Note: I'm so terribly sorry for taking longer than planned to post this final part. I've come down with a nasty cold, and I'm basically a sniveling mess wrapped in blankets. It's not attractive. I promise to get to your lovely reviews when I am feeling well enough to respond appropriately! But thank you all for your kind words and favorites! I hope you enjoy the conclusion to this story!

When Kimmy Jin finds out the white girl has been arrested, she's not the slightest bit surprised.

And she certainly doesn't feel any concern about it—not when Chloe knocks on the door and tells her about the absolute 'fiasco that was all a 'complete misunderstanding'. Not when Chloe— blue eyes shining in concern and worry—gives Kimmy Jin a hug that is most definitely one-sided after she finishes her tale.

Maybe Kimmy Jin fleeting thinks that Chloe is actually rather sweet for turning up at the dorm room to wait for Beca. But that moment of charitable thinking is ruined in the very next moment by the arrival of Beca's entire stupid singing group. And even if Kimmy Jin doesn't mind Chloe Beale, she's not about to let her get away with bringing all these abnormals into a space already violated on a daily basis by a surly, wannabe DJ.

But then a very large and very loud blonde shoves through the doorway, pushing a contrite Chloe Beale aside with a vigorous hip check as she enters the dorm room.

"Awwwe yeah! Asian roommate! Konnichiwa, bitches!"

Kimmy Jin gapes at the girl, and it is this distraction that allows for the entrance of the other, slightly less objectionable individuals (though 'less' is an relative term; it becomes clear in about three seconds that none were people Kimmy Jin would ever be caught dead associating with).

"You can go if you'd like, Kimmy Jin. " Chloe Beale says, her eyes wide and apologetic. "I know this isn't super cool for us to barge in on you like this, but we didn't want Beca to think that we abandoned her or anything! It's just that Jesse said he would take care of it and…" Chloe's eyes flicker over to a blonde who is looking at Beca's side of the room as though she thinks she may find barrels of toxic waste hidden there (Kimmy Jin can relate). "And so we figured we would wait here. I could take you out to lunch, or something, next week! As a thank-you/sorry?"

Kimmy Jin finds the gesture… not completely abhorrent.

"Whatever," she mutters, sitting back down at her computer.

She's not about to leave, after all. The fat one with the funny accent would probably eat her (gold) bonsai tree, or something.

When Beca returns, the brunette is unable to hide the look of surprise (and, yes, happiness) that covers her face during the split second before she can cover it with some stupid faux-gangster expression (only encouraged by her friends' inappropriate comments).

She does, however, glance at Chloe Beale, and with a smile that actually shows teeth, and say (in a tone that Kimmy Jin knows is normally reserved for the redhead alone), "You guys waited up for me?"

The sight swelling in her chest that Kimmy Jin feels at Chloe Beale's earnest response ("Of course we waited up for you") probably has something to do with the fact that she hasn't eaten anything in quite a while.

Probably.

Kimmy Jin deems a quick and spiteful comment ("It's a real inconvenience, Beca") necessary, just in case.

It doesn't really help—as Kimmy Jin leaves the room, she can't help but feel glad that her dumb roommate didn't get herself shanked.

(It's an odd, and very new feeling).

Chloe Beale doesn't take her out for a 'thank you' lunch, because Kimmy Jin never gives the redhead the opportunity.

But she does come back to her dorm one day to find some mango bubble tea on her desk, along with a case of Bacchus decorated with a bright pink sticky note that tells Kimmy Jin to study hard for the her Calc midterm—apparently Chloe remembers a lot of questions involving infinite series, which are 'a bitch'.

It's playing to stereotypes, what with the obvious Korean drinks, but Kimmy Jin finds herself smiling at the gesture, nevertheless.

Beca comes back and, wisely, doesn't say anything when she sees Kimmy Jin sipping on her tea. She does, however, smile in the way she only does when she's thinking about Chloe Beale.

(Not that Kimmy Jin notices…much).

Something happens at one of Beca's stupid singing competition things.

Kimmy Jin's not sure what, but Beca takes reclusiveness and surliness to new levels afterwards. She also gets worse about the whole personal hygiene thing.

It's not great.

It's chance though, that leads to Kimmy Jin getting part of the story.

