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wlw cecilia pederson hc's
I haven't seen ANY Cecilia content and you know what. that is just homophobic. idc I love her so much and I can't stop thinking about her so here have some thoughts. leave it to me to love the character everyone despises
wlw gay stuff ahead // I try to keep her in-character but yknow I'm not perfect so - pls feel free to reblog/comment it truly means the world to me xoxo love you all!
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—Being with Cecilia is. Something. To say the least. She’s difficult to keep up with, even harder to be with. She’s mean, cold-hearted, and doesn’t really open up to you, ever. She doesn’t necessarily go out of her way to physically harm anyone, but she also doesn’t have much of an issue of morality when she needs to use violence. Whenever you find out about her scams, you’re undeniably angry, but she has you wrapped around her little finger so tightly, you don’t dare to even think of turning her in, or even worse - leaving her. So you take all of her bullshit in stride and try your hardest to stay on her good side.
—She’s manipulative as fuck. Obviously. But she has an extreme soft spot for you and you only. Any other person in on her scams are expendable, and she chooses to not give a fuck about them, but time and time again, she chooses to care about you. You’re not entirely sure how that makes you feel about yourself, but she’s so good to you, and she fucks you so sweetly, you find yourself also not giving a fuck about your situation, either - so long as she keeps fucking you and treating you the way she does.
—You lowkey hate yourself for how easily she has a hold on your life. She can tell you to do anything and you’re scrambling to get it done like a dumb little puppy, just for her. Your entire identity, your entire sense of self was gone in her presence. You would burn the world to make her happy, to keep her attention on you (you secretly wished she would feel the same about you, but you know you’re just as expendable as the rest).
—(You’re actually not expendable, to her. You’re the one most important thing to Cecilia in her life, but she would absolutely never, in a million years, make that fact known. She, too, would destroy the world for you.)
—She expects a lot from you. She sees you as her equal, her only real friend - and she expects you to act like it. You’re intelligent, level-headed - just like her, and she knows it (regardless of your intelligence, Cecilia is your main weakness - she makes you stupid for her). She absolutely will make you feel like garbage sometimes, if you fuck up or do something not up to her (high) standards, she’s livid. She’s not above slapping, hair grabbing, cussing at you - and you take it all, you’re in too deep with her to argue, and because you know you wouldn’t win against her, anyways. Plus, you figure you have it pretty decent, being on Cecilia’s good side - she definitely love bombs you and is overly sweet on you as a manipulative tactic (and, she genuinely likes you. Not that you know that.)
—She is possessive as HELL. She will make it well known you are hers and hers only.
—Cecilia spoils the fuck out of you. If she likes you, you would pretty much be set for life. I hate to say sugar mama buttttt, if there was anything you wanted or liked, you would get it (and you never question how she gets her hands on some things). She has money, and she likes to spend it, especially on you. She spoils you with extravagant gifts, jewelry, clothes, perfume (HC Cecilia has tons of high-end perfumes cause why not), and even dates - she loves to dote on you and show you off, show the world what she has (you’re her most valuable asset). Cecilia is surprisingly romantic, very elegant and pretentious, very hedonistic - her pleasure is of utmost importance, and your pleasure is her pleasure as well, so you enjoying yourself is something she takes very seriously. Yes, she’s a very cold person and she is not above bloody violence, but she is also very womanly, therefore, treats you very much so like a lady - so different than how she treats her victims or how she acts when she’s angry. She takes you to the fanciest restaurants, always buys the most expensive bottles of wine for you to share (HC she’s definitely a Cabernet girly!). She won’t stand for you to go wanting for anything.
—And she absolutely spoils you with orgasms, too. Cecilia likes to make you come. A lot. Too much, sometimes - your time in bed with her always ends with you hardly able to walk because your legs are like gelatin. Knowing she can make you scream, can make you come that hard that many times, it’s her favorite fucking thing in the world and she can never get enough. She’s really fucking talented at learning your body and what you like, what makes you tick - she maps you out, calculated, like she is with everything in her life. She knows exactly how to touch you to get you shaking, exactly how you like your cunt to be eaten, exactly how to slide her fingers just right to get you squirming - and she’ll keep doing it, over and over, until you can’t keep up with how many orgasms you’ve had.
—You absolutely have to ask (beg) Cecilia’s permission to come.
