#red euler

[karmesean]

AIN'T no way e^i(π) is his cuddle buddy

[valentiine-png]

OHMYGOSH YOUR LIAM SPRITE IS SOOOOO CUTE. INSTANT FOLLOW ❤️❤️❤️

could u possibly do julien (toothpaste) also from hfjone? if not (he is a very minor character) then could u do bryce (soda bottle) or airy???? thank u for ur time!!!

transparent (smile and frown) —

julien, amelia, and bryce web charms! (requests open)

request note —-x-— enjoy! hopefully the transparency works properly, wasn’t entirely sure how to handle the bottle and glass being see-through for both dark and light backgrounds, but i think it worked out. thank you for requesting!

(created by me — feel free to use without credit — reblogs appreciated)

[unastrawberrywolfartist]

Little Red Riding Hood Pie

Cast:

Pie As Little Red Riding Hood

Pi As The Big Bad Wolf

Euler's Constant As Grandma

Tau As The Hunter

Square Root Of Two As The Red Riding Hood's Mom

[r-gm]

self indulgent serving amelia stimboard because i genuinely cant stop watching that video

★★★|★|★★★

[virtual-bunny]

“ HEY NERDY BOY ! ”

random headcannons about nerdjo because he turns me on

pairings: nerd! gojo x chubby fem! reader

WARNINGS: SMUT but not too detailed, some body image issues, probably some writing errors :3

a/n: i might come back every now and then if a new idea pops up in my head hehe

ARTIST CREDS: @/N06ARA ON TWITTER

✧ nerdjo who can almost cry over how beautiful he thinks you are

✧ nerdjo who stammers over his words when you wear shorts that squeeze your thighs just right

✧ nerdjo who clings onto your body and inhales your scent and gets a boner instantly as he grips your love handles

✧ nerdjo who slouches so you can give him a kiss, his glasses slidding down his nose bridge as your lips touch his cheeks, his cheek warm from him being flustered, and when you pull away, nerdjo’s eyes are almost crossed eyed as he sighs deeply

✧ nerdjo who uses your tummy as a stress ball when you sit next to him while he does his physics homework

✧ nerdjo who lays on your tummy as you play with his hair while he sleeps, saliva spilling from the side of his mouth

✧ nerdjo whose so head over heels for you that he begs you to let him carry your books and backpack so he can trail behind you to see the way your ass and thighs jiggle

✧ nerdjo who helps you with your homework and pinches your cheek, side or thighs whenever you get something wrong

✧ nerdjo who holds onto your stomach when you’re riding him, his face flushed and glasses crooked as he looks up at you with drunken eyes

✧ nerdjo who stumbles to catch up to you because he was too caught up watching you walk infront of him

✧ nerdjo who rolls his eyes when his jock friend geto teases him when he sees that gojo isn’t paying attention to lecture “she’s got you wrapped around her finger doesn’t she?” “wrapped around her thighs” nerdjo sighs without a second thought

✧ nerdjo who likes to put his hands around your tummy and gently squeeze it whenever you two are watching tv and you’re sitting between his legs

✧ nerdjo who fivershly pumps his cock at the thought of your round body jiggling when you ride him, or when you laugh, or when you walk

✧ nerdjo who makes snarky comments at you when you try to show him that “you’re way smarter than he is”

✧ nerdjo who reads out his physics notebook out loud just to make you mad because you hate physics

✧ nerdjo who goes all red whenever he brings you gifts on his way to your dorm

✧ nerdjo who doesn’t like going outside and rather stay home watching Teen Titans but still does because he knows you like to go out on dates

✧ nerdjo who used to bite his pencils out of habit but now bites your chubby hands if you’re sitting next to him as he does his homework or helps you with yours

✧ nerdjo who has to assure you he loves you and thinks you’re as beautiful as “The Euler-Lagrange Equation” (you have no idea what this means)

✧ nerdjo who puts his hands under your stomach, thighs and boobs to keep them warm

✧ nerdjo who bores you to death as he talk about quantum physics but you don’t say anything because you find it cute the way he sometimes spits by accident when he rambled and how his glasses slowly fall when’s he’s making movements as he talks

✧ nerdjo who likes to prove you wrong whenever you try to be a “smarty pants”

✧ nerdjo who softens when you go up to him while he was working on a project and tell him you’re worried about him because he looks like he hasn’t slept in three days

✧ nerdjo who mutters to himself in class when a stupid frat guy tries to answer the professors question, obviously saying the wrong answer but clearly only doing it to get laughs out of everyone. “what an idiot.” gojo grits to himself

✧ nerdjo who looks seriously shocked when he’s helping you with your homework and you get the wrong answer even though the right answer is CLEARLY right in front of your eyes “love… you seriously don’t know the answer…?”

✧ nerdjo who spends HOURS in the library to a room all by himself, books, papers, pens and pencils all scattered around the table while trying to get his work done, his hair messy and eyebrows furrowed, but when you text him saying you were gonna drop off food for him, his whole demeanor turns soft and giddy thinking about how he’s gonna be able to see you

✧ nerdjo who if he’s not doing homework or reading, is playing or watching digimon in your dorm, explaining everything he possibly can so you can catch up to the lore (you stopped listening a long time ago)

✧ nerdjo who doesn’t really talk much in class but when he does, the professors have to cut him off because gojo can talk for HOURS

✧ nerdjo who makes you sit on his lap as he codes on his computer

✧ nerdjo who can solve a rubix cube in a minute and always does when you ask him to (for your own entertainment)

✧ nerdjo whos into physics and computer science

✧ nerdjo who awkwardly puts his arm around your shoulder when the two of you are walking back to your dorm (he nearly trips)

✧ nerdjo who when you tell him a fun science fact, crosses his arms, leans back on the couch and goes “well ACTUALY-“ it’s too late to stop him, he’s already yapping to you on how the fact is wrong

✧ nerdjo who starts looking stupid now because you two have a class together when the new semester started and he can’t concentrate at all because he’s too concentrated looking at YOU

✧ nerdjo who tries to be freaky by putting his shaky hand on your upper thigh but you smack it away and he gives you a sad puppy look as he fixes his glasses, you swear you could see tears forming in his eyes

✧ nerdjo who runs to you when he finishes a prototype for whatever sciencey class he has and with full confidence says “you’re looking at the new science prodigy babe!” “uh huh” you say

✧ nerdjo who goes to the library again to study, he’s so stressed but he’s glad you came along, that’s until you went under the desk he was sitting at, undoing his belt and pulling down his pants and boxers JUST barely, hes literally gripping onto the table, face flushed hair messy crooked glasses and chest heaving trying so hard not to make it obvious you have his dick in your mouth

✧ nerdjo who makes you tag along with him to the nearest store to get the newest Digimon cards

✧ nerdjo who makes you gasp when you turn around for one second and look back to see him fighting a literal ten year old for a box set of Digimon cards

✧ nerdjo who doesn’t show you memes, but shows you reddit posts that you have no interest in looking at

✧ nerdjo who makes you sit on his face, but not to eat you out, but so your thighs can squish his face. he says that “it de-stresses him” and when you go to complain he says “it’s scientifically proven that it does”

✧ nerdjo who SOMETIMES is a cocky asshole in class, and when an acquaintance of yours who’s also in gojos’s class tells you how much of an asshole your boyfriend is, you straighten nerdjo up by riding his face nonstop to the point he’s crying because HE’S not getting any action

✧ nerdjo who you convince that overstimulating him will “de-stress him” and “make him focus better” so when you tied him up in your bed with a vibrator wrapped on the head of his cock, he’s whining, crying, squirming, eyes rolled all the way to the back of his head and pleading you to “let him do anything to you” (when you finally let him cum he tells you the next day that his focus is 97.56% better than it was the day before)

✧ nerdjo who’s so competitive when the two of you play video games he forgets you’re his GIRLFRIEND and is brutal with the insults when you loose

✧ nerdjo who’s actually really strong and likes to carry you around your dorm or outside when the two of you go for a walk. and even though you’re protesting and telling him you “don’t wanna hurt him” all nerdjo says is “just cause i’m smart doesn’t mean i’m not strong”

✧ nerdjo who likes to suck your clit while gripping your tummy

✧ nerdjo who likes to grip your fupa cause he’s weird like that

✧ nerdjo who ANALYZES your pussy and your actions whenever he’s fingering you or fucking you so he can make you feel better for the next time you two fuck (you always have a stronger orgasam each time after the other)

✧ nerdjo who bites his nails and gets told off by you (he immediately begs for your forgiveness)

✧ nerdjo who kisses your tummy whenever he lays down on your lap and turns his head so he’s looking up at you and says “you’re the most angelic thing i’ve ever seen, you know that?” he sighs contently while pushing his glasses up and giving you the stupidest toothy smile

[ckret2]

i am FASCINATED by the little scraps i've heard about bill's uncle. am i allowed to know more about him. and if the answer is no do you have a chapter estimate for when i am

yeah sure, I already made a post on Bill's mom, I've finally got enough material to make a post on Bill's dad.

Bill got his gorgeous eyelashes, warm color scheme, black limbs, and personality from his mom. He got his shape, his brick lines, and his slitted pupil from his dad. His dad's a self-made businessman*! (*His dad got suckered into joining a multi-level marketing scheme and now he makes money by suckering other people into joining the MLM scheme.)

And: his dad has a brother. They're twiiins!

Bill keeps targeting twins. (The Stans, the kids, TBOB says Pyronica's got a twin sister Hydronica...) I imagine Bill's twin obsession is rooted in something close to home.

