continued fraction

okay so! i’m married now! wow!

anonymous asked:

what do u think of that apparently sasusaku's first date was only 2.5 mins lmao

when they pass by that same seaside town, sakura insists on a stroll down memory lane and guides them back to that bench where she nervously reminds him that this is where they had their first date. she’s blushing as she twiddles her thumbs and feels all the more nervous when sasuke looks positively scandalized by her words.

“that wasn’t out first date,” sasuke says tersely. his brows are furrowed and he’s staring at her with confusion, as if doubting his own memories or wondering if he married someone who didn’t value their time together. 

“excuse me?”

“that wasn’t our first date.” he appears utterly distraught by her apparent lack of care.

Keep reading

What is the direction of my heart?
i am looking for something that could possibly build into a wonderful story that unfolds all the chapters through and through. i will read the pain and kiss the wounds but it won’t choke me or rip out my chest because it is inked into a healing cycle. the painted stars in between the pages will remind me of the endless possibilities that the universe is willing to negotiate with me amongst all the uphill and downward spirals that sometimes my existence throws at me at a ferocious speed.

So how much time do i have?
the question itself doesn’t guarantee anything and the answer only dissipates and vaporises in a fantasy that hardly matches the reality as time in itself is not definite. i am not limited, i am merely in a state of being with all that i am in a single moment that continuously repeats itself in fractions to all that is.

What can be done?
i will cultivate a garden of all that the universe has to offer, to build onto who i am. an eye witness to all the aspects that built into who i am. intimate. a boundless friend unraveling the mysteries and imagine how a joyous state that will be.

Prompt(s): 8. “Were you ever going to tell me?” & 52. “I think I’m in love with you and that scares me half to death.” w/ jimin // requested by anonymous

Pairing: park jimin x reader

Genre: angst | dance!au

Warning: I don’t know anything about dance, so if you’re a dancer maybe don’t read this because I might dissapoint lol

Word Count: 2.8k


A/N: I kind of really like this, so um… I might make it into a 2-4 part drabble series *side eyes emoji*

Keep reading

Feynman’s study habits through time

[Quoted from James Gleick, Genius: Richard Feynman and Modern Physics, Abacus Books, 1993.]

As a teenager (p. 35-36, 47): 

In school every problem had an answer. In recreational mathematics one could quickly understand and investigate problems that were open. Mathematical game playing also brought a release from authority. Recognizing some illogic in the customary notation for trigonometric functions, Feynman invented a new notation of his own … He was free, but he was also extremely methodical. He memorized tables of logarithms and practiced mentally deriving values in between. He began to fill notebooks with formulas, continued fractions whose sums produced the constants π and e.

… By the end of this year he had mastered trigonometry and calculus, both differential and integral. His teachers could see where he was heading. After three days of Mr. Augsbury’s geometry class, Mr. Augsbury abdicated, putting his feet up on his desk and asking Richard to take charge. In algebra Richard had now taught himself conic sections and complex numbers, domains where the business of equation solving acquired a geometrical tinge, the solver having to associate symbols with curves in the plane or in space. He made sure the knowledge was practical. His notebooks contained not just the principles of these subjects but also extensive tables of trigonometric functions and integrals—not copied but calculated, often by original techniques that he devised for the purpose. For his calculus notebook he borrowed a title from the primers he had studied so avidly, Calculus for the Practical Man. When his classmates handed out yearbook sobriquets, Feynman was not in contention for the genuinely desirable Most Likely to Succeed and Most Intellectual. The consensus was Mad Genius.

… Each book Richard possessed burned itself into his memory. When a primer on mathematical methods baffled him, he worked through it formula by formula, filling a notebook with self-imposed exercises. He and his friends traded mathematical tidbits like baseball cards. If a boy named Morrie Jacobs told him that the cosine of 20 degrees multiplied by the cosine of 40 degrees multiplied by the cosine of 80 degrees equaled exactly one-eighth, he would remember that curiosity for the rest of his life, and he would remember that he was standing in Morrie’s father’s leather shop when he learned it.

As a graduate student (p. 130):

Feynman had not yet finished his second year of graduate school. He remained ignorant of the basic literature and unwilling even to read through the papers of Dirac or Bohr. This was now deliberate. In preparing for his oral qualifying examination, a rite of passage for every graduate student, he chose not to study the outlines of known physics. Instead he went up to MIT, where he could be alone, and opened a fresh notebook. On the title page he wrote: Notebook Of Things I Don’t Know About. For the first but not the last time he reorganized his knowledge. He worked for weeks at disassembling each branch of physics, oiling the parts, and putting them back together, looking all the while for the raw edges and inconsistencies. He tried to find the essential kernels of each subject. When he was done he had a notebook of which he was especially proud. It was not much use in preparing for the examination, as it turned out.

