# Tagged Questions

Plane curves are continuous (or smooth) functions $\gamma\colon I\to\mathbb R^2$ from a real interval to the plane. Sometimes also the image $\gamma(I)$ is called curve.

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### Can every possible curve be expressed mathematically [closed]

Can every possible curve/parabola shown on a graph (for example $x^2$ or somthing much more complicated) be expressed in an equation like $y=x^2$. Or are there some lines you can't express?
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### The circle does not intersect the unbounded component of $\mathbb{R}^2 \setminus C$

We get the following problem in our differential geometry class. Let $C$ be a smooth, non-degenerate simple closed curve traveling counterclockwise. Suppose that the curvature $\kappa$ of C is ...
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### Problem with $arg(\gamma (t))$

I am see my notes about curves on complex spaces and I do not understand why it is so... I need help. I do not understand what way take to do it, I need someone explain slowly please, thanks
I'm trying to compute the genus of the normalization of the curve: $y^5=x(x-1)(x-2)$ Now I calculate the ramification points of the projection x: they are $(0,0),(1,0),(2,0)$ and they are of ...