Because Euclid & Euler's eye split in half mid-development, they have unusually oval-shaped eyes—a common sign of twins. They've been going to an optometrist since they were toddlers to deal with poor eyesight and floaters in their peripheral vision. They've had a mix of surgery, corrective lenses, and medication to narrow their field of view to the area they can see clearly. So when baby Billy said he was seeing "bright white dots" on "the outside of everything," Euclid went aha! He knows exactly what Bill's seeing!

He did not, in fact, know what Bill was seeing.

Bill's parents didn't regularly visit family, but Euler was the one relative they saw most often. He was the first person to snap out of the "haha it sure is funny how Bill can guess when somebody's about to knock on the door" rationalizations to realize that Bill really could see things no one else did.

And since Bill's parents are sort of disasters who think starting a cult is a great get-rich-quick scheme, Euler was one of the most emotionally stable role models in Bill's life. It sure is a good thing that Euler was a constant presence and nothing happened to him during Bill's tender formative years!

"But wait," you say, "you told us that Bill got his shape and slit pupil from his dad. But wouldn't that mean he got genes for a square? And how could he have gotten a slit pupil if that wasn't a genetic trait, but a consequence of an eyeball splitting in half?"

Triangles and slit pupils don't run in Euclid's side of the family. But squares and twins do.

I imagine Bill's twin obsession is rooted in something close to home.

"So Steve exists in your headcanon—?" No. He's a stillbirth his parents pretend doesn't exist. He's a crime Bill committed before he was born. He's the imaginary phantom Bill's parents are searching for when they look at Bill—starting fires, hallucinating, spitting up his medicine—and wonder what he'd be like if he was different. He's a symbol representing a source of unconditional love and support that Bill deserved and needed, but never had. Steve's all those things—but he doesn't and never has existed.

And there at last is my Euclid headcanons post. If y'all are interested & didn't see it, here's my Scalene headcanons post! And some headcanons about shape twins that still basically work post-TBOB, we just know now that Euclideans don't need a line and a polygon to reproduce.

(95% of my headcanons about Bill's dad & uncle are pre-TBOB. The only difference is that I originally designed Euclid & Euler as green trapezoids that had split from a hexagon. Trapezoids so that Bill and his dad could do this, green so that Bill's dad could be the original color Bill was designed as before the Gravity Falls crew made him yellow & so that his family could be money-colored: gold-colored Bill & mom, dollar-bill-colored dad.)

(After TBOB/TINAWDC revealed his dad's a triangle and either red or blue, I decided to make the twins blue-green (because I wanted to keep in that "bill's original color scheme" reference) and finagle it so that Euler could still be a trapezoid; after Pyramid Steve came out, I suddenly had a really good thematic reason to make them blue-green. I'd been playing with the idea of making Bill a shoulda-beena twin, Steve finalized that decision by giving me a physical design that could tie into Bill's extended family.)

[ipso-faculty]

Infinity symbols: a guide to their variations

Infinity symbols are popular in graphic design for good reason. In this post, I'm gonna describe ways to vary up the designs of infinity symbols. My goal is to educate fellow neurodivergent people on how to make infinity symbols that don't look like the Métis flag.

The neurodiversity community has been using rainbow infinity symbols since 2005. Here are neurodiversity flags from 2013, 2016, and 2019:

However, there's a problem with some of the new flag designs for a flag that is autism-specific. Here are some of the contenders:

These use a solid white infinity symbol. The solid white infinity curve is a symbol of Métis.

The Métis flag, created in 1815, has a white lemniscate on red background. Nowadays the Métis use the blue version more often. And to the right is the Métis queer pride flag:

For those unfamiliar, the Métis are one of the major Indigenous groups in what is now Canada, with most of their >600,000 population in the western and central parts of the country. The word métis means half-breed in French; lower-case m métis refers to those with mixed Indigenous and European ancestry. Capital-M Métis refers to the specific culture of métis that emerged, distinct from both Indigenous and settler cultures, and speaking hybrid languages such as Michif.

The issue of likeness has been brought up many times. While I can believe the autistic flag makers didn't know about the issue when making their designs, I know at least one of them was promptly informed of the issue and dismissed it.

The autistic community writ large has been pretty dismissive about this issue. I wonder if some of the defensiveness comes from not seeing an alternative - thinking that infinity symbol design is all or nothing.

I have some good news: it's possible to make infinity symbols that don't look Métis!

HOW INFINITY SYMBOLS VARY (PART ONE)

ASPECT A: TOPOLOGY

The first way we can categorize infinity symbols is their topology. These four varieties are most common

Topology 1: Open infinity symbol - this is the oldest style of using a figure-8 shape to represent the mathematical concept of infinity. On the left is the version Euler used.

-

Topology 2: Lemniscate - a closed curve. On the left is the Metis flag. The curve is one solid entity: notice how the rainbow gradient on the right fills the whole thing.

-

Topology 3: Infinity *loop* -  imagine you take a hair tie or rubber band and twist it. One part of the infinity loop is clearly in front, with another part clearly behind it. Loops are well established for neurodiversity and I think we should stick to using these.

Notice in the left example how the pattern flips between left and right. Also compare the rainbow gradient on the right to the lemniscate rainbow gradient above it. -

Topology 4: Infinity *ribbon* -  instead of a hair tie, use a ribbon. Ribbons have sides, producing an infinity loop that shows two sides.

-

ASPECT B: THICKNESS

Line width can vary, which also helps to convey a loop! Again, I think we should be sticking to infinity loops when it comes to autistic/ND designs.

Option 1: Constant Thickness The lemniscate on the Metis flag has a constant line width, as does this neurodiversity rainbow gradient from 2016. I think we should avoid constant thickness.

-

Option 2: Variable Thickness A variable thickness can help to reinforce that an infinity symbol is a loop rather than a solid lemniscate. There are a lot of ways to play with line thickness!

Many neurodiversity infinities are variable thickness and I think we should opt for this to steer clear of Metis territory.

THIS WILL BE CONTINUED IN A SECOND POST (tumblr has a limit of 30 images per post)

But just in case the second post gets lost in reblogs: I think variable thickness, combined with a loop topology, is what we should be using for neurodiversity & autism. E.g.

CONTINUED IN NEXT POST

[nyancrimew]

what if i told you about Euler's Line? it's a line that goes through every type of center a triangle has, from the circumcenter to the orthocenter, the centroid, even the nine-point center!! it's actually a really cool property triangles have. i would recommend u read more into this its a quite interesting topic and very deep. if u wanna learn more about this u should search up "among us impostors kissing red sus" on duck duck go images

wow that's so cool let me duck duck go images that real quick- hm this is awakening something in me, triangles are so cool

[rbrooksdesign]

"DMT-EDMT Series for December Geometry #5"

The Butterfly Fractal 1 (BF1) is a fractal resulting from the simple doubling of quantity "1" -- 1 -- 1x2=2 -- 1x2x2=4. -- 1x2x2x2=8,...

When you lay it out into its "Butterfly-like" array, you can see that every "1" becomes a new source for the self-similar, re-iterative redundancy of the same "fractal" pattern within.

The BF1 pattern is repeated on both sides (of the "wings.")

The new source is circled in RED.

Counting the number of REDs at the bottom = 2, that is also the value of "x" ("x" is the short side of the PN rectangle, xz. z=Mp=the long side.)

Another tidbit that plays out: p=2, is the number of levels up, starting with level one encircled RED.

Math: Euclid-Euler Theorem = 2ᵖ⁻¹ (2ᵖ -1) = Perfect Number (PN) where 2ᵖ⁻¹ = x = 2¹ =2, and, 2ᵖ -1 = z = 3 = Mersenne Prime (Mp), as xz=PN.

[quillusquillus]

HELL YEAH I'M DOING THIS AGAIN BITCHES!! After literally over a decade since doing the last one, I decided to once again throw my OCs at this ridiculous how-do-your-OCs-react adventure text.

This was very cathartic because I haven't written anything for my OCs in a really long time, but I also made it REALLY LONG sorry. Content warnings for: cringe, gore, lots and lots and lots of swearing, very mild spoilers for the 2016 Dirk Gently's Holistic Detective Agency tv show, and me getting way too into making my OCs fight each other

Blank template is here!

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THE ULTIMATE OC ADVENTURE MEME!

RULES

Don't look at the questions before you fill this out! That's cheating!

Tag three people (or more) at the end of this meme and you'll get a cookie.

Try not to skip any questions!

Have fun!

Fill out the forms below:

CHOOSE EIGHT ORIGINAL CHARACTERS:

Kasrou Euler

Pat Grundy (human bound form)

Quentin Barlington (Level 4)

Beau Boggart

King Imsara (wastelander version)

Effa

Happon

Zombie James

CHOOSE ONE OF YOUR FAVORITE CHARACTERS FROM A FANDOM:

.21. The Mariner (Waterworld (1995))

CHOOSE YOUR LEAST FAVORITE CHARACTER FROM A FANDOM:

.41. Gordon Rimmer (Dirk Gently's Holistic Detective Agency (2016))

CHOOSE #5's LEAST FAVORITE FOOD:

.61. "long pork"

--------------------------------

.1. Each of your OCs receive a letter in the mail. Upon opening the letters, they realize that the letters were sent to them by the king! The letters ask your OCs to report to the king's palace at once. How do your OCs react?

King Imsara: Heheh :) Quentin: Did you send this? Imsara: No, I'm the king of the -wasteland- not the king of the fantasy land. This will be interesting though. Effa: Fuck this, they better be paying me for this. I don't do work for free. Kasrou: *nodding shyly but solemnly* Quentin: Well I'm sure we will, and even if we aren't how wonderful to go and visit a king!- Ah, oh, no offence… Imsara: None taken :) Pat: Oh yeah, this'll be something all right heh heh Happon: <Awesome!> :D

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.2. Upon reaching the palace, 3, 5, and 8 are grabbed by guards - they apparently resemble wanted criminals! What happens?