As a scientist (p. 437):

In one corner of [Feynman’s] dusty office blackboard he had written a pair of self-conscious mottoes: “What I cannot create I do not understand” and “Know how to solve every problem that has been solved.” Nearby was a running list under the heading, “TO LEARN” (”Bethe Ansatz Prob., 2D Hall …”). 

Darkened Night

the series read as follows:

SupermanMondayCheezy PouffsBaconStumblingTrail Mix …  PunchFridayPreparationUncle MudlerNormalBackseatMudler-senseThe FBIUnthinkablePatienceElephant JokesCooking Rickety TablesMr. SkimmerBert and ErnieMidnight ConfessionsThe MoonBright Sunshine … Graying Skies

@today-in-fic  @fictober


Hell existed in that room. The devil resided there, lingering in corners, filling crevices, cracks, shadowing air with evil, thick, heavy, palpable.

Mulder wanted to set the entire place on fire and walk away laughing.

Banging his head against the wall became secondary relief to arsonary evidence destruction. He wasn’t alone in the two-bedroom, unassuming apartment but he might as well have been, his mind buried so far in wanton annihilation that everything else disappeared. Skinner crossed his path every so often, leaving Mulder to stare at papers, journals – why the fuck did they always keep records of their rambling, Schizophrenic, fragmented psyche to taunt him – and that damn religious icon.

Cross, image, vestment, book, candle, verse … he may not believe in any god, be it little ‘g’ god or big ‘G’ God but he was damn certain that you didn’t show your love for your god/God by killing somebody else.

He seriously could have been a mousy professor in some dusty college who followed supernatural blogs and crawled into bed with his Scully every night, life unassuming, heart full, soul intact, ignorance bliss.

With a final bang to the dirty white walls, his forehead throbbed while he returned to shitty reality.

What the fuck was wrong with humanity?


Keep reading

anonymous asked:

Hello, saw you are taking Daniels/Walter prompts and I had one I would really like to see. I did send this prompt to someone else taking them but they never replied. My idea was going with a happier ending, they end up on origae-6 (sans David, lol) and have been in the process of building the settlement and the colonists are awake now too. It's fairly obvious Daniels likes Walter but he sort of denies any feelings on his end because he's Walter. He wants her to be happy with another human.

Oh, hello! Also, yESSS, more Walter/Daniels shippers on deck! Good. They deserve to be happy, damnit.

I wrote something vaguely similar to your prompt on AO3 buuut…you’ve given me another idea. Hold on to your butts, kids, this one ended up longer than I thought it would. But hey I did promise that other anon some fluff SO 


“Ruskin,” Daniels repeated.

“Ruskin,” Walter affirmed. 


“You share several common interests.” 

She put a hand over her face and rubbed at her eyes. It had been a long day, and explaining the intricacies of human courtship was not on her list of things she wanted or needed to be doing at ten o’clock at night. “That’s not - Walter, that really isn’t -”

“I have also noted that he becomes visibly nervous in your presence, which is normally an indicator of attraction.” 

“No, he’s nervous because I was the captain and he has a whole complex about authority figures. I overheard him telling Hernandez that whenever I’m around he wants to crawl under a table and die.” She noticed the flash of distress on the synthetic’s face and clarified: “Humans often say they want to die when they’re embarrassed. It’s called overreacting. Which is what you’re doing right now.” 

A raised eyebrow. “I am sorry if I came across that way. I am just concerned for your wellbeing.” 

She felt her heart do a funny little flip in her chest and abruptly stomped on it. Daydreaming was for when the object of her affections was not actually in the room with her and she could blush all she liked without being asked if she was unwell. (He had even taken her temperature once, just to make sure). She’d had plenty of practise with Jacob, not deliberately playing hard to get but certainly making it a bit of a chore to ensure that her feelings were definitely not just a crush, but Walter was severely testing those limits. 

She liked him. She had been shocked at first, especially since he looked so similar to someone so…utterly alien to the very concept that was Walterness (kind, attentive, funny, whatever the opposite of genocidal was - benevolent? Yes. That was a good Walter word) but over the months had come to accept it in the same way she had accepted how empty the Covenant’s bridge had been without her friends, and that all that remained of her husband was a nail on a piece of string. 