—The PRAISINGGGGGG AND DEGRADINGGGGGG with this woman is INSANE. She talks a LOT while she’s fucking you and man, she says some dirty shit. She definitely talks you through it constantly, sweet nothings in your ears while she’s sitting behind you, her chest pressed to your back and one of her hands in-between your legs, the other clasped across your chest, her lips planting kisses on your up-turned neck. She’s really good at balancing being incredibly mean to you and incredibly sweet, touching you gently but whispering some of the iciest words to you. Like sometimes she leaves you in tears she’s so mean to you. Look at you, filthy slut, gonna come on my fingers? Let’s see how many times that worthless cunt can come for me tonight, hm? You would be nothing without me, sweetheart, you need me to take care of you, just like that whorish cunt needs me to take care of her, too. Dumb bitch, making a mess all over me like the dirty harlot you are. Look at you, about to come already - I don’t think so, baby girl. You think you deserve to come? You think you deserve me? Think you deserve me fucking you? No one else will ever fuck you, except for me. No one else could ever fuck you like I do, baby. Say something smart to me again, whore, and I’ll never touch your pretty little pussy ever again. That’s all you want, right? Is for me to keep playing with that spoiled little cunt? Aw, the little slut is crying. What a rotten, stupid baby you are, pretty girl.
—In addition to how cruelly she speaks to you, sometimes she just straight up refuses to let you come for long periods of time. I’m talking hours, days, even, of no relief for you at all. She loves to see you defenseless, powerless, begging her to give you something. It’s either you don’t come at all, or she’s making you come so many times you can hardly see. Yknow a good mix.
—But her praises would be just as intense, when she was in the mood to treat you a little nicer. Being with her is a whirlwind, she 180’s like crazy. The pet names are endless, constantly calling you baby, baby girl, love, sweetheart, good girl, princess, etc. Sometimes it’s strange hearing such sweet names pour from her lips as she’s also saying the most cruel, vile things to you, but all you know is that you cling to everything she says, drink up every word she utters to you. Oh, my sweet girl. Look how precious you are, so desperate. Tell me how it feels, hm, darling? Is that good? You’re so pretty, grinding on my leg like that, honey. Just relax, baby girl, and let me take care of you, I know you need that, need someone to take care of you, I know you need me. Oh, tsk tsk tsk, I know it feels good, baby, let it all out, sweet thing, let me hear you. You sound so lovely moaning my name like that. You’re such a good girl for me, angel, you’re so good. God, you’re so beautiful, so perfect, so flawless, your cunt is so pretty, she’s all mine. You’re all mine, princess. Can you come for me again, baby girl? Come on, I know you can do it, come for me, come for me, elskling, just like that. Oh, I’m so proud of you, godjenta.
—She speaks half english, half Norwegian when she’s fucking you - usually when she’s praising you - a lot of the pet names she uses are in her native tongue. Hearing her speak to you in Norwegian sends you into another dimension.
—Cecilia typically prefers to keep her clothes on while you’re intimate. It’s just how she is, very hidden and secretive, not that she minds you knowing anything about her. It’s just what she’s comfortable with most of the time. You like it, though, there’s a sense of power she has while you’re completely naked and she’s fully clothed. You also love the way the expensive fabrics she wears feel against your skin when she’s on top of you, or holding you to her, or draped across your back.
—Thigh riding. With her clothes on. Her watching you smugly, trying so hard to get yourself off right there on her leg. Dirty worthless slut, trying so hard to come. Look at you. It’s a privilege to even use my leg. Just think about that.
—Speaking of that, it takes an incredibly long time for Cecilia to allow you to see her naked, or to even touch her. She is a control freak through and through, and she doesn’t like relinquishing that - but eventually, she trusts you enough, and lets you touch her, see her body beneath her clothes. She’s beautiful everywhere, not just in the face, and you’re really excited to be able to touch her, too, bring her as much pleasure as she brings you. It’s different, complicated for Cecilia to let you in in that way, but once she gives herself over to you for a change, she learns to adore it. You worship her the first time she lets you touch her, pressing your mouth to every piece of her body, amazed, in awe of just how gorgeous she was, how reactive she was to your touch. The first time you ever make her come, you feel like it was akin to seeing some sort of ancient god - seeing her, usually so ice cold and stoic and uncaring, arching her back and pulling at your hair and her pretty face flushed and scrunched up in ecstasy, her blonde hair spread across the pillow like an undeserving halo, the noises of desperation and your name coming from her lips in a whimper, the taste of her cunt behind your own lips. The sight could have made you come right then and there with her. She grabbed your chin and kissed you, hard, panting into your mouth, body visibly shaking. God, darling, you’re so fucking good at that—
And then, you’re just as addicted to pleasing her as she is to you.
—She babbles to you in both languages as she comes. Absolutely.