Quentin: Oh there's been a terrible mistake, please let me go! We've been summoned by the king and certainly aren't any sort of criminals! James: help Imsara: *completely relaxes* Yeah it's okay, we're okay, we have nothing to hide :) Guard: you've got dirty great knives on you! Imsara: Ah but they aren't -hidden-, are they? Guard: :0 … >:I James: I'm not… I'm really not dangerous I swear Quentin: Exactly! We're expected by the KING, you know. If you'll just fetch someone in charge I'm sure we can get this whole misunderstanding cleared up right away! Go on now! (+6 to persuasion)

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.3. The guards realize their mistakes and release the "criminals". As your OCs are escorted to the king's chamber, 4 realizes that they need to use the restroom. The guards point down one of the hallways, and 4 quickly goes exploring for the restrooms. But they get lost in the process! What happens?

Beau is a living patch of fear-eating darkness in the shape of a scary goth clown and absolutely does not need to use the restroom. They use this excuse to creep around the corridors and stalk and scare the absolute shit out of a poor maidservant, haunting her with howling shadows until she runs screaming down into the main hall babbling incoherently.

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.4. 1 gets worried and goes to find 4. What happens?

Kasrou: Um. h-Hello? Beau? *holds floofy tail and creeps about nervously* Is that you? Um I noticed you weren't saying much earlier and you went off on your own, is everything okay? Beau: *a door creaks open revealing Beau, standing motionless with red glowing eyes* Kasrou: Eeek! *clutches tail* Oh! Um… sorry that was rude. Are you all right? Beau: ….*tilts head* Kasrou: Well um. It's okay if you need some time on your own, I just thought you should know we're going to see the king very soon. Beau: ….. Kasrou: I was a bit worried you might have gotten lost, actually, it's awful complicated in here. Would you like to walk back with me?

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.5. 1 and 4 eventually find their way back to the other group. Everyone bows as the king approaches them. He speaks of a horrible problem that had befallen the kingdom - the world's chocolate supply went missing! The king then moves on to revealing that your OCs are the "Chosen Ones" who must bring back the kingdom's supply of chocolate. How does everyone react?

Quentin: *gasps* No!! All of it?? ALL of the chocolate?? Happon: <Ehh even the chocolate cakes?> :0 Kasrou: Oh noooo :( Effa: Why is this you guys' fucking concern in this situation Pat: Well I'm sure we can handle that, mister king- er, your majesty. Personally I'll be needing it in writing of course, technicalities of my profession and all that, feel free to cast your eye over these terms and see if they're to your liking. *does a very inaccurate bow with several spinny hand motions* Imsara: As one king to another… I'm not sure I'd recommend that. King: Oh? And why might that be? Pat: *turns slowly to look at Imsara with eyebrows raised like are you seriously doing this? here? now?* Imsara: You chose him so it's your decision of course, but from what little I know of this guy… *meets Pat's look* …I feel being in his debt means bad news for you. Pat: *turns to the king with arms spread wide* Eyy I'm a demon, okay? We all know it, we both went into this relationship eyes wide open et cetera, I'm not beating about the bush with ya here. If I'm supposed to be one of yer "Chosen Ones" this is the way it's gotta be. Couldn't change it even if I wanted to. You sign; I do. 's the way it's gotta go. King: Hmm… I have read your terms, and they seem fair. I will accept this, for the sake of the kingdom's chocolate. Sign here, you say? Pat: *turns to Imsara while the king signs his contract and does a grin and a shrug at him as if to say 'well, what can ya do?'* Imsara: *shrugs and smiles back at him, but the smile doesn't reach his silvery eyes*

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.6. Before the king sends the Chosen Ones off on their journey, a big banquet is held for the new heroes. Unfortunately for 5, all the food served has 5's least favorite food (61) in their recipes! How does 5 react?

Imsara: *completely freezes for 2 seconds after taking a particular bite, then eyes flick quickly around the table. nobody else who is eating has noticed anything* Pat: *catches Imsara's eye and grins knowingly, raising a goblet of wine in toast then stabbing a forkful of food and putting it in his mouth* Imsara: *looks around the rest of the table again, thinking, then relaxes and leans back casually away from his plate as if full, looking content. he says nothing* James: *doesn't even have a plate* This food smells kinda weird… Kasrou: Oh, are you sure you don't want any? James: No I'm… I'm good. Happon: <That's a real shame cuz this is super tasty!> Very good! *he gives a thumbs up to the king*

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.7. After being given instructions to travel to the Temple of Chocolate, the Chosen Ones set off on their journey. However, as the sun sets on their first day together, 2, 6, and 7 get into a brawl! What happens, and what are they fighting over?

This group splits off from the rest of the group for a bit. Pat immediately clocked Effa right away as someone who is really motivated and hedonistic and a good mark. Effa has zero respect nor fear of Pat, since demons in Effa's universe are entities they deal with regularly that are overwhelming powerful forces and Pat just seems to be some annoying humanoid guy and not a demon at all.

Effa: And I'm saying I wouldn't need your stupid contract to make you do as I say, unless you have some kind of hidden power you're not showing us besides making paper appear and disappear. I don't know what kind of stupid weak bitch universe you come from but in mine, THIS is a demon. *tearing, glitchy sound and suddenly a huge, rainbow arm sprouts from their back* Kasrou: Yikes! *holds sides of face* Pat: Wowie! Yeah, that's very impressive! Something I ain't never seen before that's for sure. You two buddy-buddy back there? I wouldn't wanna compete, that's a very close relationship I see, I respect that. Can't help but make the observation though, that I would surmise I could provide a, ah, different sorta skillset than offered by a giant glowing hand? Effa: *grinding teeth with a faint cricket chirp noise* You really don't fucking shut up do you? Don't you fucking get it? I don't NEED help from someone as pathetic as you! *snatches the air with their own small hand as the giant rainbow hand rockets forward and grabs Pat by the head, lifting him off his feet* Pat: *grabbing the hand encasing his head, legs kicking in the air vaguely* Hmmg! mmnf? Ermnnff! Happon: *steps in and waves hands* <Whooaaa wait wait!> Stopp, stopp! No fighting, please! Effa: *sneers at him* And you can shut up too <fucking bastard> I'm tired of hearing your stupid nihon jabbering just speak fucking english. Happon: My english is not good :( Please no fighting! <I'm beggin', put him down!> Effa: *ignoring Happon* No I'm gonna rip his fucking head off, if he's really a demon he'll be fine Pat: *kicking* Mmmf mm mmmn! Happon: <Stop!> *dashes forward and transforms in the same motion, rushing into a hovering shimmering wall of blue coils in front of Effa. his dragon snout stops right in front of their much smaller face, ears down, round yellow eyes enormous and pleading* Effa: *stumbles back, startled, waving Pat though the air* Pat: Hmmf! Effa: *recovering their composure* Oh I see, fucking magic dragons and shit, I forgot that's the kind of bullshit I have to deal with here. You want to fucking go instead, huh? *they turn and stare hard at the rainbow arm, after a second or two it opens and lets Pat fall to the ground* Pat: Owf. Effa: *another ripping, crackling sound and a second demon arm joins the first, both of them arcing over Effa as they sneer at the blue dragon* Happon: *cowers, ears drooping, making a low keening sound* <We aren't here to fight, we're here to help each other out… right?>

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.8. 1 convinces the brawlers to stop fighting. However, 2 and 7 are still ticked off at each other, even after the fight. What happens?

Kasrou: uh… um. Effa? I think everybody here thinks you're the strongest, you don't need to hurt anyone to show it! Happon: *nodding vehemently* Effa: *narrows eyes* Kasrou: And I think Mx. Grundy got the message too! Pat: *still lying on the ground* I sure fucking did. Yeesh kid, a simple "I'm taken" woulda sufficed you don't have to get catty about it. Effa: *rounds on Pat again, eyes narrowed* What did you call me? Pat: *getting up and dusting himself off* Hey no offence, most people are kids to me, ancient being from the dawn of time and all that, nothing personal. Effa: Yeah RIGHT. These losers are right, why am I even wasting my time with you… *raises hands and focuses for a moment, the giant rainbow hands fade and disappear* Kasrou: *sits down hard and holds her face in her hands* Oh thank goodness Happon: *transforms back to human and crouches next to Kasrou, putting a hand on her furry back* Are you okay? You are very… ah.. <how do I say you have courage..> good strong fight? Very small, very tough. :D Kasrou: Aw Happon that's very sweet of you to say. Magic users are so scary!! Happon: *leans in conspiratorially and stage whispers* Next time, you let them fight, okay? Pat is demon, you don't need to fight for demon. He is strong, and bad. Head off? Baaan… no trouble. Pat: Hey I heard that. I'd like to keep my head attached as much as possible, if you don't mind.

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.9. Dawn! Your OCs wake up to another beautiful day. After shaking the sleepiness out of their systems, they check their packed bags to pull out breakfast. Unfortunately due to poor planning, there's only enough food for seven people! What happens, and who doesn't get a meal?

Beau and James don't eat food anyway so this is not a problem. Pat doesn't need to eat food but does so anyway just to be obnoxious.

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.10. Your OCs arrive at a small, ocean-side village. 1 and 8 are sent into the village to look for a grocery store of some sort. After a few hours of searching, they can't seem to find any stores! When they return to the group empty-handed, what happens?

