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Eventually I noticed her twirling her hair and running her fingers through it (still not really looking at me) and then at one point started leaning on her elbow closer to me. Also, I did notice that she didn't cross her ankles (I think that's a negative sign) nor did she have crossed legs away from me.
OMG stop analysing that much. If you want sth, go for it
First I will contradict a few points.
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i) Physically can't because need to listen to prof.
You don't need to be talking all the time. You can exchange a word from time to time, making fun of the prof, etc.
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ii) Seems kinda awkward to just go up to a hot girl and site beside her especially when there are a bunch of empty seats around that area
Still you can, but in this case you would have to be more direct. You can go like that: "Hello, I am ...., Is that seat free"
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iii) random chance that I did sit close to a hot girl but then I just have no freaking clue as to what to say
Ask her about her, find out sth about her. You can also talk about the content of the lecture, but in this case avoid being boring.
Now a few tips.
_If there is indeed a free seat next to her, you can go sit there. Open the conversation in a natural way. You can tease her a bit (don't overdo it). A few examples I use sometimes: "I can't concentrate when you sit next to, cause you're too sexy". Or if she is on her computer on facebook:"listen to the lecture instead of chatting with hot guys!"
_If you can't approach during the lecture, do it during the break or at the end. You can even invite her for an instant date. example "I've got a break till the next lecture. Let's go have a coffee!"
CHAT