—Her favorite thing to do to you is go down on you. Something about it is just it for her. She likes having direct power over you, and over time she’s realized that her mouth can break you down like nothing else, having you making noises you’d never thought you’d make, sending you to places in the stars. Cecilia is one thing and that is determined, and that determination is very clear when she’s eating you out - she won’t stop for anything. She doesn’t care if you have already come three times - she’s staying right between your legs until she’s had her fill of you, not that you’re complaining. She’s honestly pretty sweet with it (as she is with lots of things involving you - the contrast between her career choices and how she treats other people and how she treats you, it gives you whiplash sometimes); she’s slow and steady, pressing tantalizing kisses all down your frontside, in the creases of where your pelvis meets your legs, up your center - landing right on top of your clit, tongue slowly dipping down into your cunt, the pace making you shove your face in your hands and wail your desperation into your palms. She murmurs soft praises and maybe some harsher degradation in between your thighs, in tune with the even softer movements of her mouth against you, looking up at you through blonde lashes all the while, gauging your reactions to everything she does. She compliments and praises everything about you. Oh, my pretty girl, such a precious little pussy, hm? I know you need it, sweetheart, be patient. I’ll give you everything you need. Her hands would be busy, too, coming up to rest on your upper thighs, your hips, your lower stomach, nails scraping gentle patterns to your skin. She’s a tease with everything - she wants you desperate and dripping for her and she likes to hold your neediness for her over your head. But once she stops barely touching your skin and running her tongue across your lips, she’s latching onto your cunt like it’s air, not letting up til you’re crying and trying to thrash away from the intensity. And all positions are game for her - she especially likes to eat your pussy from the back while you’re on all fours, elbows to the ground and ass hiked up as far as you can arch, one of her hands wrapped around your thigh and the other pressing a thumb to your clit while her tongue is pressed into your cunt. Or she likes you to sit on her face cause she can grab onto your thighs and hold you down to her. She also likes to eat you out while you’re standing, pressed against the floor-to-ceiling glass panels in her home, her mouth nestled between your legs and her arms wrapped around your thigh as your knees shook from her circling your clit with her tongue.
—Her handssssss her hands are so pretty. Cecilia is super talented with her fingers and really enjoys holding you to her chest while she plays with your pussy, dipping her fingers down into your wetness to rub your clit with, yknow yknow the good shit. Or she knows exactly how to hit every damn spot inside of you to have you howling her name into the blankets.
—Scissoring? Hell yes. She’s all for it, and she doesn’t care if she’s on top or bottom. Sometimes she likes when you take control, swiveling your hips against hers, your arms wrapped around one of her legs to fit your bodies together, being able to see her lovely face react, eyes closing, brows furrowing, as you tilt down to get the friction just right. It felt like you were fucking her instead of the other way around (even though her iron grip on your hips told you she was absolutely still in control). Or, when she’s on top, and her hips thrust so perfectly in tune with your own, your sex gliding so wonderfully against hers, her arms reaching down to rest her hands on your chest for leverage - taking one and slipping it to lay against your lower stomach to press her thumb to your clit, just to give you that extra bolt to send you over the edge. Her hair flows and swirls over her shoulders, her head thrown back with her eyes closed, focusing on the feeling, the way her muscles and bones move with her, the heat of her body radiating onto you, it’s addicting. She’d lean forward and press her forehead to yours, eyes meeting your own, forcing you to look at her while she thrusts and fucks you into oblivion. It’s an almost sweet gesture, one of her hands coming up to hold your cheek and urge you to come for her.
—She’ll make you watch her fuck you in the mirror. Seeing her hand come up to wrap around your throat from behind while she’s railing you, her breath on your neck as she’s whispering dirty things into your ear, her eyes on yours in the reflection - you like seeing her face as she’s unraveling you.
—Definitely uses toys on you - she would absolutely hold a vibe to your clit til you literally feel like blacking out, or hold a wand to you while fucking you with a strap, or suck on your clit while fucking you with a toy, too.
—She’s rough a lot of the time, slapping you and throwing you around, pulling at your hair and forcing you down. But other times, she touches you like you’d break, slow and gentle and calm. You couldn’t ever say that she loved you but, maybe in her own sick, fucked up way, she did. Above all she enjoys being around you, she enjoys making you feel good and spoiling you, and she’s down for most anything.
