Neville Longbottom had been rereading the same passage, brow increasingly furrowed with each attempt, for at least fifteen minutes, and he was beginning to suspect that it wouldn’t make any more sense to him if he spent another hour trying to figure out what in Merlin’s name the Fibonacci series was. Before him was a circular table covered in textbooks, library books, and loose sheets of parchment. In front of him, his Herbology textbook lay open to a page containing several complicated-looking diagrams of a pineapple. Near his elbow was an ancient tome entitled Studyes of the Goldenne Relatyons of Phi, which was in the unfortunate position of both being precariously balanced at the edge of the table and having an uncapped bottle of ink sitting atop it, but he did not notice this.
Sighing heavily, Neville weighed his options. He could never get an E or an O on his essay if he didn’t include some of this information. Not writing a decent essay was out of the question; he would sooner face the fury of, well, of Professor Snape, than the disappointment of Professor Sprout. Maybe he ought to find Hermione and ask her to explain it to him. This posed a slight problem, as he didn’t know where she could be found at the moment; he was pretty sure that, for once in her life, she wasn’t in the library.
Just as Neville looked around to double-check this conjecture, Harry walked through the wooden double doors, a cross expression on his face.
–Hey, Harry,†Neville said, as loudly as he dared. Harry, who didn’t seem to hear him, continued walking. –Harry!â€
Harry jerked his head slightly, as if he was being woken up. His eyes found Neville, and he stopped. –Oh. Hi.â€
–Uh, do you know where Hermione is?†Neville inquired.
–Gryffindor Tower,†Harry muttered gruffly, now frowning down at nothing whatsoever, –doing Ancient Runes.â€
–Oh,†said Neville, heart sinking; he should have known that she would have work of her own to do. He really didn’t want to bother her. Harry probably wouldn’t be able to help much, but it was worth a shot. –Did you do the Herbology essay, Harry?â€
–…what?â€
–The--the…†Neville broke off. Harry didn’t seem to be hearing him; he was obviously under more than enough stress from his own OWL studying. –Never mind.â€
–Right,†Harry said distractedly. –Bye.†He walked over towards a secluded corner where Neville knew there were a few empty tables, although there were several lines of bookcases blocking it from sight. Neville groaned inwardly. If only he had taken Arithmancy; that would have made this so much easier--
–Neville? Is that you?†came a singsong voice from behind him.
He jerked around, and in doing so, accidentally elbowed the dusty old library book off the table. The ink bottle was, of course, upset, and as the two objects landed with a thud on the floor, Neville saw that the ink had splattered all over the book. He let loose a profanity and immediately cringed, half-expecting Gran to swoop down and smack him across the arm for swearing.
–Are you all right?†Luna queried, popping out from behind a bookshelf.
–Uh. Yeah, I’m fine. It’s just--I knocked the ink over--†He quickly pulled out his wand, knelt to the floor, and tapped the ink-covered book. –Tergeo,†he pronounced, though without much conviction. Most of the liquid ink disappeared, but several large black stains remained. He grimaced; he knew he didn’t have much aptitude for spells that had anything to do with cleaning or organizing, and now he was in trouble. Even quickly re-shelving the book wasn’t likely to prevent Madam Pince from somehow knowing who the offender had been.
Smiling slightly, Luna outstretched her hand. Neville gave her the book; she drew out her wand from where it had been resting above her ear and tapped the front cover, muttering, –Scourgify!â€
As she handed him the now-spotless (or as spotless as anything over three hundred years old can be) book, she glanced at its title. Her eyebrows climbed an inch up her forehead. –Neville, why do you have an Arithmancy book?â€
–My Herbology essay--patterns of phyllotaxy, er, that is, leaf growth…well, apparently it has something do with these mathematical…I don’t really know,†he confessed. –It mentions these things called ‘phi’ and--â€
–Really? The Golden Ratio?†Luna asked, surprised. She opened the Arithmancy book and began flipping to random pages.
–Yeah, I think so, only that book about it was full of very odd-looking symbols and words I didn’t know, so I gave up on that and just tried to figure it out from my textbook…Hang on,†Neville said suddenly, watching her lean in to read the small print beneath a picture of a rectangle split into two sections. –Luna, d’you take Arithmancy?â€
Luna nodded, poring over the book. –Interesting,†she said absently.