Kasrou: Oh dear, don't they even have food printers or anything? James: Uh, I don't think this place has that kinda technology… Still, it's pretty weird there's no stores… Kasrou: Do you think if we knock on some of the houses they might share some food if they have any? James: Um. If we do that it'd probably be up to you, I'm usually not that great at getting strangers to trust me Kasrou: Really? But you seem so nice! James: Oh… uh….. thanks….. *embarrassed and mildly flustered by this* -they return to the others- Quentin: What?! Nothing?! Are you sure you looked properly? I refuse to believe this. *starts trotting off into the village to check for himself* (+0 to perception)

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.11. Frustrated, the rest of your OCs go into the village and eventually find a vendor of food. As night falls, they choose to spend the night at a local inn. It's a very small inn, however, and 2, 8 and 3 are forced to share a room! What happens?

Quentin: This is outrageous, this place doesn't sell food and has the smallest inn I've ever seen, do they even WANT people to stay here? *is pulling a blanket off the bed and laying it on the floor for himself* James: I mean I don't have to be in here, I don't sleep so… I can just be on watch. Pat: Yeah I don't need sleep either *swings himself into the bed, fully clothed and with his boots on, and lights a cigarillo* Quentin: You are NOT smoking that in here, put that out immediately Pat: *grins* Is that a formal request? Quentin: No it is not! >:( *flicks his wand and puts the cigarillo out with prestidigitation* Pat: Aw

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.12. As it turns out, 2 snores very obnoxiously. How do 3 and 8 handle 2's awful snoring?

Quentin: *throws a pillow at Pat every 10 mins for the first hour or so, getting increasingly cross* James: *is sitting knees up on the open windowsill, watching with pale eyes catching the moonlight* I'm pretty sure he's doing that on purpose Quentin: *sleepy, cross* Oh, of course he is! And he can certainly stop it! Pat: *cracks one eye open and grins* James: I mean I could probably just throw him out the window if you wanted me to Quentin & Pat: *both look at James* James: …I'm just saying I can, it's a suggestion. He'd probably be fine, right? Pat: You know, I think I like you, kid

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.13. 4 wakes up early and goes downstairs to eat breakfast at the inn's small restaurant. But as 4 orders their food, 21 approaches 4 out of nowhere! 21 announces that they are an assassin from a rival kingdom, and that it is their job to kill 4. How does 4 react?

I love this meme because it puts characters together in situations you'd never think to come up with in a billionty years. I think if the Mariner was hired to assassinate Beau specifically (because Beau previously haunted that rival kingdom and now they're mad about this evil creature becoming one of this kingdom's chosen ones?? idk), then he'd have to not know what he was up against or he would have refused. So imagine this Kevin Costner-looking guy creeping stealthily around the inn with a speargun and a big fuckoff knife. Beau doesn't sleep and so was never in a room in the first place, just sitting and staring unblinking with teeth bared at an empty table the entire night. The Mariner peeks into an open window, sees this enormous freaky clown person, catches their rancid vibes IMMEDIATELY and vanishes without a trace. Beau's head turns slowly to look at the place where he was moments before.

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.14. 6 hears the commotion downstairs and quickly rushes to 4's aid! After a bold fight with 21, 6 emerges victorious, and 21 drops to the floor, dead. How does 4 react to 6's heroic efforts?

There was no commotion and Effa wouldn't rush to anyone's aid anyway, but they encounter the Mariner on his way out by coincidentally running into him. Effa: *hissing* Watch where you're FUCKING going! The Mariner: *instinctively swipes his knife at Effa to get them out of the way as fast as possible* Effa: !!!! *stumbles back, summons arms in a sharp crackle and immediately lunges for the Mariner* [Scenes of Unimaginable Violence] I don't want to describe this because I love the Mariner very much but Effa is a professional supervillain and would absolutely destroy his fish mutant ass no question. For a visual, imagine that scene in one of the Avengers movies where Hulk grabs Loki by the legs and bashes him from side to side like a chimp with a dead snake. Beau does not react because Beau doesn't know this happens, and indeed the entire rest of the party remains unaware that the wanton murder of a beloved franchise character just occurred outside.

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.15. And they're off! Your OCs now travel along a cool, windy path running along the ocean. 7, who has gotten bored over time, suggested to the group that they go take a dip in the ocean for a break. 5 thinks this is irresponsible, but the rest of the group agrees to 7's idea. What happens, and how does 5 feel?

Imsara only thinks this is irresponsible because they should send the tougher folks in first to see if there's any unexpected fantasy beasties, but Happon is waaay too enthusiastic and persuasive and is yeeting himself ocean-ward followed by about half the group. Happon: <Wa'hoiiiii it's the ocean!> *flings his shirt off and he runs and jumps in, submerging fully and disappearing* Kasrou: *holding her tail out of the edges of the waves and giggling as they splash over her clawed feet* Quentin: *galloping through the waves with big splashes, tossing his tail and laughing* Oh this is fun! Exactly what was needed! Imsara: Well, too late now I suppose! *also pulls his shirt off and dives into the waves gracefully, emerging and happily doing some powerful strokes through the water* Effa: *is crouched on the wet part of the sand like a goblin, hunched and focused on digging in the sand. they take out a shell of some kind and hold it up without looking at it, letting go. it stays suspended in the air, surrounded by a barely visible grey-rainbow jitter, and Effa continues whatever they're doing* Pat: *chilling and smoking in the shade of the road's embankment* What's he doin over there? Is that magic? Weird kinda magic. You got magic wherever it is you come from? James: *is crouched in the same shady spot* Uhh… not sure really. Pat: But you're like some typea undead magicy sorta thing yourself right? A zombie? James: *looks awkward* Yeah but I mean like we don't have wizards or demons or… whatever that is. …I don't think so anyway. *slumps his chin into his hand* Man… the world got all fucked up, I don't know, maybe we do. Jesus… Pat: *winces slightly* Pat: Well I know what THAT thing is, that's a fucking boggart. *jerks his thumb at Beau, who is leaning against the embankment a short distance away in the shadiest spot, smoking a black cigarette that oozes thick black smoke that sinks downwards* Beau: *tiny high-pitched giggle*

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.16. How refreshing! It's such a scorching hot day, and even 5 grudgingly agrees to go swimming as they watch the others having fun. As time passes, your OCs realize that they need to get back to work. But as they leave the water, 1 suddenly gets attacked by a shark! What happens to 1, and who comes to 1's rescue?

Kasrou was in the shallowest edge of the water and was attacked by a little juvenile shark beach feeding who thought that her scaly clawed feet were delicious dead crabs. Kasrou: *shrieks horrifyingly* HYEEEEEEEEIIIIK Oh oh oh! Owwww! Ohh! Quentin: *galloping over with big splashes* What is it! Are you all right? What happened? Kasrou: *falling down butt-first into the waves, clutching her bleeding foot and keening* Something bit me! T A T Imsara: *swimming over fast* Quentin: Oh dear, let me see… oh that looks… *patting his coat pockets for any kind of potion* I don't have any healing spells, Pip's usually here for that sort of thing… :( Imsara: *walks up and crouches next to Kasrou in the waves* I'm gonna pick you up and take you somewhere dry, okay? Keep holding it just like that :) Kasrou: *sniffle* Okay…. Imsara: *bodily lifts the smaller Kasrou in a princess carry and brings her up the shore, trailing drops of water and a spot or two of blood* Quentin: *trots after, fretting*

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.17. 1 got away from the attack with minor injuries. However, this slows the pace of the group down, since they need to walk slower for 1 to keep up. 6 gets fed up with how slow the group is moving, and eventually abandons the group! A day later, does anyone miss 6? If so, who misses 6, and why?

Kasrou's foot is bandaged by Imsara (and given a "get better kiss" by Happon which surprisingly does make her feel much better). Quentin offers to let her sit on his back but, bizarrely, it's Beau who wordlessly picks her up, walking with her on their broad shoulder, supporting her with one hand. Effa is the one who leaves. They simply stop, go "tch" and start walking off in a different direction.

Quentin: Now where are YOU going? Did you see something? Effa: *without turning around* No, I just realised how stupid this is. You all have fun Pat: Wow, he just straight up gave up, huh? Quentin: Oh come on, you can't just walk off like that, what about, er, all your rewards from the king when we complete this quest! Effa: *flips him the bird without turning around* James: Guess they really don't like working in teams

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.18. The Chosen Ones now have one less comrade. Now it's a little bit more dangerous for them to travel… As the Chosens journey through a ragged mountain pass, they are jumped by bandits! The bandits team up on 2, who was the farthest away from the bigger section of the group. What happens to 2, and how does 2 react?

Pat: Whoa! Hey! Whoa! I'm not the guy you want, look at me, look at these clothes, do I look rich? Go bother those other guys! *gets jabbed in the side with the point of a sword* Ow, hey! Quentin: *a short distance away, facing off fewer bandits with the rest of the group* Oh bother this, don't you chaps have anything better to do? *flourishes with his wand and makes snapping, crackling firework sparks, causing the bandit nearest to him to back off* (+6 intimidation) James: Hey uh, Pat the demon guy's in trouble I think Quentin: *sighs disgustedly* Do we… really have to bother with that right now? Imsara: *says breezily as he slips through the others to get to Pat* Would be hypocritical if we didn't! Beau: *standing still a short distance away, holding Kasrou on their shoulder and grinning at the two bandits who look like they really don't want to get any closer* Pat: *gets knocked down by a guy with an axe and shield* Ah fuck me, come on! Imsara: *parries a sword swipe with one of his long knives and does some kind of cool twisty thing that completely disarms the bandit, moving smoothly to the next guy and dodging his axe before twirling around behind him and pressing his knife in front of his face, grabbing the man's hair* Happon: Waow :O Imsara: *in an almost freakishly calm tone of voice, still holding the knife to the man's face and throat* Okay, okay, everybody calm down, it's all right, we can stop fighting now. Bandits: *don't move, warily regard this standoff* Imsara: *turns slightly to address the man he's holding* You're the leader, yes? Sorry if I'm mistaken. Bandit leader: *a little confused* ….yes Imsara: Excellent! Excellent. Can we come to an agreement then? As you can see we can defend ourselves quite well, so maybe there's something you want that we can get you? Without any of us getting hurt? *he adjusts the knife minutely* Bandit leader: …well we were just… you know. Trying to get some money. You know? No hard feelings… you seemed like a bunch of fre- uh. Nice folks who might have something we could sell. To feed our families, you know… *he glances around at his men, who glance at each other and then all nod enthusiastically* Imsara: *with complete seriousness* Oh absolutely. I understand very well, I sympathise with that. *he takes the knife away from the startled bandit's throat, letting go of his hair and clapping him on the back instead* Pat: Hey what the fuck I'm bleeding here, you should gut that guy like a fish before he does the same to you Imsara: Absolutely not. The first step is always a show of faith. I'm sure we can come to some kind of agreement with these fine gentlemen

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.19. Surprise! 6 emerges from the shadows and helps the group defeat the bandits. How does 6 react, and how does the group react to 6's arrival?