—She does care for you - again, in her own fucked up way - and she doesn’t leave you hanging, especially after sex that was particularly rough or degrading. She will absolutely hold you close to her and let you come down from the intensity. She’s not completely heartless. She’ll rub your back, stroke your hair, kiss your forehead, get you water, have intimate, deep conversations for hours - all the sweet gooey shit. She really likes to run you baths and even join you in them (let’s be real we know this bitch has a huge bathtub). Long story short she’s not gonna say or do some fucked up sadistic shit to you and not make sure you’re okay afterwards - she’s not completely evil, she just puts herself first in most situations, but when you come around, she kinda melts for you and only you. One time, she was on top of you, fully clothed, kissing at your shoulders and grinding her hips down into yours, and she buried her face into the crook of your neck, whispering oh, god, what are you doing to me, sweetheart? referring to how soft she was around you sometimes, how warmly you made her feel, how you saw right through her cruel bullshit and melted her into a puddle. She eventually opens up to you about a lot of things in her life, her childhood, her past, how she became the woman she was. It makes your heart jump. Sometimes, she is so loving to you, and so mean to everyone else, it makes you feel like the luckiest person on the planet, to have such an intense, cold, self-centered woman like Cecilia take a fondness to you.
#cecilia pederson#saw x#saw#cecilia saw x#I want to write more for herrrrrrrrr#I LOVE HER DESPERATELY YOUR HONOR#reblogs are so welcomed!!!!
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"Can't two guys be just friends?" If they stop looking at each other like that then sure
#just saw weirdos reblog my post so lemme clarify no irl shipping especially anything to do with mcyt get the fuck out of here ur not welcome#soukoku#shin soukoku#rampoe#itafushi#haikaveh#satosugu#mitsukou#vanoe#hualian#fengqing#beafleaf#wangxian#matcha blossom#renga#wrightworth#narumitsu#klapollo#mikayuu#iwaoi#sakuatsu#bokuaka#kagehina#lawlight#killugon#prob add more later
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Let’s keep this up!
So, in case you weren’t aware:
Name: Trick Weekes
Pronouns: they/them
Additions:
Jin Maley, voice actor for Taash, is non-binary and uses they/them pronouns. Erika Ishii, one of the four voices for Rook, is genderfluid and uses they/she/he/any pronouns. Gareth David-Lloyd, voice actor for Solas, uses he/him/they/them pronouns. Jessica Clark, voice actor for Neve Gallus, uses she/her/they pronouns. Jeff Berg, one of the four voices for Rook, uses he/him pronouns. Corinne Busche, game director of Dragon Age: The Veilguard uses she/her pronouns.
I've added the ones I could verify on IMDB or their social media profiles. If anything changes I'll do my best to add them!
#dragon age#BioWare#If there’s other devs out there you wanna add to this post bc they also get misgendered#please add them! I’ll make sure to reblog#I’m not on Twitter and only follow a handful of people on BlueSky#so Twitter additions are super duper welcome#let’s all be respectful together ❤���
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Finally gave in. Watched the gay pirate show.
I freaking love it to DEATH holy SMOKES why didn’t you people tell me to watch this??? I binged it in like 2 DAYS???
Anyway, I wanted to draw the gays, but unfortunately I cannot draw middle-aged men for the life of me. I’ll figure it out one day.
HOWEVER I can draw children! So, I drew the children meeting, because they both need a hug. Really bad.
Enjoy!
#This is my first fully rendered piece in WEEKS#The power of the Gay Pirates tm#ofmd#ofmd fanart#stede bonnet#edward teach#blackbeard#blackbonnet#gentlebeard#my art#digital art#also happy September 1st lol. it’s a leap year as well#cherishing ALL the reblog tags you guys are so welcoming and sweet ☺️❤️
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mom im tired
#me if drawing pathetic sad sad roman roy was illegal#i did not mean to post this so close to mother’s day i’m crying#rubbing salt in the wound#i wanted to draw their likeness and class of 2013 roy siblings is the most sorrowful thing in the wolrd#mooooommmmmmm iiiim tiiiireeeeddddddd#succession#roman roy#succession fanart#kieran culkin#roman roy fanart#my art#reblogs are welcome
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I feel great now. I feel lousy.