Of course! Why hadn’t he thought of this before? He should ask an Arithmancy student; that’s what he should have done in the first place. –Hey, Luna?â€
–Hmm?â€
–Could you help me understand this?â€
For a moment, his request didn’t seem to have registered; she was too absorbed in what she was reading. Then she looked up slowly and smiled. –Of course I will. Is that what was making you so frustrated, before?â€
–Before? I was…well, I s’pose I was a bit frustrated...†He stared at her, confused. –But how--you weren’t there. Were you?â€
–No, it was just your voice, when you were talking to Harry.†Her eyes flicked over to where he was sitting, hidden by bookcases. –I wonder what he’s upset about.â€
–OWLs, I would expect,†said Neville uncertainly; it seemed the obvious answer to him, but then again, Luna tended to notice things that he thought most other people didn’t…or that he didn’t, anyway. He had long since come to the conclusion that she was at once the most and least observant person in the world, but it had never occurred to him to mind this, particularly since it made her such refreshing company compared with the rest of the school.
Luna simply gazed at him, which made him feel self-conscious. He cleared his throat and quickly began, –So…well, it starts here.†He pointed to a heading in his Herbology textbook, and she leaned over to see. –And then it’s the next page and a half. Not all of it is Arithmancy, but the things I don’t understand, like phi, and the ‘Fibonacci Sequence,’ whatever that means…â€
–The Fibonacci Sequence?†Luna repeated keenly.
–You know what that is?â€
She nodded dreamily. –It’s a series of numbers. It might be the most famous recursive series known to Arithmancers, actually. Each Fibonacci number is based on the numbers that came before it. That’s what makes it recursive, you know.†At Neville’s uncomprehending look, she smiled and took a butterbeer cork out of her pocket. –I was going to add it to my necklace,†she explained cheerfully to a bemused Neville, placing the cork on the table. –There. That’s the first number of the Fibonacci series: one.â€
The butterbeer cork sat there motionlessly, as inanimate objects are wont to do. It did not elucidate any of the mysterious Fibonacci-and-plant-related textbook passage, not even when Neville stared very hard at it.
–One is also the second number in the Fibonacci series,†Luna continued, and then waved her wand in a double loop, murmuring, –Duplicous.†Suddenly there were two corks where there had only been one cork before. The second cork, which was very faintly translucent, rolled slowly away from the first until there was a small space separating them. –I don’t know why, really; Fibonacci could have started with any two numbers. Maybe he thought that starting with a pair of ones was what made the whole series so beautiful, in a number-ly sort of way.†She considered this, head tilted to one side.
–So,†said Neville, trying to follow her explanation, –so those corks are…numbers?â€
–Well, actually, I believe the corks are corks,†Luna told him matter-of-factly, though he could see the laughter in her eyes. –Or the first cork is; I’m not sure about the second. It doesn’t look like it’s entirely there, does it? I’m not very good at the Copying Charm.â€
–It’s not bad. I can hardly tell,†Neville assured her.
–That is nice of you to say,†she said, smiling. –And, yes, the corks do represent numbers--the Fibonacci numbers. One, and then one…and then…Duplicous!†she said again. This time, each cork transformed into two, both of which moved slowly to the right-hand side of the first two, a short space away from the second cork, but quite close to each other.
Something had clicked: the gears in Neville’s head were at last turning. –The third Fibonacci number is two,†he said.
–Yes, it is. I copied each of the ones, and put them together, and got two,†Luna recapped. –That’s how the Fibonacci series works, you know. Copy the last two numbers you’ve got, add them together, and that’s your next number. Duplicous.†This time, the first cork did not copy itself; only the second one and the pair of two did, and the newly formed (and rather see-through) corks moved over to the right to form a group of--
–Three,†supplied Neville, who felt a little like he was learning to count for the first time, only in a new and fascinating way.
