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I don't really have much to add to this question, except the picture

enter image description here

I would think there has to be an analytical form for this surface. Also, if one could help build a vector, normal to it as a function of position on this helix, could be great.

P.S.: Sorry if this question is too fundamental, I am a physicist, not mathematician and my geometry knowledge is reminiscent...

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Parametric plot of two dimensioned helicoid surface embedded in 3-space..

$$ (x,y,z) =(u \cos v, u \sin v , k v ), (0<u <umax), ( 0<v < 6 \pi);$$

You may need Maple, Matlab, Mathematica etc. CAS to plot such surfaces.

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