How can you become very close with a girl and attract her without hanging out with her?

Try to get her attention and smile when she looks at you, and grinning then turning away will always leave her flattered and want to get to know you more. If you continue this routine for about a week, then I am sure she will approach you and want to get to know you, and if she doesnt, then try harder by introducing yourself and getting to know her, because you actually havent gotten to know her and she may not be the girl you are looking for, remember, looks arent everything. And like what most people say, dont judge a book by its cover, so dont judge this girl by her looks.