–Exactly.†Luna beamed. –Duplicous.†The pair of two corks and the group of three copied themselves and settled down together. There were now five sets of corks: the first contained one cork, the second also contained one, the third had two, the fourth had three, the fifth had five and already Luna had repeated –Duplicous†to form the sixth, which contained eight corks, all of which might have been suitable for a ghostly bottle of butterbeer, but which were much too transparent to function as real corks.
–This is why I have to collect them individually. The copies won’t stay strung on a necklace,†Luna said vaguely, and with a last wave of her wand, Vanished all of the corks except for the original, which she pocketed. Then she picked up a quill and began to write on a blank sheet of parchment, talking as she wrote: –One and one are two, one and two are three, two and three are five, three and five are eight…â€
She looked up at Neville expectantly, and to his surprise, he knew the answer--he understood. It was simple, really; all you had to do was sum the previous two numbers. –Thirteen,†he said, grinning.
–Twenty-one,†she replied, without looking back down at the piece of parchment.
–Thirty-four,†he said, after a second’s hesitation.
–Fifty-five,†she laughed.
–Eighty--uh, nine.â€
–A hundred and forty-four,†she rejoined immediately. Before he could reply, she met his eyes and added, –You’re smarter than you think you are, Neville.â€
–I’m not--I--uh…†Neville stammered, and his face suddenly felt rather warm. –I mean…well, thank you.â€
–And you needn’t be so surprised when people compliment you, either. They do it because they like you, so I think you ought to be pleased, not embarrassed.†Neville goggled at her, ears now a vibrant shade of red, but she plowed on without seeming to notice. –Unless being embarrassed is the normal thing to do when you receive a compliment? I don’t know. I’ve never been any good at being normal, but that’s all right, since it doesn’t seem like very much fun. It would feel terribly odd to me, you know? I wouldn’t feel like I was me anymore.†Her eyebrows knitted together as she pondered this.
Neville goggled at her, momentarily lost for words. At once, he felt an urge to burst out laughing, and a curious sort of empathy for her; he had never been good at being normal either, and sometimes he wished he could have been, if only to keep the loneliness at bay. Had she ever felt lonely? He thought she probably had. But it seemed that she believed that it was better to just be yourself anyway, and he found that this idea heartened him, lifted his spirits, in a way nothing else ever had.
His eyes searched for Luna’s, but she had already gone back to the piece of parchment she had been writing on and begun scribbling anew. He shook his head, as if to clear it (an Etch-A-Sketch would have been the perfect metaphor, except that he had never heard of one). Looking over her shoulder, which was easy because he was at least six inches taller than she was, he saw that she was listing fractions: 1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, 34/21…
–These are the ratios between each Fibonacci number and the previous one,†explained Luna, putting down her quill. –2/1 is the ratio of the third Fibonacci number--two--to the second number--one. 21/13 is the ratio of the eighth Fibonacci number to the seventh. You see?â€
At a nod from Neville, she went on. –At my very first Arithmancy lesson last year, Professor Vector taught us the basic calculation spells, which are good for solving fractions, as well as lots of other useful things.†Tapping her wand against each fraction in turn, she muttered, –Equidivuply.†The spell was recognizable to Neville as one that Gran used at the end of every year when she had to pay taxes: she would be sitting in front of a pile of papers in such an irritable mood that Neville would try to avoid her until every last paper was out of sight. One year, Gran had attempted to teach it to Neville, but he couldn’t seem to do it right. After a dozen rounds of making six times seven equal anything but forty-two, she had reluctantly allowed him to give up.
Luna, however, clearly knew what she was doing. The fractions had vanished and were replaced by what Neville realized were their decimal equivalents or approximations: 1, 2, 1.5, 1.667, 1.6, 1.625, 1.614, 1.619… –You see the pattern? As n goes to infinity, the ratio of the nth Fibonacci number to the (n-1)th approaches 1.618 or so,†she informed him.