#rent 2005#rent movie#anthony rapp#tracie thoms#idina menzel#rentedit#rent the musical#musicaledit#userbbelcher#userstream#cowboycoven2#chewieblog#filmtv#cinemapix#cinematv#fyeahmovies#moviegifs#dailyflicks#filmedit#filmgifs#2005#mine*#film#tango#its getting difficult to find stuff to reblog#any suggestions are welcome#meanwhile im just gonna post my gifs i have so many planned
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#artists on tumblr#furry artists on tumblr#reblogs welcome#reblogs encouraged#a commission so not my oc#furry#anthro#anime#cute#retro#dog#big comfy sweater#ikea shark#blahaj#plushie#commission
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tips for identifying stolen art:
signature not matching poster
tags on original post say "not my art"
often times artists will include a "my art" tag or something similar. if there isn't one present on the original post, this may not be their art
no caption/very detached caption like "this is so beautiful" etc etc that makes it seem like the poster did not create the art
blurry/resolution issues that don't seem intentional
link to original without clarifying caption that says "artist granted permission to repost"
#sometimes the benefit of being in the ml fandom in particular for so long is that I recognize pieces I've seen before#but these are tips I've been using since 2016#and it's in EVERY fandom#anyone is welcome to add on. this is for everyone#TYPO SPOTTED AFTER REBLOGS!!!!! NOOOOO
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what's the 3-dimensional number thing?
Well I'm glad you asked! For those confused, this is referring to my claim that "my favorite multiplication equation is 3 × 5 = 15 because it's the reason you can't make a three-dimensional number system" from back in this post. Now, this is gonna be a bit of a journey, so buckle up.
Part One: Numbers in Space
First of all, what do I mean by a three-dimensional number system? We say that the complex numbers are two-dimensional, and that the quaternions are four-dimensional, but what do we mean by these things? There's a few potential answers to this question, but for our purposes we'll take the following narrative:
Complex numbers can be written in the form (a+bi), where a and b are real numbers. For the variable-averse, this just means we have things like (3+6i) and (5-2i) and (-8+3i). Some amount of "units" (that is, ones), and some amount of i's.
Most people are happy to stop here and say "well, there's two numbers that you're using, so that's two dimensions, ho hum". I think that's underselling it, though, since there's something nontrivial and super cool happening here. See, each complex number has an "absolute value", which is its distance from zero. If you imagine "3+6i" to mean "three meters East and six meters North", then the distance to that point will be 6.708 meters. We say the absolute value of (3+6i), which is written like |3+6i|, is equal to 6.708. Similarly, interpreting "5-2i" to mean "five meters East and two meters South" we get that |5-2i| = 5.385.
The neat thing about this is that absolute values multiply really nicely. For example, the two numbers above multiply to give (3+6i) × (5-2i) = (27+24i) which has a length of 36.124. What's impressive is that this length is the product of our original lengths: 36.124 = 6.708 × 5.385. (Okay technically this is not true due to rounding but for the full values it is true.)
This is what we're going to say is necessary to for a number system to accurately represent a space. You need the numbers to have lengths corresponding to actual lengths in space, and you need those lengths to be "multiplicative", which just means it does the thing we just saw. (That is, when you multiply two numbers, their lengths are multiplied as well.)
There's still of course the question of what "actual lengths in space" means, but we can just use the usual Euclidean method of measurement. So, |3+6i| = √(3²+6²) and |5-2i| = √(5²+2²). This extends directly to the quaternions, which are written as (a+bi+cj+dk) for real numbers a, b, c, d. (Don't worry about what j and k mean if you don't know; it turns out not to really matter here.) The length of the quaternion 4+3i-7j+4k can be calculated like |4+3i-7j+4k| = √(4²+3²+7²+4²) = 9.486 and similarly for other points in "four-dimensional space". These are the kinds of number systems we're looking for.
[To be explicit, for those who know the words: What we are looking for is a vector algebra over the real numbers with a prescribed basis under which the Euclidean norm is multiplicative and the integer lattice forms a subring.]
Part Two: Sums of Squares
Now for something completely different. Have you ever thought about which numbers are the sum of two perfect squares? Thirteen works, for example, since 13 = 3² + 2². So does thirty-two, since 32 = 4² + 4². The squares themselves also work, since zero exists: 49 = 7² + 0². But there are some numbers, like three and six, which can't be written as a sum of two squares no matter how hard you try. (It's pretty easy to check this yourself; there aren't too many possibilities.)
Are there any patterns to which numbers are a sum of two squares and which are not? Yeah, loads. We're going to look at a particularly interesting one: Let's say a number is "S2" if it's a sum of two squares. (This thing where you just kinda invent new terminology for your situation is common in math. "S2" should be thought of as an adjective, like "orange" or "alphabetical".) Then here's the neat thing: If two numbers are S2 then their product is S2 as well.
Let's see a few small examples. We have 2 = 1² + 1², so we say that 2 is S2. Similarly 4 = 2² + 0² is S2. Then 2 × 4, that is to say, 8, should be S2 as well. Indeed, 8 = 2² + 2².
