Chapter 14
Ryan
“Let’s talk about linear approximation,” I announce to my class on Monday afternoon. “What’s the point of making a linear approximation to a curve?”
I’m met with silence, which is expected. The girls in the front look attentive, batting their lashes, and the guys kind of slump back in their seats, hoping I won’t call on them.
“The linear approximation is the same as finding the tangent line to the curve,” I begin. “Which is what we’ve been doing all semester. Thankfully, this is a process we’re familiar with. But why would we want it?”
More silence. They need a little warmup.
“All right, let’s back up. What is the tangent line?”
The whole class makes kissing sounds back at me.
“Right, right. It’s the line that kisses the graph of the function, barely touching it and then moving on. So why do we want to find that?”
Allison, a girl in the front row, raises her hand. “To find the tangent line to the curve?”
That’s what I just said. But I nod. “Yes. And why would we want that?”
“To find an approximation for the function?” Cruz, a veteran in the back corner, calls out.
“Exactly. But why?”
I wait. Usually when I wait, the answer comes.
Kelly, a shy Asian girl in the middle, raises her hand. “Because it’s easier to use a linear function than the complicated functions.”
“Yes!” I point at her, and she blushes, and the girls in the front row scowl at her. I want to roll my eyes, but I don’t. “Imagine you’re on a desert island.”
“What book would you take with you?” James, the resident class clown, calls out to me from the back row.
“East of Eden. But that’s not the point.
We’re not sitting on this desert island, reading books.
We’re trying to make a raft to get off the island.
And in order to build this raft, one critical part of the computation is the fifth root of thirty-three.
Unfortunately, you didn’t bring a calculator.
But you did bring your calculus knowledge. ”
Blank stares look back at me.
“It’s a joke,” I say. “But we can approximate that value by finding the tangent line to the function Y equals the fifth root of X at X equals thirty-two.” For the next few minutes, we work on the calculus to find the equation of the tangent line, and then I go to the computer and pull up the online graphing calculator.
“So let’s graph the original function, the fifth root of X, and then the equation of the tangent line we just found, Y equals one eightieth X plus eight over five.
” I move the picture over to the side, where X is thirty-two, and zoom in.
“Look how the graphs are overlapping. And as long as we stay close to our X value of thirty-two, the tangent line is an incredible approximation for the original function. So how could we use this to find the fifth root of thirty-three?”
A moment’s pause, and then Jim calls out, “Plug thirty-three into the equation of the tangent line.”
Yes. And this is the moment I live for. The moment when it clicks.
“Exactly. And THAT is a computation we can do without a calculator. Granted, it’ll take us back to some long-division from fifth grade, but it’s still better than nothing.
And even if it’s not exact, it’s really close.
” I look up at the clock and notice that there are five minutes left, but there isn’t much I can really accomplish at this point.
“Let’s end here for today. I’ll see you all on Wednesday. ”
The students gather their belongings, and I log out of the computer. As I’m packing up my backpack with my markers and iPad, a hush comes over the room.
“What’s going on?” I ask as I lift my head, then see Claire standing in the doorway. My treacherous heart leaps at the sight of her with her auburn hair around her shoulders, wearing a green floral dress. I told her last year that green looks amazing on her, and I’m holding on to that right now.
Stop it, Ryan. No matter what I’m trying to tell myself—that I need to move on—my brain has not relayed the message to my heart.
“Hey, Professor Beaumont,” I say casually, raising a hand in greeting.
“Hey, Ryan,” she says back. She glances at the girls in the front row, who I now notice are sending daggers with their eyes.
Don’t worry, girls. I’m not the one she’s interested in.
She looks back at me. “You’re done for today, right?”
I nod. “All done teaching.”
“Can we talk? About, um…” She glances at the girls and back at me again. “About the tutoring center.”
Ugh. Not again. “Oh. Sure.”
My polite students are waiting at the doorway to leave since Claire is blocking the path. She notices and awkwardly steps back. “I’ll just, uh, wait for you. At the office.”
“Okay. See you there.” I hold up a hand in farewell, and she scurries away.
“Oooh,” James says, coming up to my podium. “You and Professor Beaumont?”
“What?” I can hear my voice sounding panicked. This is how rumors get started, and I don’t want to damage her reputation. “No. No way. She’s engaged.”
“To you?”
“Obviously not.”
He shrugs. “Well, from here, it looked like more than that.”
I shake my head. “We’re just good friends.”
“Well, good friends can be tangent to romance, am I right?”