Unfamiliar with Luna’s terminology, Neville frowned, perplexed. –What do you mean, the ‘yenth’ Fibonacci number?â€
–Well, I don’t know what I would mean by the ‘yenth’ Fibonacci number, but that’s all right, because I said the ‘nth’,†she corrected him lightly. –You see, n is a variable--it can represent different numbers. So when n is five, the nth number would be fifth number, and the (n-1)th number would be the fourth.â€
–Okay…†Neville replied slowly. –So what does it mean for n to go to infinity? I thought you can never actually reach infinity?â€
–No, you can’t,†Luna agreed gaily. –That’s the only thing in the world you can’t do, no matter how hard you try. But that’s all right, because you can estimate what happens when you get to infinity. I’m not exactly sure how you do it; we don’t learn how until NEWT-level Arithmancy, but I do know what happens to the ratio of the nth number to the (n-1)th in the Fibonacci series.â€
And, probably just in time to save Neville’s head from exploding into numerical goop, Luna picked up the quill again and wrote the ratio on the parchment, next to the number 1.618. –There it is! What you’re looking at right now--that’s phi.â€
–It is?†Neville stared at the parchment, a little taken aback. So phi, the great Golden Ratio, was just a number? Judging by the centuries-old library book’s extravagant descriptions of the many applications of phi, he had thought it must be something much more complicated.
Luna nodded emphatically. –Phi is lots of things, really; this is only one of them. Another thing I know about it is that if you add one to phi, you get phi squared.â€
Neville puzzled over this for several seconds. –So…1.618 squared equals 2.618?â€
–Yes--well, not quite,†Luna rectified. –The decimal digits in phi go on a lot longer than .618. Probably they go on forever. But we can’t know that, can we? Since we can never get to infinity… as long as we haven’t found the last digit, we can only guess that they go on forever.â€
Brain beginning to hurt, Neville decided not to try to understand this. –So, phi is about 1.618, then?â€
–About.â€
Neville exhaled. –All right, then. I just have one more question. What would it mean for an angle to be 360 degrees over phi? What sort of angle is that?â€
–Sounds like a reflex angle to me. Those are the bent-over-backwards sort; look.†On the parchment, Luna drew the pale outline of a circle, with a dot in the center. A straight line sprouted out of the dot. It pointed directly to the right, parallel to the top and bottom edges of the paper. She drew another line coming from the dot, pointing in a seemingly random direction, and above it wrote the number 360/1.618. She proceeded to trace the line with her wand, and it gradually rotated around the circle, until it pointed roughly halfway between left and down. Staring at the drawing, Luna mused, –I wonder what’s special about this angle. Was there something in your textbook about it, Neville?†She removed her gaze from the parchment and looked up at him.
–Yeah, there was.†Neville bent over his textbook, eyes skimming the passage once again. –Oh! Okay. I see--that’s the angle of leaf growth, around the stem!†He quickly reread the first several paragraphs, a grin growing on his face. –It’s all making sense now! Thank you, Luna!â€
–You are very welcome, but what’s making sense now?†asked Luna curiously.
Neville looked up from his textbook with a far happier expression than he had worn the last time he had done so. –360 over phi degrees is the angle at which leaves and sprouts grow on the stems of many plants,†he explained animatedly. –Here, imagine that this is the stem.†He picked up the quill and used it to motion towards the dot centered in a circle on the piece of parchment. Then he drew a rough sketch of a leaf on top of each of the two lines protruding from the dot, so that the line appeared to merely be a vein going down the middle of the leaf. –These are the leaves sprouting out. Each leaf is a little higher up on the stem than the last; I can’t draw that on a flat piece of parchment. But they also all have an angle of 360 over phi degrees between themselves and the next leaf.â€
Luna watched in fascination as Neville began to draw more lines, imitating her trick of writing the angle and then running his wand down the line, so that it would shift to the correct angle from the previous line. Over each line, he drew a leaf. As he drew more lines, he drew the leaves larger, and layered them, so that the smaller leaves appeared to be on top of the larger ones. –It’s a good angle for them, because it maximizes the amount of growth hormone available for each leaf. The first leaf grows larger, and then the next leaf begins to grow where there’s the greatest amount of growth hormone remaining--exactly 360 over phi degrees away from the last one. They spread out around the stem, and each leaf grows more and more, and gets farther and farther away from the place where new, little leaves are growing.â€
Abruptly, Neville stopped drawing leaves, and examined his parchment-and-ink plant. –Yes! They do spiral! Look--â€
But before he could explain what he was talking about, the wooden library doors opened. Through them walked Ginny, red hair in a state of disarray, carrying a medium-sized package with her.
