a fractal
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It depends on whether they are never ending but recurrent or never ending but non-recurring. An example of the first is 2/11 = 0.1818.... where the 18s go on for ever. This is called a recurring decimal. An example of the second is the decimal representation of sqrt(2) = 1.41421356... which goes on forever, but which does not settle into a repeating pattern. These are called non-recurring decimals.
No it will meet the starting point, but you can go on the circle to make it never ending.
I know 1,000,000 is hecatommyriagon, but that is the closest i know.
There is not a shape that has 2 sides as these lines would never touch and thus would never become a closed fiqure or 'shape'.
It is called a megagon. A ∞ sided shape is called an apeirogon.