She's walking across campus the morning before she's due to leave for break when she spots a familiar head of red curls, and before she can consciously think about it, she's changed directions, and her steps take her within a couple feet of the girl who had caught her attention.

"Kimmy Jin! Hi!"

Chloe Beale's tone is warm and welcoming (as Kimmy Jin had come to view as typical for the girl), but there's an exhaustion about her—a sadness that her bright smile can't quite disguise.

"What happened?" It's blunt and to the point, but Kimmy Jin feels a little strange doing this as it is, and she sees no need to prolong things.

"Oh… at Semi-Finals you mean? Did Beca not tell you? … We lost."

Kimmy Jin tilts her head, because she's not sure that's reason enough to explain the way Beca has been acting—or the absence of a certain redhead.

"There was… Beca got into an argument with Aubrey—our captain—and it… didn't end well." Chloe's eyes drop. "I don't think she wants to see any of us."

The words slip out of her mouth without thought. "She would want to see you."

Chloe stares at her for a long moment before shaking her head. "I don't think so, Kimmy Jin. But maybe…tell her to have a nice spring break, okay? I…we miss her."

Her goodbye to the senior is nothing more than a quick nod, but when she re-enters her dorm to find Beca still at her computer (headphones off, for once), she feels as though she should say something. Kimmy Jin's just not sure what.

Still, when her ride arrives and it's time to leave, she pauses before opening the door.

"Happy Spring Break."

Beca turns in her chair, and Kimmy Jin sees the very same sadness she had seen in Chloe Beale, creeping around the DJ's eyes, even as the brunette fakes a smile and a 'thanks'. She tries not to think about it much.

(Kimmy Jin happens to tune into the campus radio station a few times over break; it seems a bit more depressing than is the norm.

She tells herself she's not worried.

It's a lie).

Beca's not much better when Kimmy Jin returns. In fact, she's worse; adding watching movies alone in the dark to her list of depressing activities.

She's not sure how to handle the whole situation, because that would involve a lot more talking with the white girl than Kimmy Jin is comfortable with. But when Beca's phone lights up one night, and the girl stares at the text message for far longer than is likely necessary, Kimmy Jin feels compelled to speak up.

"What?"

Beca shakes her head. "Nothing. The Bellas are back in since one of the teams dropped out." Another head shake. "Whatever. It doesn't matter."

Kimmy Jin thinks about that for a moment.

"It matters to whoever sent the message."

Beca's head snaps up, and even in the dark, Kimmy Jin can see the way her eyes widen, just slightly.

(It doesn't take a genius to figure out who sent that text message. Kimmy Jin would bet her 104 average in Calc on her answer).

Beca leaves the room a few days later, and Kimmy Jin actually sighs in relief.

Relief that is short lived, because when Beca comes back, she's not any better. Still. In fact, she looks confused on top of depressed and Kimmy Jin hasn't taken any psychology classes, so she's really not prepared for this.

"I talked to my dad." Beca laughs. "I actually asked my dad for advice. God!"

"That's why you left?"

"Well, no… I mean, first I went to talk to Jesse and that was a complete failure. And it didn't… I still felt… so I went to talk to my dad. But now I… God! Why do I feel like this?"

Kimmy Jin knows Beca's not expecting an answer; not when she flops back onto her bed with a loud and aggravated sigh. But she gives the girl one anyways.

"It sounds as though you didn't speak with the right people."

(Beca's up and out the door less than a minute later).

When Beca comes back (much, much later), it's with a giggling Chloe Beale in tow, blowing notes into some annoying round musical instrument, and Kimmy Jin feels as though maybe she can finally stop wasting time worrying about her white girl roommate.

Thinking such a thing was a huge mistake, of course—the equivalent of saying 'at least it can't get any worse'.

(If only Kimmy Jin had known then, the headache that was in store for her).

It's coincidence that puts Kimmy Jin in New York during the weekend of Beca's final singing thing.

There's a mathematics competition in the Big Apple that same weekend, and Kimmy Jin is invited to attend. And yes, there had been three different weekends she could have chosen. And sure, she had a huge exam on Monday, so the other dates may have worked out a bit better. But this weekend had felt… lucky.