–Hello, Ginny,†Neville and Luna called, almost simultaneously.
–Hi Luna, hi Neville,†Ginny greeted them, a little tiredly, and tromped over to their table, resting the brown package against her hip.
–How are you? Are you all right?†Luna asked concernedly.
–Yeah, I’m all right,†Ginny answered briskly, shrugging. –Quidditch practice wasn’t great, but…†With a shrug, she turned to survey the room, and frowned in confusion. –Isn’t Harry with you? Or has he left already?â€
–No, he’s still here. He’s over there, by himself,†Neville told her, motioning towards the tables in the corner that were blocked from view by bookshelves.
–Sulking, probably,†Ginny muttered, though she was smiling faintly. –Well, this should cheer him up a bit. See you later,†she said to Luna and Neville.
–Bye,†said Neville, as Ginny turned away.
Luna did not say anything; instead, she simply watched Ginny walk off towards where Harry was, at the corner tables and out of sight. A thoughtful look appeared on her face. Her eyes seemed brighter than ever, and the ends of her mouth turned up just so.
Curious as to what Luna was thinking, and also wondering when she had become capable of looking like that, Neville found himself standing there silently, the Herbology essay entirely gone from him mind. Then the noise of the library doors opening again startled him out of his reverie; a Hufflepuff girl he didn’t know very well, Hannah Abbott, had just walked in.
–Er…†Neville hesitated until Luna’s expression signaled that she was listening. –So, if you look at the leaves, you can see that there’s actually a spiral pattern. Each spiral begins with one of the leaves closest to the center; the ones that actually touch this dot.†He pointed at the center dot, in the middle of the plant. Muttering a Color-Change spell to turn his ink green, he set his quill down on top of the very first leaf that had been drawn, one that was connected to the dot. Without lifting his quill up from the parchment, he moved it over the leaf behind and to the left of the first leaf—one that was not touching the dot, but was touching the first leaf (or at least seemed to be, on the flat parchment). Then he moved the quill to the leaf behind and to the left of that leaf, and then the leaf behind and to the left again, and so on, until the curved green line that had begun at the very first leaf reached all the way to one of the outermost leaves. In fact, the line was in the shape of a spiral.
He dipped his quill into the green ink again, and started a new spiral, starting with a different inner leaf (one that was also near the center dot) and continuing outwards, from leaf to leaf. The third spiral he drew across the leaves next to those in the second spiral. He drew two more spirals in the same fashion. The plant now had five spirals coming from its center, and every single leaf was part of exactly one of the spirals.
–It’s a Fibonacci number!†noted Luna, bright blue eyes wide.
–And these are just the clockwise spirals,†Neville chuckled, changing the color of the ink again. He had intended it to come out a darker shade of green, but instead it was blue--the sky blue of Luna’s eyes. How had that happened? Hoping she hadn’t noticed this, he placed his quill on top of one of the inner leaves, but this time began drawing counterclockwise spirals, so that each leaf was behind and to the right of the previous one. They didn’t spiral as steeply this time; he ran out of leaves for each spiral more quickly. He continued drawing spirals, each one beginning with a different inner leaf, until once again, every leaf was accounted for in one of the spirals.
Luna exclaimed in surprise, –They’re both Fibonacci numbers!†And indeed, this time, eight spirals had been produced.
Neville nodded; he finally understood what his textbook had been trying to tell him. –Somehow it comes out that if a plant uses that angle, it gets a Fibonacci number of spirals going clockwise--and a Fibonacci number of counterclockwise spirals!â€
–Wow!†said Luna excitedly, tracing a finger down one of the spirals. –Do all plants do this?â€
–No, but this is the most common phyllotaxic pattern. Pine cones usually have Fibonacci spirals, and so do--†He checked his textbook. –--pineapples and artichokes. And daises and sunflowers have Fibonacci numbers of petals, and sneezewort has Fibonacci numbers of flowers…and there are a lot more plants listed here.â€
–Pineapples? Artichokes make sense, they have those little leaves, but--do you mean the leafy crown on top of the pineapple?†guessed Luna.
