"Lexaaa," Clarke whined, helplessly looking around. Her entire kitchen table was filled with books, calculators and notes. "What does p xo–"
"That's a zero."
"P x zero. Why is differentiating p the same as differentiating f when p is just… and what is an abc doing there when it's– Lexaaa!"
Clarke's head was spinning. Lexa chuckled and reached out to point at several digits and letters on Clarke's sheet. "Don't bother with the abc right now, that's just an example. P(x0) is a point somewhere on the function f. Okay?"
Clarke weakly nodded, so Lexa continued. "Okay… This is just the Taylor series, Clarke, it's really no magic."
"What the hell is the Taylor series now?" Clarke whined again.
The brunette shook her head with an amused smile. "It's a representation of a function as an infinite sum of terms that, um… are basically calculated from the values of the function's derivatives at a single point. Hint – P(x). Got it?"
Clarke blinked at the brunette. Lexa huffed in mild frustration and bit her lower lip, trying hard to come up with a simpler explanation. "So… a function can be approximated by using a finite number of terms. Which is funny because a function usually has an infinite number of terms," Lexa explained and giggled again. Clarke shook her head, she was clearly missing the joke.
"That's why we use Taylor. This theorem gives quantitative estimates on the error introduced by the use of–" Clarke dropped her head on the table. "Clarke?"
"I'm listening," Clarke mumbled, "go on."
"Look, it's really simple. The Taylor series of a function is just the limit of that function's polynomials as the degree increases," Lexa raised her head and absentmindedly scanned the wall, "well, provided that the limit exists." She finished happily. Clarke didn't move. "Clarke?"
Clarke, her forehead still on the table, slowly shook her head again for the umpteenth time that afternoon. She really had no idea what Lexa had been trying to teach her. She simply had no idea. She'd been trying to follow and understand, really. Okay maybe she had been a bit distracted by Lexa's tight tank top, but most of the time, she had been trying. She weakly raised her head to look at a very bubbly brunette. It was obvious that Lexa was completely in her element.
"You're a great teacher, Lex. Really! … but I think I'll quit maths." If it had been about anything else than math, Clarke's heart would have broken when Lexa's face fell and she quickly dropped her eyes to the book in front of her with a light frown… but this was about math and Clarke was frustrated.
A moment of silence passed, until Lexa spoke again. "Why are you angry?"
"What?"
"You're frowning, which usually means that you're angry, and I don't…" Lexa flicked her fingers a few times, "I don't know why you're angry."
The blonde's features softened immediately. "I'm not angry… I mean, not really. I'm just really frustrated that I just don't get this Taylor thing… or math in general."
"Oh," Lexa nodded, quickly processing the new information. "But Clarke, look, it's really simple. It makes sense and you just… I mean… it's really beautiful because it–"
"Hey, Lex." Clarke said softly, laying her hand on top of Lexa's that had began to fiddle with a sheet of paper in front of her. She couldn't exactly tell whether Lexa was frustrated as well or just trying to defend something she really loved or was sad, but the brunette was clearly growing upset and a wave of swear words and insults against herself washed through Clarke's head. That was the last thing she had wanted when she asked Lexa for some extra lessons.
"Let's just go outside a bit," she suggested. "You know, clear our heads, and maybe try again tomorrow?"
Lexa sighed and looked back at the blonde with those puppy eyes that Clarke just couldn't resist. She knew that if Lexa asked her to climb the Empire State Building like Spider Man, or surf on a shark right now, she'd more than happily agree. Fortunately for her, Lexa just nodded and her lips curled up into a smile again. Clarke mentally high fived herself. Well, she mentally high fived herself after completely melting at the sight of a happy Lexa.
They decided to sit on a bench in the park where they had talked to each other for the first time. It was a sunny afternoon, but November was around the corner and Clarke was glad that she had thought of bringing a blanket.
"Here," she said and gently put it around the brunette's shoulders when she noticed the girl was slightly shaking. Lexa shot a thankful smile in her direction and snuggled into the warmth.
They sat in silence for a while, just content with the situation, enjoying each other's company, both lost in their own thoughts.
"Lex?"
"Hm?"
"Can I ask you a question?"
"Okay."
Clarke took a moment to phrase her thoughts. "Have you ever been in a relationship? Or, you know," she quickly added when she realized that Lexa wasn't really one to quickly trust a person or grow close to someone, given that this relationship would come with a package that not everybody could or wanted to carry, "been interested in someone? I mean, liked someone?"
Lexa slowly started to fiddle with one corner of the blanket she was wrapped in, and Clarke waited patiently.
"Yes um…" the brunette paused and took another moment to consider her answer, "well not in a relationship but there was… well I was…" she stopped and Clarke turned her hand to offer Lexa her palm, just in case. The girl automatically took it, and Clarke bit her lip to not let out the huge smile, well aware that Lexa probably hadn't even realized that she had taken the blonde's hand.
"Her name was Costia."
Clarke knew that this really wasn't the time to explode from happiness over the female reference, but she couldn't help but feel a little fuzzy inside.
"She was… nice. At first, at least. It was the last year of High School, and I had just changed schools because people… because they weren't…" Lexa was helplessly trying to come up with words.
"I understand, you don't have to say it." Clarke reassured her and Lexa nodded, bit her lower lip for a second and then continued.
"Costia was really nice to me. She talked to me a lot and she didn't mind that I was… different. I never told her though. Um… I think we were friends. I really liked her. I told Anya one day and she kept teasing me about my girlfriend and I said we're not girlfriends, but she said that what I was feeling wasn't what friends usually feel. It was really confusing for me." She let out a puff of air. "One day she took me to a football match and when one team scored the final points, I… it was so loud."
She let go of Clarke's hand to fumble with the blanket with both hands, and Clarke noticed how her breathing was picking up on speed. Lexa squeezed her eyes a few times before she continued.
"And I just freaked out, and Costia laughed at me and said I was a baby. She kept making fun of me and the next thing I remember… I was sitting on the ground, the match was over, and Anya was sitting next to me. Apparently someone had called her, and Costia was gone. I sent her a lot of texts, asking her what happened but she never answered, and at school, she always avoided or ignored me after that day." Lexa finished sadly.
Clarke didn't know what to feel or think. She was angry at Costia, she was aching for Lexa, and she was thankful that the girl had Anya in her life. She was still looking at Lexa, and Lexa was still looking at her hands. The blonde reached out, slowly to not startle the other girl, and gently tucked a strand of brown waves behind a tiny ear.
"I'm sorry, Lex. I'm really sorry that some people were so mean to you. You…" she sighed, "God. You deserve so much better than that. You're such a wonderful person, and I really wish there was a way for you to see this. You mean so much to me."
Lexa turned her head to look at Clarke, and Clarke just looked back for a long moment. She could see that Lexa's mind was racing, that she was desperately searching Clarke's face for any hints of what she was thinking. The blonde braced herself for the next question, because she knew exactly what was about to happen next.
"Why are you looking at me like that, Clarke?" Lexa asked with a small frown, clearly clueless of what was going on in Clarke's head. The blonde took a deep breath.
"I would really like to kiss you right now, Lexa."