Effa: You guys really do suck ass. Agreement? This is what you do when weak bitches get big ideas [MORE SCENES OF UNIMAGINABLE VIOLENCE] Quentin: Oh my gods D: Imsara: *rubs forehead and sighs* James: *in the background not watching and being sosososo glad he didn't have to fight humans either way*

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.20. Dun-dun-dun-duuuuun! 4 has leveled up! What's this? 4 has learned a new skill! What new skill is that?

Beau learned…… Empathy???

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.21. 3 is starving, because they forgot to pack plenty of food before they started journeying through the mountain pass. While the group is taking a break, 3 spots an absolutely ADORABLE bunny in some tall grasses a few feet away! 3's stomach growls mercilessly. What happens?

This wouldn't happen because Quentin doesn't like eating meat and thinks small animals are cute, however it's really funny to me specifically because why does the universe keep pitting Quentin against rabbits anfghtg (this will only make sense to me and my DM). Quentin instead goes "aww, a bunny :)" and then goes and acts forlorn and weak and whines at the others until somebody shares their food with him.

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.22. 7 catches an awful sickness. During one night out in the wilderness, 7 keeps everyone awake with their persistent coughing. How do the others react?

Happon: *coughing* <I'm dying, I'm definitely gonna die> T_T Effa: Stop being so fucking dramatic and shut upp Imsara: How do dragons get better from sickness? Do you want some more water? Happon: Yes please T_T Kasrou: Have you ever had this type of sickness before? Happon: I'm never sick, don't get sick… ocean magic sick maybe… Quentin: Oh dear, is that a thing? Do we all have that now? D: James: Nah it would spread faster to the smaller people first. …I mean, I think Happon: Bad bad bad sick *groans and coughs* <Aahh I want to become a pond loach…>

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.23. The Chosen Ones are nearing the end of the mountain pass…when they come across an ancient, dilapidated temple amid the trees. 3 dares 1 and 6 to enter the temple, no matter how creepy it looks. Do 1 and 6 take the dare, or are they chicken?

Quentin WOULD do that… He dares Kasrou because it looks pretty safe and he wants to cheer her up and get her feeling brave again after her injury (and also just because he wants to poke around in temple ruins. he's a ttrpg character after all, he's GOTTA). He doesn't dare Effa but they tag along anyway.

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.24. Whether 6 and 1 like it or not, the group decides to take a chance and enter the temple. Ancient runes cover the walls, and many plants have broken through the ground and have taken over the place. And there, in the center of the main chamber, lies a stone dais. On top of the dais lies eight weapons. As the Chosen Ones approach the weapons, the walls and the weapons start to glow! A voice speaks out to the Chosen Ones… "Take the weapons and use them against the evils of the world. You are the only ones who can save the world, Chosens." The Chosens take their weapons and leave the temple with renewed hope. How do they react to this experience?

James: *staring at his ornate machete-like shortsword* This is the sickest shit ever Imsara: Ohoho yes *spinning and feeling the balance of his new blades* Effa: You basic bitches got it easy I have to figure this shit out first *examining a multi-faceted crystal that they've suspended in the air, they flick it in annoyance and it spins around, sending sparkles everywhere* Happon: *holding his pendant and feeling the small localised rainstorm around him falling on his palm* :D Kasrou: I'm um, I'm not sure I understand mine yet either… *she is holding a delicate ornate monocle to one of her large eyes, with a hook that goes over one ear* Imsara: Seems like a magic-y thing, no? Perhaps Quentin can help Quentin: *stops galloping around excitedly trying out his new wand* What? Oh. Want me to take a look at it? Yes, I can do that, just give me ten minutes. *he begins to cast Identify* James: Well there's no need to identify the use for… that… *he points over at Beau* Beau: *curiously hefts an absolutely ridiculous giant wedge of a blade, more like a plank of rusty iron with a point and an edge, with two handles along the back and several spikes sticking out :) they lift it up to their mouth and play their three snaking tongues over the rusty metal, drooling* James: Okay well that's horrifying Kasrou: And what did you get, Pat? Pat: *slipping a large ring-shaped piece of coppery metal into his coat and winking* Never you mind Quentin: Got it! Looks like if you focus, you should be able to cast illusions with this! :) Kasrou: Ooooh :o Effa: *teleporting from point to point in the background using their crystal*

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.25. Alas, the final destination lies in the distance! Atop a hill, the Chosens can see the Temple of Chocolate, standing heroically in front of them. They begin to trot down the hill, when it starts pouring rain. 5 slips in the mud and slams into 7, causing 7 to drop their legendary weapon. How do they react?

Happon: <My pendant!!> D: Imsara: I'm so sorry, are you all right? Happon: Necklace, necklace! *scanning around the muddy ground* Imsara: Oh dear, did you see which direction it went? Effa: What are you two dummies fussing about *is using wizardry to make an almost invisible "umbrella" and is completely dry* Quentin: I think Happon lost his magic item, I don't see it anywhere… Oh this rain is AWFUL James: *super zonked out* Uh-huh… Imsara: Ah-ha! *sticks his hand into the mud and pulls out the pendant, handing it to Happon* Happon: Uwaaa thank you! Haha very dirty. *he starts brushing the mud off it* Quentin: Oh, here, let me *he taps it with his wand and casts prestidigitation, flicking the mud off and cleaning it immediately* Kasrou: Oh that's so handy :O Quentin: Isn't it?!? Pat: Aren't you a rain dragon, can't you do something about this fuckin rain? My smoke keeps going out *grumbling as he's relighting his cigarillo* Happon: Yes… <_< But… I like rain Pat: *glares at him* <Don't you wanna show them you're good for something? You've done nothing but slow them all down so far> Happon: *pales, then blushes and looks away. Slowly, the rain around them stops* Quentin: Oh it's stopping! Imsara: What did he just say to you? Happon: *bouncing up again brightly, only a little strained* All okay! I stop the rain :D Quentin: Oh hurrah! Imsara: *looks at Pat suspiciously* Pat: *ignores him and cheerfully puffs his cigarillo*

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.26. The group reached the Temple of Chocolate! The stairway glows as the Chosens approach, and the Temple seems to come to life. There, at the end of the hall, hangs the Sword of Chocolate on the wall. It must be pulled to save the kingdom from a chocolate-less fate! But as your group runs down the hallway, they're jumped by none other than 41! What happens?

They don't get jumped, Gordon and his comrade freaky cult bald guys with crossbows and cattle prods are already there. They've rigged up a welded-together framework of sparking cable and metal braces to the Sword of Chocolate, some weird chocolatey energy pulsing through it and snaking down through the cables into another, smaller device with about 50 levers and buttons, held together with spot welds and hazard tape. The whole thing hums dangerously. The Chosens burst in from the long hallway and Gordon-- a hunched middle-aged man wearing big square glasses and a huge off-white fur coat-- whirls to see them.

Gordon Rimmer: What the hell, who the fuck are these guys?? Effa: *manifesting two giant rainbow hands with a glitchy crackle* Who the fuck are YOU Gordon: Who the fuck are YOU?? *gestures to the drone Men of the Machine* Get these guys outta here, we have to get the rest of the chocolate energy. Come on! *he turns away and lets them deal with it while he presses some buttons on the device* Men: *stride stiffly towards the group, two of them hanging back and raising crossbows* Imsara: *sighs and flicks his knives out of their holsters* Men: *one of the crossbow men fires at Quentin, who has spread out away from the group. The bolt shanks him in the side and a second later a buzzing crackle of electricity surges down the attached wire* Quentin: *yelps and bucks, knocking the bolt out* Ohhhh that! Hurt!! :( *he flicks his wand in the air and a blinding light shines down on his attacker briefly, singing his skin and setting his sleeve on fire* Men: *while the one who shot Quentin is awkwardly patting out the fire on his clothes, another advances on James with cattle prod outstretched* James: *doesn't dodge* Aw come on please I really don't wanna- *jerks and exhales as the prod jabs him in the chest. sparks buzz between the metal bars of his mask and he looks up at the man, annoyed, then whacks the cattle prod out of his hand with the back of his sword and slips behind his guard to deliver a gut punch* Men: *the one who James punched doubles over slightly and gives a wheezing monotone 'Ouch'. elsewhere, the second cattle prod wielder advances on Happon, who yelps and runs away behind Beau, who has Kasrou on their shoulder again* Kasrou: *as the man strides towards them, cattle prod sparking, Kasrou taps the lens over her eye and suddenly both her and Beau scatter and are lost in a dizzying rain of pink cherry petals, the Men of the Machine drone man looks around in confusion, blinking* Beau: *from the edge of the petal storm, one enormous pale, purple-clawed clown hand reaches out and grabs the man by the head, yanking him into invisibility. there is a very heavy, meaty clanging sound*

