#line integral

[peeterjoot]

Multivector form of Leibniz integral theorem for line integrals.

[Click here for a PDF version of this post] Goal. Here we will explore the multivector form of the Leibniz integral theorem (aka. Feynman’s trick in one dimension), as discussed in [1]. Given a boundary \( \Omega(t) \) that varies in time, we seek to evaluate \begin{equation}\label{eqn:LeibnizIntegralTheorem:20} \ddt{} \int_{\Omega(t)} F d^p \Bx \lrpartial G. \end{equation} Recall that when the…

[hawberries]

vultur volans | paradisaea

[fluffyartbl0g]

If you asked me to describe them in one picture it would be this

Here’s the scene in question ^^^^ ITS SO GOOD ITS SO GOOD ITS SO GOOD

And here’s the exact screenshot I redrew

[welcometogrouchland]

ANOTHER SKETCH DUMP! Featuring more of me playing with lineless art. Batman reborn era trio (dick, damian and steph) I miss you...when will you return from war. Also featuring Steph designs bc I've seen ppl dissatisfied w/ her current look, some good mom Talia, and Jason Todd poetry club. Duke is confused not that Jason would start a poetry club but that he'd have such mid poetry opinions. (ID in Alt)

[the-art-of-sanshoku]

So they call the grongi markings "tattoos" because that's their best understanding of them but what if it's just something that occurs naturally...

[meidui]

so confused when people hate miss agent margaret carter because what do you have against a woman with big beautiful brown eyes who pummels people with her entire body weight

[sixoclocker]

UTY: PLATINUM - LUCILE KETSUKANE

UTY: Platinum is an ‘Integrity Lives’ AU, and this is the first reference sheet of said AU, featuring Integrity (or Lucile) :D

LUCILE KETSUKANE

• they’re 17 years old, but fell into the underground at age 12. they are the fifth fallen human with kindness taking their former spot as the third fallen human.

• they had gotten aggressive in snowdin after hearing about how much monsters wanted to destroy humanity. kanako (much to chujin and dalv’s horror) managed to talk them down from it before they killed anyone due to the fact that they were both children. not many were around to see it due to a lot of the monsters hiding. they were allowed to stay with the ketsukanes due to kanako’s persistent asking and in return for assistance with research and helping around the house. eventually, they had practically become part of the family.

• kanako made them a mask similar to ceroba’s in order to help them feel more welcome as well as hide their identity as a human. it’s nice.

additional info

• lucile ditched the ballet skirt and shoes to rid themselves of their ties to humanity, though they may still secretly keep them somewhere…

• they share their soul with axis sometimes! it helps give him a little more personality beyond his code, though he still doesn’t really break away from it. typically, when they are sharing their soul, they and axis don’t leave each others side just for convenience— though they don’t really mind that.

• them and kanako are like siblings, but couldn’t have more opposite personalities. kanako is warm and energetic, while lucile is cold and lethargic. while lucile is typically stand-offish and not the friendliest, that doesn’t mean very much. they enjoy doing acts of service for those they care about, because it’s what they believe is right. they’re very strong in their morals! i’m sure this will have no problems later on :)

[akicklineisinevitable]

i was talking abt this irl a while back but i relistened to TGWDLM and it just reminded me of it- remember the Jekyll-and-Hyde back-and-forth thing Paul does in Let It Out? there's a subtle difference in the way Jon sings, between the 'normal Paul' and 'infected Paul' lines- infected Paul's' voice is brighter, slightly higher-pitched. his voice rises at the end of the lines, too.

and as a former theatre kid, whenever i hear that part of Let It Out i always remember something my old music teacher told me- your voice sounds brighter and clearer if you smile when you sing. something about the muscles in your mouth, i think? but obviously, in live theatre you have to act as well as sing, so most of the time you can't do that. but that infected version of Paul is always smiling. in Let It Out his expression changes by the line, and in Inevitable as soon as he starts singing he smiles- and his voice is brighter and clearer and happier.

