So I was at the library yesterday doing my work (at university), and all of a sudden some girl comes and sits across from me (there was a low cubicle screen separating us). She was truly quite breathtaking. I'm not one to seek women purely for their appearance, but she made me feel a way that I haven't felt for a long time. Something instantly clicked in my mind--like I identified with her in some way, or that she felt familiar.

I was distracted for the remainder of the afternoon, and couldn't get much work done. Eventually I tried thinking how I might go about making her acquaintance. But whatever scenario I thought of simply felt too forced. She didn't know me; she was doing her work; she didn't want to be bothered. So I spent 90 minutes grappling over this until she eventually left, and when she did, she did not mind me one bit.

Now I'm torn over it. I want to go back and see if I see her again, if she regularly frequents that spot. Maybe I'll become a familiar face to her. Idk.

But I'm giving all this context to see if anyone has any advice. I'm sure this question has been asked before.

The way I see it I've got two main options. I can be bold and slip her a note, or I can go the slower route and try to make her acquaintance first. Judging from the books on her desk, we broadly study the same subject (medieval history).

I just don't want to come off as a weirdo.

Anyone have had similar experiences with success stories, or else have any useful tips?