Men: *the second crossbowman fires at King Imsara, who deflects the slow bolt with a lightning fast movement of his knives, leaving it sparking as it rolls across the floor* Gordon: *whirls around, taking in the state of things* What the hell are you guys doing?? *huffs and mutters and throws his hands in the air in exasperation, turns back to the machine. suddenly a massive rainbow hand grabs him by the back of his enormous coat and pulls him back* Effa: Better question is, what the hell are YOU doing? This machine looks pretty interesting, tell me what it does! Gordon: You came all the way here and you don't even know? What the hell are those hand things? Effa: This is a demon that can pull the skin off your entire body like a fucking snack wrapper, now tell me what this thing does or I'll let it- Hey!! *Effa's second demon arm has twisted around and seized the bundle of cables that feed into the machine, the weird chocolatey energy pulsing into the translucent rainbow appendage as well* You let go of that right now, we can take it apart later! D:< *the hand seems to be ignoring them, growing larger and starting to emit light, gripping tighter. the eye patterns on it suddenly move, the pupil dots on it and on the other hand flicking over to look at Effa between them* Gordon: It's using the energy! Let go of me I gotta shut it down! *he reaches into his coat and pulls out a gun* Effa: *before he can even finish levelling it at Effa they flinch and the hand holding Gordon reacts, slamming him down into the ground with brutal force and then flinging him across the room like a grey rag to crash into some distant rubble. the hand then flicks over and snaps onto the cables as well, pulsing larger. Effa raises from their startled crouch and takes in the situation* Shit!! Come on you bitch, you will DO WHAT I SAY! LET GO!

Men: *continue to harass the others, the crossbow men have switched to short nasty knives. they are unskilled but don't seem to react normally to pain and it takes a few moments for the group to successfully bring them down. the one Beau vanished is never seen again* James: *crouched on the back of one of the men, who is moving feebly but not getting up* What the heck is going on up there Quentin: *poking gingerly at his bleeding wound* I was wondering the same thing, is their magic getting out of control? Effa: *hissing* This is unacceptable behaviour, you'll regret this later… *another arm fizzles and glitches into existence, as if forcing itself through, followed immediately by a fourth. the hands are now massive, more than twice their usual size, and lazily pulsing with a weird energy that distorts the light around it. sparks are beginning to shower from the machine, and the Sword of Chocolate itself is vibrating slightly with the sheer power of vanilla and cocoa* Happon: I think we go now? Machine looks baaaad bad… James: We still gotta get that sword though. …somehow Kasrou: *from Beau's shoulder, who has reappeared* Demons where Effa and I are from are like forces of nature with intelligence. Effa's the one who summoned it, so if they can't control it I'm not sure there's anything we can do D: Pat: *chuckling* Demon. Yeah sure. *he fishes around in his coat as the others turn to look at him* That thing? *he takes the coppery ring object out of his coat. it's revealed to be a slim circlet made of twisting, intertwining metal* I'll show you a real demon. *he slips the circlet over his head, and immediately tiny red flames ignite along the top of it. it rises and floats above his head as he begins to grow in size. he's laughing wetly, the sound getting deeper and deeper. the others step back as a wave of heat emanates from his growing form. his clothes wither and slough off his body like old skin as his actual skin thickens and turns a dull red. he drops to all fours as his neck and face lengthen, long teeth sticking out of his face and his eyes sinking into hollow sockets that duplicate out of the sides of his face from two to six. the light in the entire temple begins to turn a weird diffuse orange, heat and the taste of ash making the air thick. everyone else backs to the walls of the chamber as he almost entirely fills the space: a gargantuan quadrupedal beast with legs like elephantine pillars, a huge spike on his back around which the flaming crown-- now giant-- lazily rotates. his wrinkled, sucker-dotted neck is tall enough that he holds it bent and pressed against the ceiling, hollow eyes in a face like a horse skull with a brick in it leaking fine dribbles of liquid metal as he looks down over Effa and the device* James: Okay. What the fuck Effa: *has finally noticed something's going on, looks around, then up* Oh shit, what the fuck are you supposed to be? *there is a hint of actual distress at this unexpected manifestation in the middle of being unable to control their powerful arms. they raise their own, much more fragile arms and a crackling, jittering angular shape appears in the air above them like an angry shield* Pat: *in a voice the same but much lower, wetter, that reverberates around the entire temple* I'm the Wandering Waste, bitch *he begins to raise his head, his thick neck cracking inexorably through the temple's stone ceiling. massive chunks of worked stone begin to fall and smash the device in huge showers of sparks and screeches of metal. the eyes on Effa's hands flick to Pat and the pupils tremble and jitter but it doesn't let go of the cables*

Effa: *the crackling shield is struck by rubble and the stone simply explodes softly like a clump of ash, instantly turned into powder* Oh you think I'm scared of a big cow? I'm a fucking WIZARD *a rainbow glitter crosses their faceted red eyes for a second as they raise their hand and a thin shaft of grey-white rainbow light appears from floor to ceiling like a blade. terrifyingly fast, it swishes horizontally across the room and through Pat's rotund middle. the light scores a deep smoking line in the floor and where it hits the pillars on the side of the chamber they crack and shatter along a perfect vertical slice, part of the supports collapsing* Pat: *freezes for a moment, then pulls his head out of the hole he's made in the ceiling and looks at his middle, then back down to Effa* Was that supposed to do something. Cuz it sure didn't. Effa: *looks genuinely afraid for the first time, antennae curling down flat against their head and their mouth hanging open slightly* Pat: *opens his skull-like jaw as he chuckles thickly* I'll take that as a yes. *with a great big stomp, he surges one giant leg forward and crashes it down on the machine. a big explosion goes off, a prismatic glitter sparks among plumes of electrical smoke as Effa disappears behind writhing cables, clouds of dust, and another pile of rubble from the collapsing ceiling. Pat lifts the enormous cylinder of his foot away and the pulses of energy surge back into the Sword of Chocolate and a shockwave blasts from it, sending the framework that was draining its energy crashing to the floor. as the dust settles, there's no trace of Effa or their demon arms, and the machine is quite literally flattened like a coke can. the crown on Pat's back begins to break apart and unravel, the flames sputtering, and he starts to shrink to his regular self as the others creep out of hiding*

Quentin: WELL.. That was… certainly something. Is the rainbow demon thing gone? James: Wow… just, wow. There's nothing left Pat: *brushing off his coat, which grew out of him horribly as he returned to his human form* Imsara: How… *shaking his head* did you do that? Pat: *grins* A little jaunt back to my usual self, shall we say. Looks like a one shot wonder though. *he nudges a piece of copper with his toe; the remains of the circlet scattered across the floor* Happon: <Bastard, if you could do that kinda thing from the start you shoulda said right away! People got hurt for that!> >:( Pat: Hey, bad guys getting hurt doesn't count, right kids? Everyone knows that *he turns to the rest of the group and grins* James: :/ I'm just gonna… I'll go get the sword I guess.

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.27. The Chosens finally reach the end of the hallway, and 8 pulls the Sword of Chocolate from its place. They have fulfilled their destiny! They return to the king's palace and are honored by the rich and the poor alike. Chocolate has returned to the kingdom. How do your OCs act to their sudden rise to fame?

James: Cool cool I'd really like to go home now actually Quentin: Oh but this is the best part! *trotting happily down the main street and waving to all the people* This is where they get to show us how happy they are, and we get to show them that we were happy to do it! AND they're giving us stuff :3 Karou: Quentin, are you sure you're all right, you were bleeding pretty badly yesterday :( Quentin: Oh I had a night's sleep, I'm fine! Wound's completely gone James: …What

---

.28. Your OCs say goodbye to one another and return to their old lives. How do they handle the memories of their travels with each other?

Effa: *crouched on a hilltop moving the teleportation crystal back and forth in their grasp, idly watching its facets glitter. they are thinking violent thoughts of revenge*

---

.29. WHAT? Your OCs roll over in their beds, startled awake by thunder and lightning outside. IT WAS ALL A DREAM! How do they handle such a stunning realization? Do they miss the people they traveled with?

Kasrou: Ohhhhh that was an exciting dream!! I'm going to write this down on my blog before I forget! Pat: …*smokes contemplatively, wondering how the hell he had a dream. maybe he's been bound in this form long enough for weird shit to start happening*… Quentin: *yawning and stretching delicately on his bedroll* Oh you guys are NOT going to believe this insane dream I had, I was working with a zombie, and a little furry person, and a dragon and… I mean… well I suppose that part wasn't all that different, anyway I- Imsara: *holding face in hands* Heh. I could probably take some parts of this and turn it into a story for Gem. Effa: *jolting awake, wrapped and twisted in their silk sheets, they'd be sweating if they had sweat glands* Gah! Ooooohhh… fuck that guy. Fuck him! *gets out of bed shirtless and pours themself an expensive drink in an expensive glass to calm down. it doesn't really help* Happon: *yaaawns expansively and stretches his talons, before curling up in his river embankment nook and falling back asleep, entirely unbothered by the mysteries of his own subconscious* James: *snaps 'awake' from whatever strange dissociated version of sleep he was in that allowed him to dream. he goes over to the edge of his lookout tower and leans on the windowsill* …..damn… DO we have wizards? Beau: … *in the pitch dark of a closed funhouse, Beau taps their shoulder thoughtfully and gives a little high pitched giggle* …Sweet little thing….

[mathematics-official]

Hi! I'm Mathematics (it/she/any), you may know me from school :3

I'm excited to join the gimmick verse!