Another, slightly less trivial example. We've seen that 13 and 32 are both S2. Then their product, 416, should also be S2. Lo and behold, 416 = 20² + 4², so indeed it is S2.
How do we know this will always work? The simplest way, as long as you've already internalized the bit from Part 1 about absolute values, is to think about the norms of complex numbers. A norm is, quite simply, the square of the corresponding distance. (Okay yes it can also mean different things in other contexts, but for our purposes that's what a norm is.) The norm is written with double bars, so ‖3+6i‖ = 45 and ‖5-2i‖ = 29 and ‖4+3i-7j+4k‖ = 90.
One thing to notice is that if your starting numbers are whole numbers then the norm will also be a whole number. In fact, because of how we've defined lengths, the norm is just the sum of the squares of the real-number bits. So, any S2 number can be turned into a norm of a complex number: 13 can be written as ‖3+2i‖, 32 can be written as ‖4+4i‖, and 49 can be written as ‖7+0i‖.
The other thing to notice is that, since the absolute value is multiplicative, the norm is also multiplicative. That is to say, for example, ‖(3+6i) × (5-2i)‖ = ‖3+6i‖ × ‖5-2i‖. It's pretty simple to prove that this will work with any numbers you choose.
But lo, gaze upon what happens when we combine these two facts together! Consider the two S2 values 13 and 32 from before. Because of the first fact, we can write the product 13 × 32 in terms of norms: 13 × 32 = ‖3+2i‖ × ‖4+4i‖. So far so good. Then, using the second fact, we can pull the product into the norms: ‖3+2i‖ × ‖4+4i‖ = ‖(3+2i) × (4+4i)‖. Huzzah! Now, if we write out the multiplication as (3+2i) × (4+4i) = (4+20i), we can get a more natural looking norm equation: ‖3+2i‖ × ‖4+4i‖ = ‖4+20i‖ and finally, all we need to do is evaluate the norms to get our product! (3² + 2²) × (4² + 4²) = (4² + 20²)
The cool thing is that this works no matter what your starting numbers are. 218 = 13² + 7² and 292 = 16² + 6², so we can follow the chain to get 218 × 292 = ‖13+7i‖ × ‖16+6i‖ = ‖(13+7i) × (16+6i)‖ = ‖166+190i‖ = 166² + 190² and indeed you can check that both extremes are equal to 63,656. No matter which two S2 numbers you start with, if you know the squares that make them up, you can use this process to find squares that add to their product. That is to say, the product of two S2 numbers is S2.
Part Four: Why do we skip three?
Now we have all the ingredients we need for our cute little proof soup! First, let's hop to the quaternions and their norm. As you should hopefully remember, quaternions have four terms (some number of units, some number of i's, some number of j's, and some number of k's), so a quaternion norm will be a sum of four squares. For example, ‖4+3i-7j+4k‖ = 90 means 90 = 4² + 3² + 7² + 4².
Since we referred to sums of two squares as S2, let's say the sums of four squares are S4. 90 is S4 because it can be written as we did above. Similarly, 7 is S4 because 7 = 2² + 1² + 1² + 1², and 22 is S4 because 22 = 4² + 2² + 1² + 1². We are of course still allowed to use zeros; 6 = 2² + 1² + 1² + 0² is S4, as is our friend 13 = 3² + 2² + 0² + 0².
The same fact from the S2 numbers still applies here: since 7 is S4 and 6 is S4, we know that 42 (the product of 7 and 6) is S4. Indeed, after a bit of fiddling I've found that 42 = 6² + 4² + 1² + 1². I don't need to do that fiddling, however, if I happen to be able to calculate quaternions! All I need to do is follow the chain, just like before: 7 × 6 = ‖2+i+j+k‖ × ‖2+i+j‖ = ‖(2+i+j+k) × (2+i+j)‖ = ‖2+3i+5j+2k‖ = 2² + 3² + 5² + 2². This is a different solution than the one I found earlier, but that's fine! As long as there's even one solution, 42 will be S4. Using the same logic, it should be clear that the product of any two S4 numbers is an S4 number.
Now, what goes wrong with three dimensions? Well, as you might have guessed, it has to do with S3 numbers, that is, numbers which can be written as a sum of three squares. If we had any three-dimensional number system, we'd be able to use the strategy we're now familiar with to prove that any product of S3 numbers is an S3 number. This would be fine, except, well…
3 × 5 = 15.
Why is this bad? See, 3 = 1² + 1² + 1² and 5 = 2² + 1² + 0², so both 3 and 5 are S3. However, you can check without too much trouble that 15 is not S3; no matter how hard you try, you can't write 15 as a sum of three squares.