I sigh heavily. “James, don’t use calculus against me.”
He just laughs and walks away. “See you Wednesday, Professor.”
Great. Now my students think something is happening between me and Claire. I’ve got to rein it in or things are just going to spiral out of control.
Back at the office, Claire is waiting in front of my cubicle and fiddling with her hands. No, not her hands. Her ring.
“Hey!” she says brightly.
“Hey.” I walk past her and set my backpack down on my chair, then turn to face her. “Conference room?”
“Yeah, that’s probably best.” For someone who just wants to talk about a tutoring center, she’s acting weird. I follow her to the conference room and take a seat at the round table, but Claire closes the door before sitting down. Strange. We usually leave the door open.
I fold my hands on the table. “Have you been able to get a location yet?”
“I didn’t want to talk about the tutoring center,” she says quickly.
I furrow my brow. “Okay,” I say, drawing the word out. “What are we talking about?”
“Us.”
My mouth drops open slightly before I catch myself. Is this the moment? Did she finally realize she shouldn’t be with Zach and should be with me? My heart rate picks up speed. It has to be! Why else would she want to talk to me in private?
I swallow hard. “What exactly about us?”
She sighs and looks up at the ceiling. “This is so awkward. But I feel like something is weird between us. I sent you that picture on Friday night, and you just sent a thumbs up, and you never responded to how your date went. And things have just felt…distant.”
“Distant,” I repeat.
“I feel like we haven’t been able to, you know, be us,” she continues. “Is it because of the engagement? Because I don’t want to lose you as my best friend, even if I’m getting married.”
I need a minute to catch up. So she’s not breaking up with Zach. She’s just asking what happened to our friendship. A pang hits my chest at the realization.
Use your logical brain, Ryan. You can handle this conversation.
I breathe in deeply through my nose. It is because of her engagement, but I have to be careful not to betray my true feelings. “Yeah, I guess.”
“I know you don’t approve of Zach,” she says softly.
“But if he makes you happy, that’s all that matters,” I reply. The words taste bitter on the way out, and I want to throw up after saying them.
She presses her lips together, pausing before she smiles. “He does.”
Was that a pause of hesitation? Or a pause where she’s thinking about how much she loves him?
I’m going to be sick.
“I just want to be respectful of him,” I say carefully. “I don’t know how a man would feel about his wife being best friends with another man.”
Actually, I do know. If I were married to Claire, and her best friend was another man… Yeah, that would never fly with me. When I do get married, I want to be my wife’s best friend, and I want her to be mine.
She waves her hand. “Zach doesn’t care. He just said this past weekend that he’s glad I have someone else to talk to about my problems.” Her eyes widen, like she realizes how bad that sounded.
“He doesn’t want to hear your problems?” I ask, leaning into it.
“No, of course he does!” She laughs lightly. “But he has so much going on with the app and everything that I don’t want to bother him.”
Sure.
She speaks faster now. “Anyway, I just want things to go back to normal with us. Back to how it was before I got engaged. Don’t you think we can do that? If Zach had a problem with it, he would’ve said something before. But he really doesn’t mind. So you’re worrying over nothing.”
I want to say no. I want to tell her there’s no way I can just be her friend when she’s married. That everything will change between us when she’s going home to someone else, and all I want is to have her by my side.
But I can’t do that to my best friend.
So instead, I say, “Sure. We can do that.”
The smile on her face warms my heart, but it sends a pang through my chest. She stands and opens her arms. “Should we hug it out?”
I snort a laugh and stand. “Sure. Let’s hug it out.
” I wrap her in my arms and take advantage of the opportunity to hold her against me.
It’s a friendly hug, sure, but of course I’m thinking some not-so-friendly thoughts.
Like how good it feels to hold her, and how well she tucks in against me.
I could lean my head down and kiss the top of her head… but I won’t. Of course I won’t.
My head tells me to back away, but Claire’s arms are wrapped tightly around my waist, and she’s not letting go.
It’s almost like she’s settling into me, too, her cheek resting against my chest. I hope she can’t tell how hard my heart is pounding.
I let myself imagine, just for a moment, that she is mine and no one else’s.
That there’s no one else she’d rather have wrap their arms around her.
Because right now, it almost feels true.
Her arms stiffen, and she lets go in an instant. I release her, and she takes a couple steps back, smoothing her hair behind her ear. “So, um, good talk.” She nods at me and waves, then rushes out the door. “See you later!” she calls on her way out.
“See you later,” I call back. With a sigh, I pack up my things and head out.