There is this girl I have been seeing at the gym for a while now. She appeared to be of the same ethnic group as me and she seemed to be looking in my directions on a several occasions. I eventually realized I think she's kinda cute. One day her and her friend happened to be working out in the same multipurpose room I was in. She asked if it would be ok for them to put on some music, and I said sure. I then took the opportunity to ask her if she was from my ethnic group, turned out she wasn't, but close. The next time I saw her after that, we didn't say anything to each other. But then another time, I ran into her into the multipurpose room again, and she was apologizing for the loud music. I took the opportunity to ask her something about the types of music she was listening to. We talked briefly and she was really friendly. But again, next time I saw her she didn't say hi to me or anything. But another time I saw her working out with her friend and I said hi how's it going. She said hi back to me and was friendly when I asked her about where a piece of equipment was. But then after that I saw her 3 more times and she walked by me without acknowledging me or anything. Today she was literally RIGHT IN FRONT OF ME putting back a piece of equipment and she totally ignored me.

So I am really confused about what I should be doing. I can't help but feel like I am being rude and unfriendly when I pass by her and don't say anything, despite the fact that she didn't say anything either. But do I really keep talking to a girl who just ignores me? But she could just be shy and socially awkward, right? See, this is the problem with the whole feminist taboo against approaching uninterested girls, you can never really tell if a girl is uninterested or just shy. Things would be so much easier if approaching girls was just always acceptable.