How many dimensions does an arc of a circle have? Well, it may have one, or two dimensions. I would argue that it has two dimensions, and here is why.
It only seems reasonable that an arc of a circle is two dimensional because you are bending a line segment in the second dimension.
The true reason
A real reason that shows an arc of a circle is two dimensional is this: how many perpinduclar lines do you need to label every point on the arc of a circle? You need to perpindicular axis, so an arc of a circle is two dimensional. It can only exist in two dimensions or higher.
This may sound stange, and you may be a tiny bit emotinal, but think about it. It just makes sense. It makes sense because curves behave in ways you might not expect. So the outline of a circle is in the same dimension as a real circle, in fact they are the same shapes, they are just showing different regions of the circle.
I hope this makes sense, let me know if your mind is still blown away. Or mabye I did something wrong. Who knows?