And, if she wasn’t mistaken, she was fairly certain that Walter returned her affection on some level. He certainly seemed to have zeroed in on her, stopping by ‘for a chat’ at least once per day, and she had caught him staring at her several times for no reason she could adequately explain. (One time had been because she had spilt ketchup on her shirt, but the other times still counted). 

“I’m not going to the Valentine’s Day bonfire with Ruskin,” she said, realising she had been woolgathering in lieu of actually answering Walter’s not-a-question-but-was. “It’s my first one without…without Jacob, and I wouldn’t want to go with someone I asked just to not be on my own.” 

“Of course.” 

“If you were to ask me, I would say yes.” 

The gentle smile continued for a fraction of a second longer before faltering. “I’m sorry,” the synthetic said, tilting his head slightly to one side. “I don’t think I heard you correctly.” 

“You have amazing hearing,” said Daniels, “and you heard me just fine. If you want me to go with someone, then there’s no-one else on Origae-6 that I’d rather go with than you.” 

Walter nodded once, processing the information, then brightened. “I see. Platonic support at social events is very important.”

“No,” said Daniels, who reflected on the fact that she had been saying ‘no’ a lot recently, mostly to Walter - or Tennessee, who had created a moonshine still out of some debris from the Covenant and kept asking if she wanted to try some. “As my date.”

For the first time since she had met the synthetic, he avoided meeting her eyes. “That would be inappropriate.”

“If you don’t want to, then that’s fine. But that doesn’t mean I’m going to turn up with a relative stranger just because -”

She was surprised when he interrupted her. Walter was the epitome of polite and could spout several books on good manners, and she couldn’t remember ever hearing him talk over anyone else. He continued to not look at her as he spoke, and his words were soft. “It’s not a matter of not wanting to. It’s a matter of duty.” 

“Duty to…?”


She nodded. “I don’t understand.” 

He finally managed to drag his gaze back up to meet hers, and his face was heavy with emotion. “As your friend, I have a duty to you. To ensure your continued safety and personal happiness on Origae-6. To be clear…I would find attending the bonfire with you…” He struggled for the right word. “…Acceptable. But acceptable only to myself, and that would be selfish. I cannot be selfish. It would be doing a disservice to you.” 

She hesitated, then reached out one - barely shaking - hand and placed it against his upper arm. “Making me the happiest woman on the planet would be ‘doing me a disservice’?” 

“It would only be a temporary happiness. Maybe even for just one night.” He looked at her hand, then took it with one of his own and held it in front of her, his palm over hers. “I may look human, Daniels, and I may even feel human to you - but I am not. There’s no heartbeat under the tips of your fingers, and if you were to break my skin you’d find only hydraulic fluid underneath. You belong with your own kind. They’re the only ones who can truly give you what you need.” 

She frowned. If I ever meet the idiot at Weyland Industries who was in charge of the self-depreciation files in your head, I am going to hit them with a cargo lift. 

There were a million things she could say and more, but Walter was clever. He knew how to reason, how to argue with maddening calm, how to avoid uncomfortable topics and divert conversations with the practise finesse of one who believed they could never be a part of them.

So instead of pouring out her heart, she gave him a yes/no question. 

“Do you like me?” She asked.

He frowned. “Daniels -”

Do you like me?” 

Averted eyes. His hand closed around hers. “Yes.” 

“Then you can give me what I need.” 

She pulled on his hand so that he staggered forward - taken for once unawares, and she mentally congratulated herself for that - then pushed herself up on her toes and wrapped her arms around his neck. His own remained outstretched for a moment, frozen, then slowly curled around her, the stub of his left hand against the small of her back, the fingers of his right splayed between her shoulder blades. She could practically feel the confused look on his face as he pressed it, gingerly, against her hair. 

“Ruskin,” she muttered. “Fucking Ruskin. He likes opera, Walter. The shouty kind.” 

“All opera is the ‘shouty’ kind.” 

“Exactly.” She pulled back slightly so that she could look him in the face. “You have an awful taste in men.”

He gave her a wry smile. “Then it is beneficial that I make up for it with my excellent taste in women.” 

Fighting for the Delinquent’s Love - Jimin

Before entering university, you had thought that people were exaggerating about how hard uni was. But, after a semester spent in university, you had truly understood their perspective. University had definitely turned you bat-shit crazy. Your grades were never a problem, it was almost always smooth sailing, but one of the biggest change that you have noticed was that you have started to develop feelings towards a boy. But, he wasn’t a normal boy, he was Park Jimin.