i dunno there's something there

[thelemoncoffee]

just realize how load bearing the sentence "cause i'm a liar" is to Kokichi's whole character

if you took that sentence out of his dialouge, his entier character would implode. it's like that one random png every other game has that if you remove it from the files the game stops working

you probably think "well no duh" but it's deeper for the character than it sounds.

it's one of the first things he tells you directly, and just the fact that he's the one who says it is a paradox. the liar tells you he's a liar, but the liar lies so is he lying about being a liar? but that would make him a liar right?

that one line is the whole reason the other characters are hostile to him before he even does anything worth getting mad over. he said he's a liar in his introduction, and that will be the first and last thing that he tells them about himself the rest of the cast will truely believe to the end. throughout the game we then see him tell mostly nonsense harmless lies, reminding us after each one that it's okay because he's a lair and nothing that come from his mouth is to be trusted, but when the time comes for the ugly truth to be said- he's the one who delevers it.

he claims to be a liar, makes himself out to be a a liar and bad person with confusing lies that are basically net zero information when you actually think about them, then uses that to lessen the blow when he delevers the truth no one wants to hear- so if they don't want to accept it he can be their plausable deniablity. without the "cause i'm a liar" line none of this could actually work, without him reminding everyone every other minute that "i'm a liar, source: trust me bro" this his whole purpose in the game becomes near impossible to pull off, at least in the way he does in canon.

they might see him as a bad person, or suspect him to be dishonest, but i don't think they'd be able to handle the truth bombs he drops or even fall for his plan without their assurance that he's untrustworth because "after all, he's a liar". sure they could figure out he's lying on their own, but not everyone would come to that conclusion. they'd all be devided on how much they'd be able to trust him, and none would get to be able to let the truths he spits roll off their backs- they'd linger and eat away at their minds.

he would actually be pretty intimidating i think if he acted the exact same way but never called himself a liar at any point. he's this unsettlingly childish guy who talks about world domination casually over tea, and then turns around with a blank expression in a trial and forces you to face the upsetting truth you've been trying to avoid. it'd create a stronger tonal whiplash than he already does in canon, with no saftybars for them to reorintate themselves with.

he's still doing it for the same reasons as canon but the characters around him are having very different and somtimes visceral reactions to his behavior

he'd end up becoming a bit of a truth harbanger in a way

[slavhew]

gods' night out

lines + source pic under cut

[meamiki]

vtuber loop !!!

[reverse entry au? the reverse isekai part of it? tangentially related to this post here, and also the last part of this post too]

[ikilledtvguy]

i don’t usually post my weird ass collages here but this is fandom related so i think maybe it has an audience this time

[ducktracy]

Moose with implied skwerl

[meyhew]

i have something to say 👩🏽‍🦯‍➡️

[theamazingmaddyas]

*Essay on Children of the Big Three, original characters, and canon compliance*

Trigger Warnings: Death/Murder

During ace week this year, in one of my oneshots I had a, minor, original daughter of Zeus named Enid, which has sent me down a rabbit hole of thoughts about big three children, and how to make original characters with Zeus/Jupiter, Poseidon/Neptune, or Hades/Pluto as their godly parents while still maintaining the integrity of the story. That is to say, Percy being the child of the prophecy and the acknowledgement that the Big Three Pact was created and subsequently disbanded from the mid-1940s [while Grover says in the Lightning Thief that the pact was post-WWII, I have reason to believe that the prophecy itself, (and therefore the pact), was given during the war, between 1941 and 1943, rather than after it's conclusion. The reason behind this has to do with Riordan's wonky timeline, which I will probably make a separate post about] to the end of the Second Titan War in The Last Olympian, which is quite a large window of time; about seventy years. Note, this is solely talking about the creation of OCs that do not contradict canon at all, and therefore is not talking about OCs such as another Jackson kid, a third Grace kid, or a different prophecy child, those stories are not meant to fall under the realm of canon compliance.