The fact that she ends up at Lincoln Center at exactly the time when Beca's singing competition is due to begin is less easily explained, but whatever—Kimmy Jin does what she wants (and wearing large sunglasses and an oversized hoodie makes the whole thing a little more bearable). She doesn't know much about singing (doesn't care to, either) but (after an acceptable performance by puppy dog boy) as soon as Beca and Chloe's group steps out onstage, she knows they've at least tried to make some improvements to their routine, because her roommate (along with the rest of her teammates) is not wearing the horribly unflattering airline hostess outfit she'd worn to these events in the past. It looks less…tired, overall. Not that Beca's style has improved dramatically—she still wears those awful ear monstrosities, but it's an improvement for the group as a whole.

Still, despite the lack of enthusiasm Kimmy Jin feels (or tries to feel) for the entire event, when the Bellas build up to Beca busting out in the chorus of 'Don't You Forget (About Me)' and the lights flash along with her dramatic fist pump, Kimmy Jin is right there with the crowd, cheering in her seat for the duration of the performance.

And that's when she sees it—really sees it—for the very first time; Beca Mitchell is electric—it flows out of her in her voice and in the mix of songs Kimmy Jin knows she so painstakingly put together (nights spent scribbling in a notebook and tapping at keys, a determined redhead at her side). And it's amazing to her that one person had seen that after only a single meeting—even when it had been disguised under the surly, tattooed, and pierced persona that was Beca Mitchell. And, even more amazingly, Chloe Beale had never felt the need to change or alter or look down on that package, unlike every other person in Beca's life (Kimmy Jin very much included).

If that's not love, Kimmy Jin thinks, she doesn't know what is.

But she soon finds out what it isn't.

It isn't Beca running up to puppy dog boy and kissing him in front of the entire crowd—Kimmy Jin is quite sure of that.

She shouldn't be surprised—not even slightly—because if there was one thing she'd known about her roommate from their very first encounter, it was that Beca Mitchell was a complete and utter moron who cared far too much about not caring.

Kimmy Jin wipes her hands clean of the whole thing.

There is no cure for stupidity, she thinks, and Beca Mitchell is infected with the worst sort.

(Self-delusion—in which you have no one to blame but yourself).

Turns out, it's not that easy.

It's a week later when Kimmy Jin knows she has been so thoroughly affected by her stupid roommate (and the terrible decisions the girl makes) that she has been damaged beyond repair.

Dr. Carlson has given them an easy review quiz to help boost some of the grades before the final (not that Kimmy Jin needs the help, of course), but as she flies through the various problems, one of them gives her pause.

Find the equation of the tangent line to the graph of f(x) = √(x^2+3) at the point (-1 , 2).

It's not the solving of the problem that gives her hesitation (of course it's not; it takes her about three seconds to get the solution: x + 2y = 3)—it's afterwards, when she stares at the paper for a full minute and really thinks about it.

Because it's sad—this problem—sad that this function and its tangent line only meet at that one point for all eternity, and will never meet again.

Without any conscious thought at all, she considers that if Beca is f(x) = √(x^2+3), then love is x + 2y = 3. And Kimmy Jin thinks that Chloe Beale might just be (-1 , 2)—the only point where those two things will ever, ever meet.

And goddammit, but tears prick at her eyes at that and it's just 100% unacceptable that she has been reduced to this level of pathetic.

Something clearly needs to be done.

Because okay—yes—fine—she actually cares.

This is something she can admit to herself as she rushes toward her dorm after hurriedly handing in her quiz. Of course she cares about her white girl roommate and Chloe Beale and how they are the level of adorable that she's only ever seen in books and movies.

She cares because—even if she will never admit it to another living soul—she likes the Beca that Chloe brings out—likes the stupid, white girl with her big headphones and ugly clothes who gets excited about a cappella, of all things. Because when Beca is with Chloe she smiles in a way that turns her (the most cynical person Kimmy Jin has ever met) into someone who cares and loves and is almost annoyingly happy. And maybe, just maybe, Beca does something similar to Chloe Beale—because Chloe is always smiling and chatting away, but when she's with Beca, she turns into something softer and more content.

Kimmy Jin doesn't have a math metaphor for that—cannot reduce it to fractions and logic—it's just two people who make each other better in a way two numbers or functions or equations never could.

There's something beautiful about that.

And her imbecilic roommate is going to, in every single conceivable way, mess all that up.

…Unless Kimmy Jin tells Beca Mitchell something she's been dying to tell her roommate since day one.

"You're an idiot."