Park Jimin and his friends were the bad boys of the campus and basically ruled the entire place. They were very controversial, many rumours flew around about them, like smoking weeds, dealing drugs to being members of the underground gangs. But, they didn’t care about a single thing said about them. They never did and it looks like they never will. Despite the warnings given by professors about them needing to stop flicking girls’ skirts, they still kept on doing that. Despite the campus rule of no tattoos should be able to be seen, they still had them on their arms and legs, especially Jimin.

Jimin’s body was beautifully decorated with tattoos, which made him look 15234x more badass. On his right arm, a phoenix was drawn with the black ink. The tattoo stretched from his shoulder to his wrist. On his opposite arm, there was a star constellation and a few random ones. The biggest tattoo that he had was probably the one on his neck that seemed to spread all the way to his back. The picture seemed to be a tree with flowers, but you didn’t know what tree it was. And he still had a million more on other parts of his body. The reason behind this was because Jimin owned a tattoo parlour and it was one of the biggest in the city.

You have had your heart broken by a guy, which was why your friends weren’t ecstatic when you told them you had started liking him. But, you were sure that this time, it wasn’t just a simple crush or like. You knew that your like would soon develop into love, and, you were right. After six months, your simple crush had grown into something else, something stronger.

Every time when you felt stressed out because of your studies, a quick glance at him would refresh your thoughts, your sight would be cleared and everything around you felt like blooming. When you see him laughing along with his friends, your stomach would burst with butterflies. And every day the main thing that kept you going to your classes was because of him, you were always eager to go to university because you were eager to see him. You were 100% sure that you love him and you were going to chase for it. He was going to be a tough one since both of you literally belonged to opposite sides of the campus, you being the model student and him the rebel, but you didn’t care. But your friends did.

“WHAT? Are you crazy, (Y/N)?Jimin? Park Jimin out of every single boy in this campus?” asked Minhee, your friend.

“Yeah, you could’ve gone to Cha Eunwoo, he’s a total looker,” said Sera with hearts in her eyes.

“Dude, Cha Eunwoo is a flower boy, you guys know how I don’t like flower boys. Besides, I don’t think Jimin is that bad,” you said.

“Did you not hear the rumours about him beating up guys in the clubs yesterday ?” Mine asked again, her face showing full disagreement.

“Exactly, that is all we know, we only know him from the rumours, but rumours aren’t always true. He might be a softie under all of those tattoos and piercings,” you said.


“Minhee, she knows what she’s doing and we’re all adults. I think it’ll be best if we let her do what she wants this time,” said Sera.

“Thank you. Minhee, don’t worry, I know my consequences and I promise you that I won’t do stupid things. If I sense that this is not going to the right direction, then I’ll stop.”

You took Minhee’s hand and squeezed it. These girls had been with you since the first day of high school and you were grateful that they were actually concerned about you. But, Sera was right. All of you were now adults, it’s time to make big decisions and as an adult, you were aware of the dangers that can happen if you try to match his pace of life. So, you made a promise to yourself that if in the process of fighting for Park Jimin’s love, you started heading towards the bad side of life, you’ll stop.

Minhee sighed and you knew that she gave up. “Fine, but be careful, I don’t want you knocking on  my door at freaking 3 am saying that the cops are after you.”

“Yes, ma’am!”

“But, how would you do it though? I mean like, both of you are very different, he’s like covered with tattoos and you’re scared of immunisation jabs, he doesn’t touch books and you’re surrounded by books. How are you going to get him notice you?” she asked.

“Well, I was thinking that I should sort of match his way of living, like get a few tattoos and pierce my ears. And maybe dye my hair,” you shrugged.

“Woah, all of these coming out from our Saint Mary’s mouth? Jeez, you’re so head over heels,” Sera scrunched her nose. You just simply shrugged and grinned at your friends.

Today was the day. You were going to get a tattoo at Jimin’s tattoo parlour. It was very nerve-wracking, your hands were sweating and your heart was beating very fast. You stood outside the shop, took a very deep breath and pushed the door open. The bell above the door ringed, indicating a customer.

“Welcome!” Hoseok bursted out of the curtains behind the till desk with a bright smile.

“O-oh, Hi” You nervously asked.

“Come, come, you want to get a tattoo, right?” He asked.

