Light Bulb Filament: What Equations Describe Its Shape?

schulzy
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Homework Statement


I want to modelling a light bulb filament in MATLAB, but I don't know, what functions describe this shape. My question is, what are equation (x,y,z) which describe the light bulb filament.
 

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If you just mean a spiral shape then something like (x,y,z)=(Sin(t),Cos(t),t) should work using a parametric plot (in mathematica anyway, I don't use matlab).
 
I know that
x=cos(t)
y=sin(t)
z=b*t
these equation describe a simple spiral, but I want to drawing complicated shape, like in attachment.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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