It's a bit dramatic, the way she bursts into the dorm room, all out of breath and angry. But it's rather effective as well, she thinks.

"A...excuse me?"

Beca is on her bed (of course), and the way she sits up with widening eyes gives Kimmy Jin a great sense of satisfaction.

"You are an idiot."

"W—what the hell, Kimmy Jin?"

"You are an—"

"I heard you! Jesus! But what the hell is your problem?"

"My problem is that you are an id—"

"Oh my fucking god! Kimmy Jin!" Beca's up now, and angrier than Kimmy Jin had ever seen her. Good. "I get it! What's with the goddamn verbal assault?"

"It deserves reiteration—your level of idiocy."

"I swear, Kimmy Jin, if you don't tell me what the…"

"You went for the puppy boy," Kimmy Jin says flatly, and that shuts Beca up quite effectively. "You went for the puppy boy when you could have had Chloe Beale."

"I don't—that wasn't—it isn't—"

"Oh, shut up, Beca."

Beca's mouth closes with an audible collision of teeth.

"Listen closely, because I will only say this once; Chloe Beale is your person—she is the one that completes your set—the one that keeps you from being null or undefined. She is the one that brings out the side of you that you're afraid to show, and that side of you is, in every conceivable way, better than the one you so enjoy projecting. And you've turned that down—you've run away from it—because it makes you scared. Everyone on this earth is looking for that. And you ran away."

Kimmy Jin nods, once, in a gesture of finality.

"That is why you are an idiot. That is why you will remain an idiot until you rectify your astronomical mistake."

She thinks maybe Beca will storm out, or yell at her, or kick their trash can across the room. But instead, her roommate drops back down onto her bed, and buries her head in her hands. And Kimmy Jin finds cursing, on the whole, uncouth, but she thinks Beca's response covers the situation quite neatly;

"Fuck."

"Quite."

"Shit!" Beca raises her head slowly and meets Kimmy Jin's eyes. "What… what do I do?"

Kimmy Jin drops her bag on the floor, and for perhaps the first time, smiles at her roommate.

The brunette looks a bit frightened.

(It's an appropriate expression).

The first course of action is easy; get rid of the puppy boy.

Kimmy Jin suggests doing it 'Gone With the Wind' style ('frankly my dear, I don't give a damn') because surely the boy would appreciate the movie reference. But Beca puts a halt on that idea.

(Beca, basically, is no fun. But at least she somehow gets the job done, eventually).

The next step involves an education in romance.

Beca miraculously lasts through four full episodes Pul-hauseu, but not a second longer.

"Oh, good god. Seriously, Kimmy Jin? Seriously? God! This is worse than the lamest movie."

Kimmy Jin, who has had to surreptitiously wipe tears away not once, but five times during the show, is ready to declare Beca incapable of romantic gestures.

"This is how you woo someone."

"I—oh my god—I'm not going to take Chloe to a freaking ice rink, Kimmy Jin. We're not going to glide around in the fog holding hands while cheesy music plays in the background. I mean, really? Really?"

With a long, suffering sigh, Kimmy Jin tears out yet another page out of her notebook, crumbling up the paper on which she had so meticulously taken during one of the most beautiful and romantic scenes in all of k-drama history. Whatever. Beca is unrefined. That's no big surprise.

"And clearly, you are the master of romantic gestures."

"Hey! I comprised an entire musical number around the Breakfast Club!"

"For the wrong person."

"Well… yes. Fine. But I'm… I can be… romantic, or whatever."

Kimmy Jin raises an eyebrow and hands Beca her notebook.

(She has a feeling they are going to be at this for a long while).

She's right.

Hours later, the floor is littered with crumpled sheets containing rejected grand romantic gestures, and Kimmy Jin is about ready to wipe her hands of the whole thing. Again.

"You are hopeless."

Beca groans from her spot on her bed; the sound is muffled by the pillow she has placed over her head.

"Yeah, well, your ideas blow."

"Would you prefer I supply you with a few pickup lines and wish you well?" Kimmy Jin drones.

"Abso-fucking-lutely." Beca peeks out from underneath her pillow. "I'm serious. Lemme have 'em."

She hesitates and her roommate laughs, throwing the pillow off. "Oh my god—they're like nerdy pickup lines, aren't they? Oh, god, please tell me you know math pick-up lines. Kimmy Jin, please. Please tell me that."