“Uh, yes…”

“Okay! Cool! Do you have a picture of what you want or do you want a surprise one?”

“Well, I sort of came here unprepared, so… I think a surprise one will be good,” you gave him a smile.

“Ooh, what a brave lady! Come on in, have a seat and we’ll get started soon,” he waved you to take a seat on one of the seats.

“Uh- actually, umm… I was wondering if I can get my tattoo from the best one here. I mean, no offence but-“

“Oh! No problem, we get that a lot, hold on, darl, let me get him,” He sent you a wink and told you to sit down.

You rigidly sat down on the smooth leather chair. You were alone and the place was empty and dead quiet. The interior design of the place was quite nice though, it wasn’t like those dark, shady tattoo places, it was more classy. The main colours were black, gold and a hint of wood. The chairs were black, the walls were also painted black but had gold linings and the till table and door frames were made out of wood.  

“Your order for the best tattoo artist is here!” Hoseok popped up from the back again and returned with the one and only, Park Jimin. Your cheeks started burning up when you met eyes with him. You had managed to say a choked ‘hello’, which he replied with a charming smirk.

“Hey, beautiful,” He said.

“U-uh… h-hey…” you said, your face burning red.

“So, you wanted a surprise, huh? You must have a lot of faith in me.”

“Um… yeah, I wanted to change how I look a bit and decided to leave it to the hands of the expert,” you smiled.

“Oh, wow, I’m touched.”

He gave you another smile which made your heart beat faster, before leaving you to take the equipment. What caught you off guard, though, was how Jimin acted very differently in the campus grounds and here. You definitely liked his attitude better when he’s here.

“Okay, let’s get started,” he returned with a trolley of equipment.

You looked at him putting on black gloves and mask. Then, he grabbed the needle (idk what they call them), that’s when your fear started creeping in. The machine started, the sound was very loud it startled you. Jimin inched the needle closer to your forearm. Your eyes widened and by reflex, you stopped his hands.

“W-wait… uh, shit, sorry-“ You stuttered.

“It’s your first time right?” His eyes met yours but they were no longer full of cheekiness, it was like he was genuinely worried.

“Uh, yeah…” You dipped your head in embarrassment.

“Hey, it’s fine,” He placed his finger bellow your chin and pushed up so that he could make eye contact with you, “You’ll be fine, here hold on to my hand,” Jimin moved your hand that was gripping on the leather chair tightly to his arms.

Your cheeks burned deep crimson at the sudden contact. But, you held onto it nevertheless.

“Okay, are you ready?” He asked. After taking a few breaths to calm yourself, you nodded indicating him to go on with the process.

“Here we go.”

The needle finally touched your skin. You winced in pain and held on Jimin’s arm tighter. Tattoos weren’t an easy thing, you definitely realised that, but you remembered that you were doing this to match the person in front of you, the person you loved, Park Jimin. You couldn’t see what he was drawing since his hands sort of covered the image, so you moved your attention to his face in hopes to distract you from the pain. And, thank Lord, it did. When you looked at his concentrated face, the pain subsided and replaced with bubbles in your stomach.

“So, do you go to any universities?” he asked.


“I mean, are studying or working?”

“Oh-ouch-um, I’m currently studying…” you said.

“Oh, same, mind if I ask where?”

“Um, we actually go to the same university…” After you said that, he stopped for a fraction, but continued again.

“Oh, you do? Then, were you surprised that I was here?”

“Well, no…”

“No? So you purposefully came here, to get a tattoo from me? The campus’ s delinquent?”

“Yeah… You can put it that way.”

“That’s brave of you. You’re not scared of the rumours about me doing drugs and beating up people?” he asked.

“Well, I don’t tend to believe in rumours until I have an evidence that the rumours are true. So, do you do drugs and beat up people?” You suddenly became so immersed in the conversation, not paying a single attention to the pain from the needle.

For the first time after a long time, Jimin stopped drawing on your hand and looked up to meet your eyes.

“Well, I’ll tell you straight out and honestly. I don’t do drugs, neither of us do, but I do beat up people. I beat up people that mess with me or my friends,” He stared straight at your eyes.

The two of you stared at each other for a long time. From the tone of his voice and how he looked at you, you knew that he was not lying. And that meant that those rumours about him were false and you were right, Jimin was not the person that the rumours described him as. He couldn’t be the same person when he treated you, a person who he just met with such care. And from the short conversation with Hoseok you had, you had the feeling that he was also not the person that the rumours described him as. Because of this, you became more determined at finding Jimin’s true personality.

