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Chapter 10 - Chapter 10: Equations of Understanding and a Bookstore Encounter

The quiz arrived with Mr. Tanaka's usual flair—a mischievous grin, a dramatic flourish of papers, and a tone that hinted at both challenge and encouragement. Five problems, each more intricate than the last. It wasn't just math; it was a test of intuition, insight, and endurance. The classroom quickly filled with the rustle of pages, the scratch of pens, and the quiet groans of mental gears grinding.

Alex felt oddly at peace. He always did when confronted with a problem he could unravel. Math made sense. It was clean, structured, unambiguous. He scanned the first question, already mapping out an approach in his head. Beside him, Katarina was hunched over her own sheet, her silver braid slipping forward like a curtain, shielding her narrowed eyes.

"Так, это определённо интеграл по частям, но с подвохом," she murmured, pen hesitating. "Нужно правильно выбрать u и dv, иначе это превратится в бесконечный цикл. Классическая ловушка."(Ah, this is definitely integration by parts—with a trick. If I pick the wrong u and dv, it'll loop forever. Classic trap.)

Alex, who'd reached the same conclusion, didn't speak. He just shifted his paper slightly, enough that, if she glanced sideways, she might catch his setup. Not an answer—just a signpost. It felt fair. Maybe even right.

A few beats later, she let out a soft breath, almost a laugh. "Ах, вот оно. Если взять логарифмическую функцию за u… Да, так должно получиться."(There it is. If I take the logarithmic function for u… Yes, that should work.) She began writing with renewed confidence.

They worked like clockwork after that—him outlining frameworks, her fine-tuning the equations. It reminded Alex of their history project: unspoken coordination, one mind anticipating the other.

The third question was a beast: a related rates scenario with a sliding ladder and shadows stretching under a setting sun. Katarina stared at the triangle-laden diagram, her pencil tapping against the desk.

"Чёрт, я запуталась в геометрии. Эти треугольники… они меня с ума сведут. Где здесь подобные фигуры?"(Damn it, I'm lost in this geometry. These triangles… they're driving me crazy. Where are the similar figures?)

Alex didn't need to know every word—her tone said enough. He leaned slightly closer, lowering his voice. "Try looking at the small triangle formed by the shadow's tip and the base of the ladder. Compare that to the whole structure—the proportions might help."

Her gaze shifted where he indicated. A few seconds passed.

"Точно! Подобные треугольники! Как я сразу не заметила? Спасибо, Накамура-кун."(Exactly! Similar triangles! How did I not see that? Thank you, Nakamura-kun.)

She used Japanese for the thank-you. Somehow, that landed deeper than any compliment.

"Teamwork," Alex said lightly, trying not to show how her smile disarmed him.

They turned in their papers with minutes to spare. Mr. Tanaka beamed as they approached.

"Well done, 'Power Duo'!" he called. "Knew you'd blaze through it. Can't wait to grade this one."

Katarina flushed but didn't grumble. Alex noticed. She returned to her seat with an almost shy smile tugging at her lips.

As they waited for the bell, she leaned in, voice low. "You're… very fast with calculus. It's kind of amazing."

Then, in Russian, half to herself:"Он не просто умён, он… пугающе интуитивен в математике. Как будто он видит решение ещё до того, как начинает считать."(He's not just smart—he's frighteningly intuitive with math. Like he sees the answer before doing the work.)

Alex met her eyes and smiled faintly. "You're pretty amazing yourself. Your algebra work is sharp."

She didn't answer right away. Just nodded, thoughtful, and the silence between them felt earned, like a shared language that didn't require words.

Saturday afternoon arrived like a gift. For once, Alex had no obligations. No projects. No practice. The city felt open and light. He wandered to his favorite bookstore—a quiet, multi-level retreat he visited often.

On the third floor, he drifted into the foreign literature section. Russian authors lined one wall, their names like echoes from his grandfather's study. He reached out, running a finger along the worn spines, when a familiar voice drifted toward him.

"Excuse me," said the voice, in careful Japanese. "Do you have any collections of early 20th-century Symbolist poetry? Valery Bryusov, specifically?"

Alex turned. At the counter stood Katarina Volkov, casual in jeans and a blue sweater, her braid looser than usual. Her presence here was unexpected, but somehow not surprising.

The clerk looked lost. "Брюсов… Кажется, этот продавец даже не слышал о нём. Какая жалость. Я так надеялась найти его здесь," she muttered with a sigh.(Bryusov… The clerk doesn't even know him. What a shame. I really hoped to find him here.)

Alex stepped forward before he could think twice. "Bryusov's tricky to locate here. Sometimes you'll find him tucked in with the Acmeists—same period, different ethos. There's usually a small Silver Age section off to the side."

She turned, startled. Her eyes widened. "Nakamura-kun! I—hi. You're here?"

The clerk gave Alex a grateful look and gestured vaguely toward a nearby shelf.

"Yeah," Alex replied casually. "I come here a lot. Nice to see a familiar face among the pages."

"Он опять здесь. Как будто преследует меня. Хотя… он знает Брюсова. Это… удивительно," she whispered to herself, clutching her bag.(He's here again. Like he's following me. But… he knows Bryusov. That's… unexpected.)

Alex smiled, pretending not to have caught her murmur. "So—you like Bryusov?"

Her face lit up. "Yes! His language, his imagery… I only know a few poems, but they haunt me. Especially 'The Pale Horse.'"

Alex nodded. "That one's intense. So much foreboding packed into every line. It's hard not to feel the world unraveling behind his words."

They walked together toward the indicated shelf. The section was tiny—Blok, Bely, Akhmatova, but no Bryusov. Katarina scanned it anyway, fingers trailing over the spines.

"Похоже, сегодня не мой день. Ничего нет," she sighed.(Doesn't look like my day. Nothing here.)

Alex crouched near the bottom shelf and spotted an old volume tucked behind a stack—"Echoes of a Fading Empire." He flipped it open. Bryusov was there, nestled between Sologub and Balmont.

"Found something," he said, holding out the book.

She took it like a relic. Her fingers lingered on the cover, brushing the title as if to confirm it was real.

"Не может быть! Это… это именно то, что я искала! Как ты его нашёл?"(No way! This… this is exactly what I was looking for! How did you find it?)

"Just a lucky glance," Alex said with a shrug, though his practiced eyes knew where rarities often hid.

She clutched the book to her chest, her smile radiant and unguarded. It softened something in him, something usually braced against surprises.

"Thank you, Nakamura-kun. Truly. This means more than I can say."

"I'm glad," he said. And he was. Deeply.

They stood quietly for a moment. The quiet between them was thick with the kind of energy that comes after discovery—shared, electric, delicate.

Alex hesitated, then took a breath. "Since you've found your treasure… there's a little café downstairs. Good tea. Maybe we… talk about Bryusov?"

It sounded awkward. Academic. But it was all he could manage.

"Он… он приглашает меня на чай? После того, как помог найти книгу? Это… неожиданно. Но… почему-то… приятно," she murmured, eyes flicking to the book.(He's inviting me for tea? After helping me find this book? Unexpected. But… strangely nice.)

Her smile was small, but real. "I'd like that. Very much."

As they descended together, the scent of paper and tea mixing in the air, Alex felt something shift. The calculus problems, the poetry, the bookstore shelves—it all added up to something unexpected. Something unfolding. Something human.

[End Chapter 10]

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