Work Header

Triangles And Other Victims Of The Apocalypse

Work Text:

“Teach me something,” Ellie says one evening.

Joel looks up from the shiv he’s jury-rigging. Ellie is slumped against the shell of a car, legs folded up in front of her, hands clasped. The firelight dances over her face.

He doesn’t answer as he ties a pair of craft scissors to the end of a pipe. The twine moves easily in his hands, sailor’s knots come as natural to him as breathing.

To her credit, Ellie doesn’t press him. She’s got a good head for people; she worked out pretty quick that sometimes Joel doesn’t want to talk.

Joel sets down the shiv. Ellie looks up at the sound.

“Like what?”

Ellie shifts slightly, evidently pleased that he’s being agreeable for once. It’s a little fucked up that she’s come to expect his being mean. But, then again, everything about Joel’s life right now is fucked up.

“I dunno.” She bites her lip, gaze cast off into the shadowy wreckage they’re sheltering in. “Something you learned in school, or whatever.”

Joel grunts. Some might construe that as not wanting to answer, but Ellie knows to wait. He’s not sure if he’d’ve been able to handle any other kid for this long.

“Whaddyou know about triangles?” he says finally.

Ellie’s face scrunches briefly. “Shitall,” she declares.

Joel huffs out something like a laugh. It’s been a while since he’s been anything but too tired to laugh. Weirdly, the open wastelands filled with undead seem to be doing him some good.

“Right.” Joel reaches for his pack, rooting around for a blunt object. He comes up with the Swiss Army knife that he looted from a merc a few years back. Ellie watches him with thinly veiled interest. She tries her best to be a moody tween, but there’s a kid under there that’s filled with wonder. Then again, it can’t be easy to be a kid in this world. It’s not like she had much of a choice but to form that protective shell.

The ground is thick with the kind of dust and dirt that twenty years of abandonment breeds. Joel sketches out a right-angled triangle in the grit.

“What kind of triangle is this.”

Ellie frowns. “There’s more than one?”

She pretends not to know things like this, just to antagonise him, but she looks genuinely confused right about now. Makes sense; geometry isn’t really a major concern in her life.

“Yeah.” He squints for a second, dredging up muddy recollections of his own school days. “Equilateral,” he says, drawing it. “Isosceles.”

Ellie peers at the rough diagrams. “Equilateral’s sides are equal.”

“Yup.” A part of Joel wants to grin and call her a smart kid—‘cause she is, she’s fucking sharp—but there’s still a weight in his chest that he hasn’t been able to shake, not for two goddamned decades.

He brushes the dust off the end of his knife, instead.

“Isosceles has got these two,” Ellie says, mercifully ignoring Joel’s silence. She’s looking at the three wobbly triangles like they hold the answer to life.

“And this one has…” she trails off, eyes narrowed at the right-angled triangle.

Joel waits for a moment, just to see if she gets it on her own, then reaches out to add a quarter-square at the right angle.

“Huh?” Ellie says quietly, then, “Oh!”

A smile creeps across Joel’s face, unfamiliar but not entirely unwelcome. “You got it?”

“It’s got a right angle,” she says triumphantly, sitting back. “Ninety degrees!”

“Mhm.” Joel looks at the diagrams briefly, then at Ellie. She can take trig, he figures. He brushes away the triangles with the heel of his hand, then draws a larger right-angled one.

“Now, if we said that this side—” he labels it with an a— “was a units long.” He marks out the next side. “And this one was b. And this was c,” he says, labelling the hypotenuse. “Can you think of any relationship the sides might have?”

Ellie leans forward again to study the drawings. Her brow furrows. Joel lets her think for a moment.

“No,” she admits, looking put out.

“Didn’t think you would,” Joel says. It’s not a dig, and Ellie can obviously tell, because she sticks her tongue out at him.

“Why’d ya ask, then?” she challenges.

Joel chuckles again, lowering his head slightly. “Just makin’ sure I’m not rehashing something you already know.”