“Uh, guys? Is everything okay?” Hoseok’s voice suddenly interrupted your staring session.

Jimin quickly whipped his head down to your tattoo and you swore to God, you saw his cheeks dusted with pink colours. He wiped the excess ink from your arm and stood up.

“Okay, we’re done, I’ll be at the check out when you’re ready,” he said but never meeting your eyes even once. With that, he hurriedly left to the back with Hoseok on his tail.

“What was that?” you asked yourself. You shook your head and chuckled to yourself, then looked down to your freshly drawn tattoo. It was an image of a lotus flower. You weren’t sure about the meaning, but it sure did look pretty. You liked it a lot.

After admiring the tattoo, you stood up ready to go to the cashier. By the time you got there, Hoseok was the one who came out and served you. Your heart dropped a bit. Was Jimin mad at you? Did you offend him?

“Thanks for coming!” he said cheerfully.

“Thank you,” You forced a smile for him.

Sighing in defeat, you pulled the door open making the bell ring again. You were about to walk out when Jimin called you.

“Wait!” He took a hold of your first to stop you from leaving.

“Wait… here,” He shyly gave you a piece of paper with numbers scribbled on it. You looked at it in surprise. Did he just give you his phone number? Did Park Jimin just give you his phone number?

“It’s… my phone number. I’ve never had anybody who judged me outside the rumours, so I think you’re pretty special. Do you want to like grab a coffee or something tomorrow?” He asked while rubbing the back of his neck.

Holy cow, did Park Jimin just asked you out on a date? Did your plan work out then?

“Yeah, I would love to,” you took the paper from him and smiled at him.


Word count: 2312

This scenario did exceed my thoughts, it’s VERY long. Anyways, this was a request from an anon, I hope you liked it :)

Btw, I don’t really know how tattoos work, so I’m not sure if I got the procedures right.

overlyobsessiveotaku  asked:

19 batarou

Garou is notoriously bad about flipping channels, and maybe it’s just been too long of a day or the mix of stimuli - a word, flip, gesture, flip, commercial, flip, yell, flip - it’s just too much for Badd, who stands behind the couch, the grip on his beer getting tighter with each channel change.

“Are ya even gettin’ to see what’s on?!” he finally snaps.

Garou pauses for just a fraction, then continues. “Yeah. And none of it looks good.”

“Ya know, there’s a freakin’ guide on the TV now. You can flip through that.”

“I never recognize anything by the title,” he replies, blandly. “This way I just wait for something to catch my eye.”

Badd has been with Garou long enough to know that there is no reasoning with a creature of instinct and impulse. That also doesn’t make him any more willing to deal with the constant flicker of the television set changing and changing and changing…

So Badd decides to rely on a bit of his own intuition.

Finishing his beer and resting the bottle on the shelf behind him, Badd leans over the top of Garou’s head (dodging between the tuffs of his ridiculous hair; he really needs a haircut) and places a kiss on the end of his nose. Just the tiniest peck, Garou’s entire face scrunching in surprise, and the channel-flipping halts on some sports game.

“What the hell was that?!”

Badd nearly guffaws at the look on Garou’s face as he spins around on the couch. “What was what? Ain’t I allowed t’ kiss my boyfriend?”

“That wasn’t…I don’t even know what to say to that! That wasn’t even a real kiss, you ass!”

“Don’t be mad just ‘cause I got the drop on ya for once. ‘Sides, not like you could do better!”

Now he does laugh as Garou jumps over the back of the couch and takes off after him, into the kitchen, then down the hall. At some point, Garou tackles him, and it’s worth it. No more channel flipping. Mission accomplished.

A Way to Be Together

Fenris x F!Hawke - (read on ao3) - Fenris doesn’t like being touched, even though he wants to touch her. So they find a way to make it work.

Directly inspired by fadedforher’s post about problematic Fenris characterization.

“Hawke.” Fenris’ entire body was tense as he stood in her doorway, staring at his clenched fist and not meeting her eyes. He’d stormed into her room with purpose, but now he was just standing there.

She scooted to the foot of the bed and smoothed her robe over her knees. “What is it?”

“I want this to be easy.” He opened his hand, turning it so that his markings caught the firelight. “I want to be able to…” Fist again. “You deserve someone who can give you everything. Be with you. Make you happy. And I can’t… I can’t even touch you without…” He turned his face to the side, jaw working.

