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Intuitively we'd describe the curve of a helix like $$\gamma(t) = \left(\begin{array}{cc}x\\ y\\ z\ \end{array}\right) = \left(\begin{array}{cc}R\,\cos(t)\\ R\,\sin(t)\\\ t\end{array}\right)$$ This should be the cartesian parametrisation. However it looks exactly the same like in cartesian coordinates.

Can a distinction between both been made?

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    $\begingroup$ The parametrization is still written using a Cartesian basis. The position of any point on the helix is given by the function $\boldsymbol{\gamma}: \mathbb{R}\to\mathbb{R}^3$, where $\mathbf{r}=\boldsymbol{\gamma}(t)=R\cos(t)\mathbf{i}+R\sin(t)\mathbf{j}+t\mathbf{k}$. $\endgroup$ Commented Jun 27, 2021 at 17:12

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Cylindrical parametrisation $$ \gamma(t) = \left(\begin{array}{cc}r\\ \phi\\ z\ \end{array}\right) = \left(\begin{array}{cc}R \\ t\\ t\end{array}\right) $$

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