–No, not those. Er, well, yes, the pineapple leaves grow in spirals too,†he amended, –but those aren’t what my textbook has a diagram of. The little pineapple sections, the shapes that cover the outside of the fruit…those have spirals. Three spirals, in fact, not just two.†He motioned towards the textbook, but he realized that the diagram would be nearly unintelligible to Luna. As smart as she was, she was still a year behind him in Herbology. So he improvised: concentrating with all his might, he managed to transfigure his textbook into a pineapple.
It was a pretty poor pineapple. The leaves were very pale and covered in typed sentences; the brown skin of the fruit looked exactly like the cover of the textbook, but at least it was split into little sections. Each section had essentially the same funny-looking shape; half -rounded, half-spiky. He drew a line with his quill, beginning at one of the sections at the very top, and moving to a section lower and to the left each time. After he reached a section at the bottom, he began a new spiral at the top. He kept having to rotate the pineapple in order to continue his spirals. At last he had drawn all thirteen of the clockwise spirals.
Luna observed closely as he began drawing counterclockwise spirals, his ink now a shining red. These ones curved less steeply down and spent more time slanting to the right; he had to rotate the pineapple even more frequently. This time, there were only eight spirals.
–Can I see it?†Luna requested, hand outstretched for the pineapple.
Neville nodded and handed it over to her. She inspected it closely for several moments, tracing her finger over its bumpy texture. She smiled; it seemed that she had found what she was looking for. –The last set of spirals is hard to see, isn’t it?†she observed, drawing her finger down one of the almost, but not quite, vertical lines. These only barely spiraled around the plant in the counterclockwise direction. He could see her lips move as she counted this last set of spirals. –Twenty-one,†she announced happily.
–WHAT DO YOU THINK YOU ARE DOING?â€*
Neville and Luna both jumped, but Madam Pince wasn’t in sight. The yell had come from the corner where Harry and Ginny had been. They heard Madam Pince screech something about chocolate in the library, and an instant later, they saw Harry and Ginny running from behind the bookshelves, followed by Harry’s bag and books, which kept on beating them over the head.
As their friends scrambled out the doors of the library, Luna and Neville took one looked at each other and burst into hysterics. The sight of Harry waving his arms over his head, attempting hopelessly to ward off the violence of his own schoolbooks, had honestly been quite funny.
Unluckily for them, their hilarity had attracted the attention of Madam Pince. She appeared from behind a set of bookshelves and scowled at both of them. For an instant, Neville was terrified that she would see the pineapple; then he noticed that it was gone.
–Quiet in the library!†hissed Madam Pince.
–Yes, ma’am,†Neville responded.
Luna nodded earnestly, putting on her most innocent face. Neville looked at her out of the corner of his eye; she was clutching something tightly in her right hand. Madam Pince threw them another suspicious look, but then she noticed a seventh-year boy holding a stack of books and trying to get her attention, and she walked over to assist him.
–Nice save,†whispered Neville admiringly, as Luna produced a shrunken version of the pineapple from her hand.
She shrugged and, with a wave of her wand, cast –Engorgio†on the pineapple to return it to its original size. She raised her eyebrows and chortled, –Imagine if she had seen the pineapple… ‘PINEAPPLE IN THE LIBRARY! Despicable! How DARE you!’â€
Neville snorted as he turned the pineapple back into his textbook. –‘But, Madam Pince, it’s not a pineapple! It’s a book, see?’ Although I don’t think she would really like it that way either, not with all these red and blue lines on the cover…â€
With a giggle, Luna pointed out, –How does she know that it isn’t a pineapple that you’re Transfiguring into a book?â€
He opened his mouth and shut it again, stumped. Luna giggled again and motioned towards the bookshelves. –Maybe none of these books are really books. Maybe they’re all actually pineapples,†she suggested, sending both of them back into muffled fits of laughter.
At last, when Neville was once more able to keep a straight face, he remembered his manners. –Thank you so much for helping me, Luna. You’re a great teacher--I think I learned more from you just now than I’ve learned the whole year in Umbridge’s class, and maybe Binns’s, too.â€
–You taught me something, too,†she reminded him. –About the plants? I never knew any of that, and you did a really good job at explaining it. You’re a better teacher than I am, Neville,†she said, far too generously, in his opinion.