First, it is easiest to split the children of the big three into four distinct categories—older than 16 when the pact was enacted; under sixteen, but already born, when the pact was enacted (this category would include Hazel, Bianca, and Nico); born during the pact (Thalia, Jason, and Percy); and born after the pact was dissolved (my character in The Hearth's Children Enid). I also will be looking into the difference between Greek and Roman Big Three kids, as that has some interesting implications of the pact.

While none of the books talk about whether the pact also included in their Roman forms, I am writing this under the assumption that it is. There are many reasons I believe this, but I will detail the main ones below. While it is evident that the Twelfth Legion has never heard of the Great Prophecy, we also know that the Sibylline Books, where the Romans are known to get their prophecies from, has been destroyed for centuries and only remains in Ella's photographic memory. This is not relevant, however, because Ella, of course, is not known by Camp Jupiter until after Percy fulfills the prophecy. Additionally, the only reason they know the Prophecy of Seven is because it was transcribed before the book was burnt. It is not unreasonable to believe that the Great Prophecy, like the Prophecy of Seven, was in the original Sibylline Books but lost because of it being destroyed and was not saved. It can also be inferred that Camp Jupiter did not know of the pact made as well, given they do not seem too shocked at Jason, and later Hazel and Nico's, existence. That being said, Jason's treatment is also a big indicator that the pact was still prevalent to Jupiter, Neptune, and Pluto. While Jason being at camp didn't seem to be overly shocking to the Camp Jupiter population from what little we know about it, he is also revered by everyone, despite being in the 5th Cohort, which is known to be valued as less than. If the Big Three pact did not cross over to the Romans then wouldn't it be safe to say that Jupiter and Neptune (and to some small degree, Pluto) would have had a ton more kids to compensate for the fact that they couldn't have Greek kids? There is no feasible reason for Percy and Thalia to be Greek if Neptune and Jupiter respectively could have as many kids as they want with no consequences. But since Camp Jupiter isn't aware of the Big Three Pact, the lack of big three kids over the past half-century probably seems more like a strange coincidence than anything else. [Note, it is extremely likely that, even in series, there are legacies of Jupiter, around camp. While it is unknown just how many generations removed a legacy is allowed to be to still join the legion, Octavian is still a member despite his family being in the legion for 100 years (meaning Apollo must be, at minimum, his great-grandfather) which would put his first family member in the legion pre-pact, and therefore pre-the decline of Big Three Kids. Additionally, Claudia (from Camp Jupiter Classified) has no problem entering the Legion as a great-granddaughter of Mercury before she learns that she is, in fact, a demigod too. Shen Lun, Frank's great-grandfather, is extremely far removed from Poseidon, but I count him as an anomaly because he was allowed to join the legion due to his strength rather than his nearness to godly blood. Neptune and Pluto are far less likely to have descendants at camp (Pluto actually wouldn't have any at the time of Heroes of Olympus cause Hazel claims she would be alone if they separated by godly parent, though it is possible there are descendants of Pluto in New Rome or have already left the legion) and, as we see with Percy and Shen Lun, Neptune's children and descendants were othered, and therefore would be unlikely to send any children they had to the legion which would explain why Percy's existence seems far more shocking than any other Big Three kid] This fact can also have been why Jason, Hazel, and Nico weren't completely gaped at, since legacies of their godly parents likely have been steadily in the legion for decades.