Out of character I write in red, my name's Leona (she/her), main account is @eulers-biggest-fan

My tags are:

#ooc, for when I'm Leona :3

#mathematics, and #mathblr, for when I'm maths and talking about maths

#not math, for when I'm maths and not talking about maths

#poll, for polls

#ask, for when I get asks (pls don't ask for donations)

More to be added, maybe

[nhp-researcher180]

//INITIATING SIGNAL //SetRecip.Public //AUDIO BEGINS

Wait, so how do I know when it's on? The red light? Ooooooh, right! Thanks Euler.

Ok! Hello Omninet! I'm Leila Marris-Orion, an NHP researcher with Union Science. I'm currently taking an indefinite leave of absence out to the Dawnline Shore, hoping to learn more about my family history.

I'm joined by my close friends and research buddies, Adela, Euler, and Dio. I'll let them introduce themselves.

Welcome. I am called Euler. I am an [ATHENA]-class NHP, licensed from Smith-Shimano Corpro for use by Miss. Leila Marris-Orion. I have greatly enjoyed my working relationship with Miss. Marris-Orion, and I anticipate further intellectual stimulation from her current foray into historical records. Adela, if you would proceed?

Oh, me? Yes! Yes, alright, my turn! So, hi, I'm Adela. I was the first project that Leila worked on, which I believe makes me... an [ENLIGHTENMENT]-class, no? Leila is a wonderful friend and I'm just so happy that we're getting to travel out and see the galaxy together! I know we're all going to become great friends, so please don't hesitate to reach out and say hi! Ok, umm, I guess it's Dio's turn now? Dio, please be nice...

Hello, hello, hello! I am Diogenes, but you can all call me Dio. I'm a [SISYPHUS]-class NHP, don't worry about it. I work with these other brilliant minds, and I promise that you can trust absolutely any and all links and files I will be sending you the moment our dear Head Researcher is gracious enough to give me unsupervised access to this omninet connection. Swear on my heart, which as an NHP I definitely have!

Absolutely not. Anyway, let's see... Oh, I'm licensed for several SSC mechanized chassis, specifically the Swallowtail and the Deathshead, but I can't actually use them at the moment. Something wrong with the licensing code? Whenever I try to print anything it just makes a- Bone Gecko! We are not calling it a 'Bone Gecko'! But yes, it spits out what looks like an eyeless, skinless lizard. It's honestly pretty unnerving, so if anyone knows about like, printer coding and such... help?

How do I turn it off? Is it this sw- //AUDIO ENDS

[zkylearnstherope]

AvPhysics - An Analysis [Part 1]

[Part 1] - Part 2 - Part 3 - Part 4

Disclaimer: This will only be a surface-level analysis for Animation vs. Physics. If you expect something more in-depth, you have to wait for the physicists.

Let's get into it- shall we?

Obviously, TSC spawns from the e✖iT Euler's Identity made in the end of AvMath. For the sake of this analysis, let's call this one, TSC_0.

One minute upon arrival, TSC_0 didn't have any personal goal/objective, so he was just running around. This also demonstrates the accuracy of the UI Formula Thing (UFT) that shows up on the screen.

That is, until he found this ball, and then the others after it. Which we eventually realize, all came from The Singularity. Something or someone is trying to get his attention. He needs to reach the Singularity.

The first thing he realizes is, "Dang, this is gonna take a while".

Also, space is dark because there is no sun- specifically, no solar system.

Okay, new goal. We need to get faster. But how?

Side Note: Animation vs. Frequency? Animation vs. Color Theory? Animation vs. Sound Waves?

A Solar System (with its own star/sun) spawns in. He did not reach it, it spawned in. It literally did NOT exist prior to the flashlight.

He utilizes the space maneuver called the Gravity Assist. Also called the Slingshot Effect. It's where you use a planet's gravity, by moving around it (but not entering it) to gain significant speed.

Most sci-fi stories use this maneuver to save on propulsion and to change/correct the course of the spacecraft.

UFT shows that he got faster now, but it's still not enough.

So he does it again with two faster-orbiting planets. Gaining more speed in the process.

He was supposed to make impact with the sun here, although I'm not sure why he didn't. It's probably because a sun along with its own solar system moves through the galaxy. They don't stay in one place.

For example: Our Solar System orbits the Milky Way Galaxy for about 230 million years, which is also called a cosmic year.

And by moving around the sun but NOT hitting it, gave him even more speed.

Here's his speed upon exiting the solar system.

He eventually reached 1% of the speed of light. Yep, that whole almost-dying-in-the-sun process, is still not enough to get anywhere.

Magnets spawns in. Again, they did NOT exist prior to this.

"Hmm... we can use this," he says.

Step 1: Let's magnetize the crap out of this rocket.

Step 2: Enter the magnet gates.

Step 3: We get a magnetic linear accelerator, which utilizes the opposing magnetic fields to propel/launch objects at high speeds. Initially thought this was a particle accelerator, but turns out that's a whole different thing.

And now we reached 80% of the speed of light.

If you're still following me... good news, we have reached half of the video.

Cool graphics, 'cause why not.

Around this point, TSC_0 experiences Time Dilation. This is important for later.

This is because he has now left the galaxy.

More sci-fi stuff. Everything starts to look more red.

Red-looking black hole.

Something hits him on the head. How is this possible?

Oh no, my apple. Take note, that the apple glows red whenever gravity is messing with it.

Goodbye world, my apple needs me.

Aww... Turns out there is a photo limit per post.

Here's [Part 2].

[mysticstronomy]

WHAT IS TIME DISTORTION??

Blog#310

Saturday, July 1st, 2023

Welcome back,

Scientists could soon test Einstein's theory of general relativity by measuring the distortion of time.

According to new research published June 22 in the journal Nature Astronomy, the newly proposed method turns the edge of space and time into a vast cosmic lab to investigate if general relativity can account for dark matter — a mysterious, invisible form of matter that can only be inferred by its gravitational influence on the universe's visible matter and energy — as well as the accelerating expansion of the universe due to dark energy.

The method is ready to be tested on future surveys of the deep universe, according to the study authors.

General relativity states that gravity is the result of mass warping the fabric of space and time, which Einstein lumped into a four-dimensional entity called space-time. According to relativity, time passes more slowly close to a massive object than it does in a mass-less vacuum. This change in the passing of time is called time distortion.

Since its introduction in 1915, general relativity has been tested extensively and has become our best description of gravity on tremendous scales. But scientists aren't yet sure if it can explain invisible dark matter and dark energy, which together account for around 95% of the energy and matter in the universe.

"Time distortion predicted by general relativity has already been measured very precisely at small distances," Camille Bonvin, lead study author and an associate professor at the University of Geneva, told Live Science via email.

"It has been measured for planes flying around the Earth, for stars in our galaxy, and also for clusters of galaxies. We propose a method to measure the distortion of time at very large distances."

The method suggests testing time distortion by measuring redshift, the change in the frequency of light an object emits as it moves away from us. Bonvin said the difference here is that this technique measures redshift caused as light attempts to climb out of a gravitational well, a "dent" in space-time created by a massive object.

"This climb changes the frequency of the light because time passes at different rates inside and outside of the gravitational well," she said. "As a consequence, the color of the light is changed; it is shifted to red.

By measuring gravitational redshift, we obtain a measurement of the distortion of time."

Time distortion suggests that time is not absolute in our universe but rather passes at varying rates depending on gravitational fields.This idea is not exclusive to general relativity.

"Time distortion exists in all modern theories of gravity," Bonvin said. "However, the amplitude of the time distortion  —  how much the presence of a massive object slows down time —  varies from theory to theory."

In general relativity, the distortions of time and space are predicted to be the same; in other theories of gravity, this is not always the case.

That means that by measuring the distortion of time and comparing it to the distortion of space, physicists can test the validity of general relativity.

The team's new method could also test another leading theory of the cosmos: Euler's formula, which astronomers use to calculate the movement of galaxies. Specifically, the team's proposed measurement of time distortion could prove whether dark matter obeys Euler's equation, as prior studies of time distortion have presumed.

Originally published on livescience.com

COMING UP!!

(Wednesday, July 5th, 2023)

"WHAT IS BETELGEUSE??"

[squareallworthy]

It's Triangle Tuesday! A triangle, its centroid, a theorem, and two bonus triangles.

Greetings, seekers of triangle knowledge. Today I'm going to talk about the centroid.

Among triangle centers, the centroid is, at first glance, maybe a bit underwhelming. Take a triangle ABC. Let the midpoints of the sides be M_a, M_b, and M_c. Draw a line from each vertex to the opposite midpoint. The three lines cross at a point G. And that's the centroid.

Very simple. Simple almost to the point of banality. Don't get me wrong - the centroid is a great point. It's just not very flashy in its construction, and the fact that it exists doesn't seem at all deep. Later on, we can show how the centroid relates to other things, such as the symmedian point, the Euler line, and the nine-point circle. But for now, it's kind of hard to appreciate the centroid on it own. Let's do what we can do now, before getting into that other stuff, to see why the centroid is interesting.

It's not at all difficult to prove that the lines meet at one point, but the proofs I've looked at aren't all that enlightening. You draw a line and look at some parallel lines, and you say, "mmm, okay, that checks out, that's a proof all right," but it doesn't feel like you've learned much.

Even before proving that the lines are all coincident, it seems obvious that they should be. Each line cuts the triangle into two equal parts, and so when you draw two of them, the point where they cross is the middle of the triangle, measured two ways. So it just makes sense that the third line has to go through the same point, right?