And, well, that's it. The bucket has been kicked, the nails are in the coffin. You cannot make a three-dimensional number system with the kind of nice norm that the complex numbers and quaternions have. Even if someone comes to you excitedly, claiming to have figured it out, you can just toss them through these steps: • First, ask what the basis is. Complex numbers use 1 and i; quaternions use 1, i, j, and k. Let's say they answer with p, q, and r. • Second, ask them to multiply (p+q+r) by (2p+q). • Finally, well. If their system works, the resulting number should give you three numbers whose squares add to 15. Since that can't happen, you've shown that the norm is not actually multiplicative; their system doesn't capture the geometry of three dimensions.
#math#numbers#human interaction#this took the better part of a day to write oops#although to be fair I haven't exactly been focused#Also hi Pyro! Welcome.#that silly fast food emoji post went wild#I've gotten 30 followers just from that one post#which isn't that many in objective terms but like it's 40% of my current count so#hello everyone#I might start reblogging things again now
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When Clown talked about reading books to home, i knew i had to draw Wally reading my favorite childhood book to Home!!
Also Wally painted a little heart on Home like face painting! oh and take my line art because i love lineart!
#jazzart#wally darling#welcome home#welcome home wally#ooh it feels good to draw again!!#ive been in a rut for so long#im going through a spiritual journey rn#but im still trying to entertain my 3d world even when it feels 1d#im worried about inktober#i dont want to break my 9 year streak#but im .. very disconnected#anyways anyways#i still love wally!! so very much!!#also this is the worst timing to post so please reblog!! ;w;#give me strenth to keep going please#i draw him so plump and shapely teehee#forgive the book. i have zero experience in photoshop
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i almost got hit by several cars today trying to make this gif on my phone
#please just save the gif if you dont want to reblog hot kimharry yaoi. i understand#kostik draws#kostik speaks#kim kitsuragi#harry du bois#disco elysium#harrier du bois#kimharry#ive drawn so much hot yaoi base today its unreal#you know a ship has made it when i draw it as hot yaoi base#scarian. me and my boyfriend. and now kimharry#welcome to mount olympus
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MDZS Height Poll: Who is (technically) the tallest character. Please remember that these polls are for fun!
#mdzs#poll#Please remember that I WILL see notes and comments and reblogs. Let's have fun with this clearly very silly poll!#I am begging everyone to be nice. We can get icecream afterwards if we all behave.#Propaganda is welcome if you dare take up the bat to swing at the hornet's nest.#As always - I will have a little comic at the end of this poll based on the results!!!#I'm so tempted to sway votes but the beauty is in the community response. You guys always surprise me!#Will the winner be based on technicality? WHO'S technicality? So many choices!#NHS and JGY are a big mood for being 'tall' but labeled short due to being surrounded by 'very tall' people.#Shout out to my little cousin who's a natural 6'1"and STILL wears the 6 inch heels. That's feminism.#I wanted to have the next poll be 'who's in the middle of the bed in the 3zun relationship' but I need to draw for that one.#it's been a rough week for me. Comic resumes tomorrow though - I just have not been home to upload anything via scanner.#I'm alright I promise B'*) Just a chaotic lifestyle. Hope you have all been well <3
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Polscy mutualsi i reszta Polbrl, jest akcja wspierająca na pomoc powodzianom z gminy Głuchołazy.
Pisarz Jakub Ćwiek (pochodzący z Głuchołaz) wypuścił nowe wydanie swojej książki "Topiel" w ramach akcji "płać ile chcesz". PEŁNY DOCHÓD Z AKCJI IDZIE NA POMOC POWODZIAN.
Dostępne są: wydanie papierowe, audiobook i ebook. Wpłacić można dowolną sumę (w przypadku ebooka i audiobooka kwota minimalna to 1,20 zł, w przypadku papieru – 10 zł).
Akcja trwa do 30.09.2024!
Z ważnych informacji:
Akcja to PRZEDSPRZEDAŻ. Audio i ebooki zostaną udostępnione w ciągu kilku dni, natomiast wersja papierowa ruszy do druku dopiero po zakończeniu akcji. "Chcemy drukować bez nadwyżek, bo to ma być nie tylko książka, ale i pamiątka Waszej wspaniałomyślności. Zaraz po zamknięciu akcji dostaniecie wiadomość o terminie, gdy książka do Was dotrze."
Akcja istnieje we współpracy z władzami Głuchołaz. Środki z akcji zostaną przekazane do rozdysponowania burmistrzowi gminy.