“Hey.” She stood, stepping across the room until she stood before him. “You sound like you’re trying to talk yourself into walking out on me again.”

“No.” His eyes flicked to hers, then, and she saw pain on his face. “I want to be… I want this to be simpler.”

“Do you know what I want?” Hawke tipped her face to the side, catching his eyes with hers. “I want you. I want to be with you, Fenris. Because I love you.”

He hissed a breath at that, ears dropping the smallest fraction.

She continued. “Whatever form that takes, whatever being with you means, that’s what I want.” Hawke slipped her hand around his fist and he jerked it back. His lips parted and he squeezed his eyes shut, then held his hand out to her, palm open. She placed her hand in it, gently, and he folded his fingers around hers.

They stood there, their hands joined, before she spoke again. “Is that what you want?”

Eyes still closed, he nodded.

“We can do, or not do, whatever you need, Fenris. Whatever helps you, just… I want to understand, and I want to make you happy.”

He laughed, a startled sound. “You already do, Hawke.”

She lifted his hand and kissed his knuckles. “We can figure it out together. Think about what you need, and we can work something out. A way to be together.”

He moved their joined hands nearer to her face, drawing a finger through the hair framing her face. “It shouldn’t have to be this difficult.”

With a shrug, she said, “I don’t mind.”

He met her eyes and the look on his face was asking.

She repeated herself, emphasis on every word. “I don’t mind.”

Fenris pulled her hand to his lips and kissed her knuckles where she had kissed his. He still didn’t entirely believe her.

Keep reading

Continued fractions for the square root of 13

Yesterday we looked the equation x2-13y2=1 and used the continued fraction of √13 to find solutions. We did not specify how to construct such a representation of √13. For certain numbers you can make them, with a bit of perseverance.

Let us consider √13. The first thing we do is note that 3<√13<4 and work with √13-3 rather than √13. Next we note that (√13-3)(√13+3)=4. We can (re)write this equality as

But then you can replace the √13-3 in the denominator by the whole right-hand side, and again, and again, …, this leads to this continued fraction

That is not yesterday’s continued fraction but you can use it too to find approximations of √13. If you add 3 to the convergents of this fraction then you get 11/3, 18/5, 119/33, 393/109, 649/180, …. This is a subsequence of yesterday’s approximations. The solutions of x2-13y2=1 and 13y2-x2=1 can also be found in this sequence.

Can we use this to make yesterday’s continued fraction? Yes, all you need is pencil and paper and the first fraction, 4/(6+(√13-3)) that is. Divide numerator and denominator by 4; the numerator becomes 1 and the denominator will be 6/4+(√13-3)/4; this you can rewrite to 1+(√13-1)/4. Next: divide the numerator and denominator of (√13-1)/4 by √13-1; we get 1 and 4/(√13-1), respectively. But, as above, we observe that (√13-1)(√13+1)=12 and so 12/(√13-1)=(√13+1), or 4/(√13-1)=(√13+1)/3 which we can turn into 1+(√13-2)/3. The results of these two steps are displayed below:

If you keep doing this you will after two steps more arrive at the fraction on the left below. Now we read our initial equality as (√13-3)/4=1/(6+(√13-3)) and this gives of the fraction below on the right

But now we can replace (√13-3) by that fraction on the right, and again, and again, … and this leads to yesterday’s continued fraction.

Exercise Do the same for √2-1 and √3-1 and construct approximations of √2 and √3 in this way, and thus also find solutions to the Pell equations x2-2y2=±1 and x2-3y2=±1.

anonymous asked:

Imagine Bucky getting it into his sweet little head that Sam takes care of everyone too much and needs some taking care of his own and so plans a day of "pampering" (read: former winter soldier's interpretation of pampering) for him...but Sam has no idea what's happening

Sam’s life as an Avenger is an unpredictable one, with few constants. One he has become accustomed to is the gentle beeping of his alarm at 5:30AM, signalling the start of the new day, and telling him in dulcet electronic tones to get his rear in gear.

5:30 alarm, 5:45 stare at some toast, 6:00 out the door with Steve.

He tells people he’s a morning person and it’s mostly true. It’s still early though, no way to get around it, so when he opens the door to his bedroom and nearly collides with an intently staring Bucky Barnes, at first he thinks he’s still asleep.

“Um?” he says, and scrubs at his eyes. “Good morning?”