“I didn’t know there were three types of triangles five minutes ago, dude, I’m not gonna know that.”

“But you know how to pop a clutch,” Joel mutters.

It takes a moment for Ellie to parse what he’s said, but then she snorts and laughs. Her whole face is alight with her amusement. “You weren’t fuckin’ complaining when I played getaway driver!”

“Course I wasn’t, I was too busy almost gettin’ mauled, you little shit,” Joel snipes back, smiling. He shakes his head, going for put-upon. “You know how to drive but you don’t know how to put on a goddamn seatbelt.”

Ellie shrugs. “I mean, driving is pretty intuitive,” she says brightly. “Move the wheel; move the car. The seatbelts were, like, hidden, man.”

“Not really,” Joel says. He’s as close to unfettered happiness as he’s been in ages. His cheeks kind of hurt, and it’s only been a couple minutes.

They both must realise this at the same time, because they sober unprompted.

“Triangles,” Ellie reminds him, after a couple moments of quiet. Joel grunts to the affirmative.

He breathes for a second, gathering himself, then says, “D’you know what a square number is?”


“Right. Well, it’s—hm.” He frowns, trying to think of an explanation that makes sense. “What’s four times four?”

Ellie pauses, then says, “Sixteen.”

“Yeah.” Joel shifts slightly, stretching. “On a square, the area is the length of one side times another.”

“Like a square foot,” Ellie says, visibly puzzling through the math.

“Mhm. So you can say that four times four is four squared, ‘cause.” Joel stops up short. It’s been a long time since he’s had to explain maths to a kid; he’s not sure how to word it.

“’Cause that’s what you do for a square?” Ellie finishes for him. Despite—or perhaps because of—the world she’s grown up in, she’s a goddamn quick learner. Her brain’s always moving a mile a minute. It’s a blessing and a curse.

“Yeah,” Joel says, grateful for the save. He traces his thumb over the seam on the Swiss Army knife. “Any number times itself is a square number.”

Ellie nods, brow furrowed. “’Cause if you had a square with sides that long, then that’s how you’d find the area.”

“Yup.” Joel shifts his focus to the triangles. Ellie follows suit. “So if you get a, and square it,” he says, tracing out the equation in the dirt. “And add b squared… then you get c squared.” Joel punctuates the end of his sentence by scratching out an equal sign. Ellie watches, still wonderstruck.

“So if you had, like. If you already knew how long a and b were, then you could figure out c?” she finishes, leaning forward. Her eyes flicker up to meet Joel’s.

He gives her a tight smile. “Yep.” He wants to say more—wants to follow that up with an encouragement, but the words stick in his throat. He coughs.

Clearly aware of Joel’s inner turmoil, Ellie glances away, giving him some small amount of privacy to regulate his breathing. Lord, but she’s a sharp kid.

The fire crackles, nestled in the makeshift pit that they created. Joel stares at a spot beside it, watching the purple gather in his vision. His chest feels tight.

There’s a quiet rustling as Ellie moves slightly, drawing her legs up to her chest. Joel glances over to her, eyes skidding over her face for just a moment. She quickly veils her concern, but Joel can see it in the way she’s looking at him all intent, tracking his every move.

Joel considers with no small amount of trepidation that he needs to say something at some point—he can’t just turn over and go to sleep. Not with Ellie worried like she is.

(He wonders, in some guarded part of the back of his mind, when his concern for Ellie became anything more than self-centred. When she stopped just being cargo.)

But Ellie gets him.

“Thanks,” she says, real quiet.

Joel meets her eyes, earning himself a nervous smile.

Ellie looks so fragile like this: the cuffs of her jacket pulled up around her palms, legs folded up, her face young and smooth in the orange light. It’s both impossible and easy to believe that this girl, so small but so spirited, is the key to saving the world. There’s a scab on her chin from where she scraped herself on a tree branch. There’s an infected bite on her arm.

“Yeah.” The lone word, surely insufficient, rasps low in his throat. His mouth feels numb.

Ellie’s smile is a bit braver this time.