Let's see if we can follow our intuition on this to get at something more fundamental. The lines that connect the vertices to the midpoints of the side are called medians. In general, lines like this that extend from a vertex to the opposite side of the triangle are called cevians (pronounced ˈtʃeviən, CHAY-vee-un). Are the medians really all that special among other cevians? What if instead of marking the midpoint of each side, dividing it into two segments in a 1:1 ratio, we mark a point that divides the side in a 1:3 ratio, going counterclockwise around the triangle? If we then draw the cevians, what do they look like?

Not surprisingly, the they aren't coincident. They outline a triangle (in red) that looks like the original triangle, but smaller and tilted counterclockwise. If we divided in a 1:3 ratio going clockwise, we would get a clockwise-twisted triangle. And if we move the marked points back and forth, sure enough, only when the points are halfway along the sides do the three cevians cross at one point.

And if we take the crossing point of two cevians, and then draw the third line through that point? Where does that hit the opposite side? Here I'll go back and draw that with a dashed line on the 1:3 ratio counterclockwise drawing:

It lands pretty close to the vertex. Somehow that point has to balance the 1:3 ratio we used to measure the other points, but it's not clear exactly how.

So how are coincident points connected to the place where we cut the sides? Let's get a bit more formal. Let's have a triangle ABC, and a point P that is not located on any of the sides of the triangle. We'll draw cevians from the vertices through P, and they will cross the sides of the triangle at D, E, and F.

So we would like to know where F, for instance, cuts line AB, and how it relates to the other points. Or, to put it another way, if we knew the ratio of the length of AF to FB, and the same for BD to DC, could we say what the ratio of CE to EA is? Conversely, if we have a triangle with three cevians cutting the sides at D, E, and F, and we knew all the ratios AF/FB, BD/DC, and CE/EA, could we say whether the cevians are coincident or not?

It's easy to get lost here with statements made up of long strings of segments. If you are like me, your eyes start to glaze over when you see that and you don't learn anything. So let's lay out a plan for figuring this out. We are looking for some information about ratios of line segments. To do that, it would be helpful to have some similar triangles, because similar triangles have all the same angles, and differ only in size and orientation. So if you know something about the ratio of two sides of a triangle, you know the same thing about the corresponding sides of a similar triangle.

And a good way to get some similar triangles is to arrange to have them meet vertex-to-vertex between parallel lines, like this:

With this arrangement and a little bit of Euclid (which I won't get into here), we can show that the pairs of angles marked with the same letters are equal. The two triangles with angles α, β, and γ are therefore similar, and we can say that the corresponding sides are in the same proportions -- that is, if we compare the red dashed segment to the blue dashed segment, it is the same ratio as the red solid segment to the blue solid segment. The four colored segments together make a Z-shaped figure, and it is this kind of arrangement of segments that we want to consider as we figure out what's going on with our cevians.

So with that in mind, let's go back to triangle ABC and add a line through A that is parallel to side BC. The new line meets two of our cevians at G and H.

And that creates sets of similar triangles:

AHF is similar to BCF (in red, below)

AEG is similar to BCE (green)

AGP is similar to BDP (blue)

AHP is similar to CDP (yellow)

From that, we can get these relationships:

AF/FB = AH/BC (from the red triangles)

CE/EA = BC/AG (green)

AG/BD = AP/DP (blue)

AH/DC = AP/DP (yellow)

We are interested in the ratios that the sides of ABC are divided into, that is, AF/FB and so on. We have two of them above, which I have bolded. We still need to get BD/DC and then shuffle things around to get all of those into one equation.

The two equations above from the blue and yellow triangles have the same right hand side, so we can say

AG/BD = AH/DC

and by reshuffling,

BD/DC = AG/AH.

There's the ratio for the third side. Now let's multiply that together with the equations we got from the red and green triangles:

AF/FB * CE/EA * BD/DC = AH/BC * BC/AG * AG/AH.

Everything on the right cancels out, so if we reorder the things on the left side to be alphabetically nice, we have

AF/FB * BD/DC * CE/EA = 1

which is the first half of what we wanted to know. If three cevians pass through the same point, then they cut the sides into ratios that multiply to 1. What a nice simple relationship to remember!

What about the converse? Can we prove that if three cevians cut the sides in ratios that multiply to 1, they all pass through the same point?

Let's suppose that we have divided the three sides of ABC with points C, D, and E in a way that AF/FB * CE/EA * BD/DC = 1. Then let's draw the cevians BE and CF and say that their crossing-point is called P.

Now, if we draw a cevian from A through P, does it land at D, as our equation says it should? Well, it has to land somewhere, and we'll call that point D'.

Can we prove that D' = D?

We were given that

AF/FB * BD/DC * CE/EA = 1.

And since we just drew three coincident cevians, we can conclude from what we just proved that

AF/FB * BD'/D'C * CE/EA = 1.

Combining those, we do a little algebraic manipulation:

BD/DC = BD'/D'C

BD/DC + 1 = BD'/D'C + 1

BD/DC + DC/DC = BD'/D'C + D'C/D'C

(BD+DC) / DC = (BD'+D'C) / D'C

But BD+DC is the whole side BC of the triangle, and the same with BD'+D'C. So

BC / DC = BC / D'C

and therefore D = D'. And that's our theorem:

In a triangle ABC, lines connecting the vertices to points on the opposite sides D, E, and F are concurrent if and only if AF/FB * BD/DC * CE/EA = 1

This is called Ceva's theorem, after the Italian mathematician Giovanni Ceva (ˈtʃeva, CHAY-va), who proved it in 1678. But as usual in mathematics the theorem is not named for the original discoverer. That was Abu Amir Yusuf ibn Ahmad ibn Hud, who proved it in the 11th century. (I got the above proof from this website, though I have cut some corners by ignoring signed distances and neglecting the case with an obtuse triangle.)

Given Ceva's theorem, we can trivially prove that the medians of a triangle are concurrent. The midpoints divide each side in the ratio 1/1, so

1/1 * 1/1 * 1/1 = 1

proves the existence of the centroid. There are much more direct ways to prove this, of course, but Ceva's theorem will come up over and over again in the study of triangles so it's worthwhile to get it down now.

Now since we've proved that the medians are coincident, here are some of the properties of the medians and centroid.

The medians divide the triangle into six triangles of equal area.

Each median divides the triangle into two triangles of equal area, because they have equal bases and heights. Therefore

T+U+V = X+Y+Z

but also

Z+T+U = V+X+Y

and subtracting the second from first gives

V-Z = Z-V

V = Z

and similarly for every pair of opposite triangles. But also, X and V have equal bases and heights, so X = V, similarly T = U, Y = Z. Putting that all together shows that all six areas are equal.

The centroid G divides the triangle ABC into three triangles ABG, BCG, and ACG of equal area.

This follows immediately from the previous result, and we can immediately follow that with

The centroid lies on each median at 2/3 of the distance from a vertex to a midpoint.

ABG has the same base as ABC, and 1/3 the area, so it must have 1/3 the height. Those two very straightforward facts give us this less obvious property:

A point X divides a triangle ABC into equal triangles ABX, BCX, and ACX only if X is the centroid.

For a triangle ABX to have 1/3 the area of ABC, it must have a height 1/3 that of ABC, so X must lie on the dotted line in the picture, which runs through G. Analogous lines for triangles BCX and ACX must also concur at G.

And, of course, the most famous properties of the centroid, and the reason G is traditionally used to name it, are that the centroid is the center of gravity of the vertices, and also of the area of the triangle. (If you are coming from a physics background, you might object that the centroid of an object is by definition its center of gravity, or center of mass -- that's simply what "centroid" means. To avoid any confusion, I am using a gemometric definition of centroid as the place where the medians cross, and proving that this point is also the center of gravity.)

The centroid is the center of gravity of the vertices.

If A and B represent equal masses M, they can be replaced by a single mass of 2M located at Z. The center of gravity of C and Z, then, is a point 1/3 of the way from Z to C, which is G.

The centroid is the center of gravity of the area of the triangle.

Every line parallel to AB can be replaced with a mass Z_1, Z_2, ... at the midpoint of the line. Each of these masses will be located on the median, and so the center of gravity of all these points must also lie on the median. By a similar argument, the center of mass must also line on the other medians, so it must lie at their crossing point. (Yes I admit this is rather handwavy, but a better proof requires integration and I am doing elementary geometry here, not calculus. I have an idea for a proof using purely geometrical methods but I haven't finished it.)

To be complete, I will note that the centroid is not the center of gravity of the perimeter of the triangle. That's a different triangle center, which we will perhaps consider on a different day.

Finally let me introduce two triangles related to the centroid and the medians. The medial triangle, shown in red, is the triangle formed by the midpoints of the sides. The antimedial triangle, shown in blue, formed by lines passing through the vertices A, B, and C and parallel to the opposite side, which meet at A', B', and C'. The anti- part comes from the fact that ABC is the medial triangle of A'B'C.

Both of these new triangles are similar to the reference triangle ABC and can be formed by reflecting ABC through a point and scaling up or down by a factor of 2. That point of reflection is, of course, the centroid.

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

An index of all posts in this series is available here.

[i3utterflyeffect]

untitled-3, TCO, and TDL probably have to find other hobbies than destroying websites in the decade or so before the showdown. TDL might disguise themself when rampaging so untitled doesn't know, then hollowheads might not have the horrible reputation they have in the original timeline/universe

i just love the idea of them doing things. untitled designs some buildings for the new stick city. TCO plays some video games. TDL attends a miku expo and gets her autograph. they attend stick classes. TCO fights euler's number. don't forget the constant undercurrent of doom that untitled-3 experiences...

bonus: i've imagined untitled's fire to be a dull red, since hotter things burn bluer.

OUGHHHHHHH, SO TRUE..... SO TRUE.... i don't have much to add to this sorry anon </3