The advantage of two dimensional pieces is that you have less of a chance of walking into two dimensions than three. Two dimensional pieces would include most paintings, photographs, a dollar bill, the words on a page of a book, but the book would be 3 dimensional. Two dimensional is formed by length and width and three dimensional is length and width and also thickness. If you went to a movie in a theater you would see the movie in 2 dimensions and every once in a while a special movie would come out featuring 3 dimensions which you would need special glasses for you to see, various animals or cars etc. seem to jump off the screen, so to answer your question the advantage of two dimensional is they take up less room than three dimensional objects.
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Two.
It's true that a point has no dimensions. But a line has one dimension, not two. A plane has two dimensions, a solid has three, and that's about all that ordinary people can visualize.
relative and polar
One dimension is a line. It has length, nothing else. Picture a number line. Two dimensions is a plane. It has length and width. Picture a graph.
Two dimensions of length: [L2]