Kimmy Jin does not even consider complying with the ridiculous request.

Not that it deters Beca, who pushes herself off of the bed and grabs her laptop with more speed than Kimmy Jin had thought her capable of. A quick web search has Beca cracking up within seconds, her eyes wide with disbelief and amusement.

"'Hey, girl, let's make love like pi; irrational and never ending!' Oh, no. Dude, no! 'You must have been a square in a past life, because, baby, you got all the right angles.' No!"

Beca is practically rolling around on her bed at this point. Kimmy Jin rolls her eyes, and for the 342nd time that evening, regrets agreeing to help her hopeless roommate.

"Oh, yeah, because that's the way to go about confessing my love," Beca continues. "'Chloe, babe, I wish you were x^2 and I was (x^3)/3… so I could be the area under your curve. Dude—what does that even mea—?"

She has her back to the door, but Kimmy Jin immediately knows who has just entered the room by the stupid slack-jawed expression that distorts Beca's face (into something even less attractive than was typical).

And that person most definitely knows exactly what Beca's awful pick up line had meant.

"Chloe! I—uhh—hey?"

Kimmy Jin shoots out a quick prayer that the walls of their dorm were more sound absorbent than the sounds they heard from their sex-crazed neighbor would suggest.

"You—you love me?"

Son of a…

"Uh… yeah."

…bitch.

This was so much less satisfying than a romantic skate on the ice rink.

Or… it should have been. But Kimmy Jin finds herself staring at the scene before her (at the very intense, very prolonged stare that said so much without any words at all) with the same level of enthrallment that she had when Ji-Eun and Young-Jae had glided across the ice.

"Kimmy Jin do you think you might…maybe give us a moment?"

The words come from Chloe Beale, but the woman does not move her eyes away from Beca's for even a moment. Which is good, because Kimmy Jin would not have much enjoyed the snarky comments Beca surely would have later thrown her way had the DJ broken her gaze with the redhead for even a second to look in Kimmy Jin's direction. (She imagines the words 'creeper', 'stalker', and 'fangirl' would have been involved).

"Whatever," Kimmy Jin says as she hurries out of the room.

(It's difficult, but she manages to keep the too-large smile off her face until the door shuts behind her).

She doesn't, however, manage to get rid of that smile, and it's still in place when she returns to her dorm at an hour that's typically considered as being more morning than night. She doesn't try to hide the way it grows, either, once she opens the door to room (dark except for the lamp on Kimmy Jin's desk, so thoughtfully left on), and catches sight of the two women cuddled up in Beca's twin.

They're still fully clothed (thank, God), but the way Chloe curls herself around Beca (actually spooning the sarcastic brunette in a way Kimmy Jin finds hilarious and adorable all at once) tells her that her roommate has finally, finally, gotten it right.

It's several weeks later when Kimmy Jin takes her Calc II final.

(When she had left the dorm that morning, Chloe had given her a chipper smile and a genuine 'good luck'. Beca, in the middle of an end-of-the-year panic, had whined at her girlfriend to save the good luck for her and the psychology exam that was going to tank her GPA. And Kimmy Jin, as usual, had tried not to smile too much at their antics when Chloe had responded with a quick kiss and a whispered comment that had the brunette flushing in a way Kimmy Jin did not want to contemplate).

Dr. Carlson is a fair and forgiving professor, so even though the exam is moderately difficult, he gives a few extra credit questions at the end, and Kimmy Jin has to smile when she gets to the last one, because it's so very fitting.

Give an example of how the subjects learned in this year of calculus might be applied to a real life situation.

Kimmy Jin has thirty minutes before the end of the exam period. And she's not about to go back to the dorm room earlier than she said she would return (she'd learned that lesson very well a few weeks back, when her early arrival to the dorm had interrupted a 'study session' that had involved far less clothing than Kimmy Jin would have hoped).

It's quite a bit of time. More than enough time to give Dr. Carlson an answer that he, Kimmy Jin is sure, has never seen before.

Her smile grows as she puts her pen back down on the paper, and begins to write:

Suppose that a girl (let us define her as 'b') is represented by the function, b(x) = √(x^2+3)…

(Kimmy Jin gets ten extra credit points for her response.

It would be totally lost on her white girl roommate, but she emails a copy of it to Chloe Beale.

She knows the redhead will understand).