Where are complicated polynomials found in nature?

[SamBridge]

So I know the common physics ax^2+bx+ or aT^2+VoT+X0 among its other various geometric uses, and I've seen a couple 4th degree polynomials in advanced particle physics, but where would you find something like X^9-2.3x^8-45x^5+23x^4+30 in nature?

Or where would you find pseudo polynomials like x^(3/2)+1/2x^(1/2)-x^(-1/3)?

Edited February 9, 2013 by SamBridge

[ajb]

The quadratics are nice, you can solve them exactly and they have nice graphs; parabolas. These things can be used to describe the path of a projectile, for example.

Higher order examples I can think of include:

• Modelling data- "polynomial lines of best fit"
• Eigenvalue problems
• Bézier curve's in computer graphics
• Truncated Taylor series approximations
• Theory of small oscillations (application of the above)
• Behaviour of dynamical systems

and the list goes on

[uncool]

Finding equilibrium in chemical reactions with large numbers of reactants.

=Uncool-

[imatfaal]

Power radiated per unit area is proportional to the fourth power of temperature - stefan-boltzmann law

 

[latex]j^{\star}=\sigma T^4[/latex]