Więcej o książce:
"W sierpniu 1997 r, ukraińscy żołnierze, przybyli na pomoc powodzianom z Głuchołaz, dokonują makabrycznego znaleziska w korycie wciąż wezbranej rzeki. Na ułamanym, zanurzonym w wodzie drzewie wiszą zwłoki nastolatka.
Niespełna miesiąc wcześniej dla czwórki młodych chłopaków – Kacpra, Darka, Józka i Grześka – rozpoczynają się upragnione wakacje. Mimo strug deszczu, wzbierającej rzeki i zagrożenia powodziowego, wszyscy czterej są przekonani, że to będzie ich lato. Trzy dni później rozpoczyna się “Powódź stulecia”. Wydarzenie, które na zawsze odmieni życie… tych, którzy przeżyją."
“Topiel” to oparty na osobistych doświadczeniach autora, szczegółowy, emocjonujący zapis pierwszych dni wielkiej powodzi w 1997 r.
#poland#polska#głuchołazy#zbiórka dla powodzian#akcja nie trwa dlugo jak mozecie to przekazujcie dalej#for my english speaking followers its fundriser for flood victims in glucholazy in poland#the book is in polish so idk if it makes sense to translate the post to english but you're welcome to reblog it
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Tw: eye contact
I paint what I see
#HEEEEEEEELP I HAVE BEEN DRAGGED INTO HOME AND I CAN’T GET OUT#A NEE HYPERFIXATION HAS BEGUN#EVERYONE WHO HAS FOLLOWED ME FOR FNAF BE WARNED#I had so much fun with this drawing-#it was an extremely fun experiment!#and to anyone who doesn’t know who this is: His name is Wally and he’s from an ARG Project called Welcome home!#Hightly recommend you check it out#derpiedoxie#digital art#fanart#welcome home#welcome home wally#welcome home fanart#wally welcome home#also I actually recorded the progress for this one so I’ll be linking the speedpaint in a reblog as soon as I’ve posted it!#edit: aaaaaa I should’ve put the trigger warning there earlier I’m sorry I forgot :’)
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blurryface era sketch
#the character design of this era went so crazy#cant stop drawing josh's hair like hes in a tim burton movie#they’re kinda meant to be sitting on a bus in this#sketch#twenty one pilots#tøp#tyler joseph#josh dun#twenty one pilots fanart#clique art#my art#reblogs are welcome
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BOO
SKETCHY!!!??!?!
HELLO!?!?!?!?!?!??!!??!?!!?
THIS IS!?!?!?!?!? GORGEOUS!?!?!? WHAT DID I DO TO DESERVE TO DESERVE SUCH LOVELY ART!!!!!
IM SOBBING AND SLAMMING MY HANDS ON THE FUCKING TABLE I CANNOT EVEN BEGIN TO FORM WORDS TO DESCRIBE THE SHOT OF PURE DOPAMINE THAT JUST ROCKETED INTO MY BRAIN!!!!!!!! SKETCHY!!!!!!!! SKETCHY WHEN
WHEN
I
GET
YOU!!!!!!!!!
WHEN I FUCKIN GET YOUUUUUUUU!!!!!!!!!!!!!!!!!
#welcome home#welcome home oc#wally darling#welcome home puppet show#welcome home arg#welcome home fanart#dandy leon#ivy darling#others art#reblog#my art#sketches#IM LITERALLY GOING FERAL#AND SLAMMING MY HANDS#THE WAY I VIOLENTLY BEGAN TO HIT MY CHAIR WHEN I SAW THIS#ITS MY PHONE LOCKSCREEN#IM WEEPING#SOBBING UNCONTROLLABLY#THIS IS EVERYTHING#I LOVE THIS SO FUCKING MUCH I JUST!!!!!! ARRUUUUUUUGHHHHHHHHHHHHHH#ARAAAAAAAUUUUUUUUUUUUUGH#I GET TO JUST LOOK AT THIS AND HAVE THIS!?!?!?!?!?!??!?!?!?!?!?!??!?!?!??!?!!??! YOU MADE THIS FOR ME!?!?!?!?!?!??!?!?! IM FLABBERGASTED#IM JUJST#LOOK AT THEM#RESTING#RESTING AND HAPPY AND CALM AND NESTLED AND THE GRASS AND IVY AND WALLY AND AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA#ARARJNAFJNKDSAFNDJSKFN JSNFJ KSDNFJKNFDJ KSDNFJK NJKJKF jnfjknfjk n jkn jkn . fdgfg#sketchy to sketchy communication
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