“I heard your alarm.” Bucky hasn’t backed off at all. In fact, he’s leaning in a little, crowding Sam back into his room. “It’s early.”

“I’m going running with Steve. Can I?” Sam gestures to the hall with one hand. Bucky watches the movement, then folds his arms across his chest. Sam swallows, and takes a second look at Bucky’s face, his eyes and stature. His expression is intense and he’s standing with his feet wide apart, his shoulders taking up most of the doorway. Still, it’s not an angry look. If Sam didn’t know better, he’d call it concern.

“You should go back to bed.”

Sam blinks. “Bed?”

“0900 is a more acceptable time to wake up,” Bucky says, and pulls the door shut firmly, leaving Sam standing behind it, bemused.


Later, when Sam is in the kitchen eating lunch, Bucky materializes out of nowhere and slides a full plate (peanut butter sandwich, carrots, and a cupcake) next to him.

“Hey man,” Sam says. “Pull up a chair.” Bucky grunts.

“It’s for you.”

Sam sets down the remainder of his turkey wrap. Bucky is doing the same earnest staring as before, leaning into Sam’s personal space. He reaches out with one finger and pushes the plate closer.

“You need to eat more,” he says, and pulls himself gracefully onto a barstool at the counter. “Eat.”

“Right,” Sam says, and reaches for the cupcake. Vanilla with sprinkles. Nice.

Weird, but okay. Nice.


“Bucky. Bucky. C’mon, man, what’s this about?” Sam asks, slightly exasperated as Bucky herds him toward the bathroom. His arms are laden with bottles of lavender and eucalyptus oil and soaps, and a loofah that Sam thinks might be Natasha’s.

“You work too hard,” Bucky says from behind him. “This is for relaxing.” It’s the most he’s said since he dragged Sam from his desk and started plying him with toiletries.

“I need to work,” Sam says, trying to gentle his voice. “This is very nice of you, but I do need to work.”

Bucky stares at the floor, hands shoved deep into the pockets of his baggy jeans. “I thought. I thought you might want to relax,” he mumbles. “Just once. You work. Too much.”

Sam nods, comprehension dawning, and bends to set the bottles on the ground at their feet. When he rises, he rests both hands on Bucky’s shoulders and waits until he stops tensing and looks up to meet Sam’s eyes.

“Did I tell you how much I appreciated the lunch you brought me?”

Bucky shakes his head slowly.

“I did. It was really nice of you.” Sam waits until the ends of Bucky’s mouth curve up a fraction, then continues. “I think I’ll enjoy those too -” he dips his chin forward the pile on the floor. “Give me half an hour to finish catching up on my email, and then I promise I’ll try them out. What do you think?”

Bucky’s gaze is fixated on the ground, but he nods, and the tips of his ears are pink.

“And then you’ll rest?”

Sam smiles. “Sure. I can always go for a nap.”

TITLE: I Guess This is Growing Up


AUTHOR: the-stuttering-kiwi


Imagine being another child that Odin has brought back to Asgard to raise along side Thor and Loki.  Thor is always the older brother but even from a young age there is no denying the connection between you and Loki.

RATING: Mature

NOTES/WARNINGS: So, here I am trying my hand at some smutty stuff.

And you smell like,

How angels oughta smell

And you look like

You’re ready to go

So hold my hand

I’ll take you everywhere


You wanna go

The way your words keep me in a line

I know what I’m here for

Waking up to the green of your eyes

It’s something I’ll get used to (Oh!)

New Found Glory- Hold My Hand

The next few weeks passed pretty uneventfully. Everyone had gotten over the fact that Loki and Sigrun were together now, and Sigrun was grateful the novelty had worn off. She was also glad she and Loki had settled into a routine; which, admittedly, wasn’t much different than before now it just included kissing and fondling.

Keep reading

Math Mistake at Boston Museum of Science Found by a Teenager

15-year-old Jordan Rosenfeld found a mistake in the Boston Museum of Science’s exhibit “Mathematica: A World of Numbers… and Beyond.” For those of you who have been to the museum, you know this exhibit is not new at all and has been around for nearly 35 years. Still, the young man realized there were minus signs rather than plus signs in one of the formulas for the Golden Ratio. After leaving a note about the error, he was contacted by the museum and told they will fix the mistake.

I can’t find an article that says exactly which formula had the mistake, but I’d guess it was either the continued fraction expression

or the continued square root expression

I would be surprised if a high school student recognized a mistake in the infinite series expression, but then again, the error has been there for 35 years…