemical Equilibrium Examples.

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Bruno Buchberger once told me something along the lines of "you can solve your problem if you can express it in polynomials." (Heavily paraphrased, highly innacurate, long-time-ago memory: please, nobody read very far into it :) ) That was right after a talk about automated proofs, so I imagine he was thinking along the lines of encoding proofs in polynomials. Much later, I saw a really cool automated proof of the concurrence of medians in a triangle using Buchberger's algorithm. –  rschwieb Oct 9 '13 at 17:51
The volume of the sun is a degree-three polynomial of its radius... –  Rahul Oct 9 '13 at 17:55
The ideal gas law can be thought of as an equality between a degree-three polynomial and a degree-two polynomial. –  vadim123 Oct 9 '13 at 18:04
I've always been intrigued by the $r^4$ occuring in the Hagen-Poiseuille law. –  Hagen von Eitzen Oct 9 '13 at 18:04
1st and 2nd orders very common but it is true that from 3 onwards it gets harder. I could generalise the answer above to any volumes but it's a rather small family still. Perhaps you could use them for approximations using Taylor series for example getting rid of $x^n$ onwards for some $n>3$ but it would only be an approximation of nature. Kepler's third law uses a third degree relationship. One more idea that come to my mind would be describing dynamical systems, could it be animals interacting or anything else really. –  user88595 Oct 9 '13 at 18:07