He shook his head vehemently. –You’re a wonderful teacher. You say exactly what you mean, and you’re helpful, and gentle. And, Luna, most importantly, you love what you’re teaching.â€
–Thank you, Neville.†She looked at him, eyes wide as ever, and reached for his hand. His ears, he was sure, were going as red as a Gryffindor tie, and he willed his palms not to sweat. Her small hand squeezed his larger one. Then she let go slowly, and said, –But you would still be a much better Herbology professor than I would be an Arithmancy professor. Arithmancy isn’t my favorite subject, you know, like Herbology is yours. It’s only that my mum loved it, and loved to teach me interesting bits of it…She was the one who taught me about the Fibonacci series, not Professor Vector. I love it because it’s a piece of my mum. She died when I was nine.â€
–Oh,†breathed Neville, hit by a crushing wave of empathy and sorrow. Without thinking, he took a step forward and hugged her. –I’m so sorry.â€
–You lost your parents, Neville, didn’t you?†she murmured, head turning to give him a profound, searching look. –I didn’t know, not till just now. I’m sorry, too.â€
–They’re not--dead, but…their minds are gone, after what the Death Eaters did to them,†he confided softly. –I go to see them in St. Mungo’s, but they don’t know who I am, or who Gran is, either. Sometimes I’m not sure they can see or hear us at all.â€
–That’s awful,†Luna whispered, eyes brimming with water. A teardrop ran off her face and onto his shoulder. She gave a quaky laugh and pulled away from him, blushing a little. –Sorry, Neville, I didn’t mean to cry on you.â€
–Don’t worry, it’s okay,†he assured her, feeling somewhat embarrassed himself. –And, well…I was a baby when it happened; I never really knew them. Gran brought me up. And it wasn’t so bad--I love Gran, she’s a great person, just…strict.â€
Luna smiled, wiped her eyes on the sleeve of her robes, and stared up at him pensively. After a moment, her jaw twitched; she was stifling a yawn.
–Oh, I shouldn’t be keeping you awake,†Neville said hurriedly. –I’m sorry; you don’t have to stay here. I still need to finish my essay.â€
–Well…†Luna deliberated. –…Yes, I suppose I should go up to my common room. It is pretty late, isn’t it? I don’t know, because my watch mysteriously vanished several months ago. She looked straight up, as if to suggest that its disappearance owed to the existence of some unusual creature hiding in the ceiling. It seemed that she hadn’t seen it up there, because she shrugged and looked back down at the table. He saw that she was rereading the sheet of parchment, which by now was covered in Fibonacci numbers, ratios, the approximate value of phi, and a drawing of a plant with its leaves connected in spirals. Then she remarked, –Isn’t it beautiful, how in our world, nothing seems to make any sense, and yet it’s all still perfectly logical?â€
–Yeah, it is,†said Neville, understanding exactly what she meant.
As she made to leave the table, he thanked her again, and offered her the piece of parchment. Smiling, she shook her head. –No, I don’t need it. I promise I’ll remember the spirals, and this way you have that drawing to use in your essay.â€
It would indeed be useful for his essay, but that wasn’t the reason why he was glad to keep her parchment.
They said goodbye, and as Neville’s gaze followed her to the wooden doors of the library, he reflected that she and the world must have a good deal in common. After all, Luna Lovegood was beautiful as well; she didn’t make any sense at all, and yet, she made absolutely perfect sense at the same time.
Pineapple in the Library by 1000timesingoldenink
Chapter Notes: My eternal gratitude to Wren for beta-ing this in record time so that I would have it ready to submit to the Cotillion.
Disclaimer: J.K. Rowling wrote the Harry Potter books. Also, Vi Hart made some completely awesome Youtube videos about math, plants, and other things.
Chapter Endnotes: *Line from OotP, page 655.
Muahaha, I just taught you some math and botany! (Unless you already knew about all this.)
Reviews are appreciated! Also, if you have any questions about the math, I'll try to answer them.