Now that we have covered the Greek/Roman divide when it comes to Big Three Kids, and that your OC being Roman or Greek has very little effect on their existence, only on their peer's perception of them, let's move onto years. (Before we begin that, I would like it noted that I will be referring to the gods collectively as their Greek names; by that meaning Zeus will refer to both Zeus and Jupiter, unless otherwise stated for simplicity sake) The easiest two, and the only two where there isn't any nuance and will be plausible in canon timeline 100% if the time are: over 16 at the time of prophecy and born post-The Second Titan War. If your OC is already 16 by the time a "Child of the Eldest Gods/Shall Reach Sixteen Against All Odds" than the prophecy could not be about them. While, yes, part of the reason the Big Three Pact was enacted was due to the overpowered nature of Big Three children, a larger portion of it was so that the prophecy was postponed as long as possible. It would be a lot easier for a seventeen year old, who is not the prophecy child, to fly under the radar rather than a fifteen year old, who very well could overthrow the Greek gods in accordance to the Oracle of Delphi. No matter who you make your OC's godly parent, they could, plausibly, exist within the realm of the series. Same goes with children born after the Last Olympian. When Percy is being awesome and declaring that the gods pay child support, he also mentions the fact that the pact was kind of stupid since two thirds of the gods broke it anyway. And with the prophecy already fulfilled, much of the gods (especially Zeus') fears were greatly diminished. Personally, I believe that the Zeus cabin would fill up pretty quickly about a decade after the Percy Jackson series conclusion due to the rather adulterous and promiscuous myths involving Zeus, and that the Poseidon Cabin isn't that far behind in size. (In fact, Poseidon even jokes with Percy to say to expect siblings in due time, which could mean he already has plans to have more kids now that he knows he won't subject them to a life of pure horror). Hades is a bit more subdued, and is often portrayed as being overall pretty loyal and not so promiscuous so his cabin probably would not fill up too fast, but rather have a few kids sporadically here and there rather than a bucketload at the same time like his brothers.

In order to maintain canon compliance, if an OC were to be born post-pact but pre-the dissolving of the pact, there is no way their story wouldn't be inherently tragic. The only somewhat happy end for a Big Three character in this category would be to join the Hunters of Artemis, as Thalia and Bianca did to take them out of the running for Prophecy Kid, but if the OC were a boy? Well, they'd have to meet a tragic end before turning 16. Again, we know from the books that no big three kid attends camp after the pact is dissolved before Thalia is discovered, which leads me to believe that, if Zeus or Poseidon (In my opinion, the fact that Hades does not break the oath is a rather poignant and important factor in his characterization and how we, as the audience, are meant to interpret Hades in this medium. In Blood of Olympus, Nico talks about the justice of Hades to Bryce Lawrence, and a key aspect of justice is the keeping of one's words. Sure, Hades is often seen as a villain, but he never lies, but rather he manipulates the truth and omits, example being he said to Nico in The Last Olympian he would hurt Percy, which he didn't, but he never claimed he wouldn't hold him hostage. So, personally, I do not think a child of Hades OC born in this time frame could be seen as canon compliant, but one could try and argue if they see another way to keep the integral bits of Hades' personality while still breaking the oath. But, honestly, I don't see it as plausible.) were to sire a kid in their Greek forms, they'd most likely be dead before twelve, as that is the age that Camp Half-Blood typically begins looking for campers. As for their Roman aspects, again, the child would be dead before sixteen, but if we were to look at what was previously stated about Jason's characterization, it is safe to assume no Roman Big Three kid could make it to Lupa (as we know all Big Three kids would be able to pass her, as Jason succeeded at two). Why they fail to reach her is up to the creator of the OC, but personally, I think a Neptune kid would probably be struck down by Jupiter and a Jupiter kid by Neptune or Pluto (Jason's survival is strongly tied to the fact that he was from Sonoma and therefore didn't have to travel far to get to Lupa) would not only be plausible, but also have that inherently tragic Big Three thing.

There is a little caveat if the Big Three kid were born after Percy, which is to say that they could, possibly, survive past sixteen. Personally, I think this will depend on how much younger than Percy they are. If they were born within four years, their chance of survival is slim to none. They'd probably be killed. (Jason, of course, is an exemption, which is why their is a slim chance of survival, but the author would need an extremely thorough explanation on how they survived without either camp up until twelve to fifteen.) While it technically goes against compliance to have a Big Three kid arrive during the course of Heroes of Olympus and Trials of Apollo, there is the possible argument that can be made that an OC this age could still respect the integrity of the story, which is the most important aspect of Canon Compliance in my opinion. Over four years younger than Percy has a highest survival chance of kids born during the pact, with the younger they are, the chance of their survival increasing massively. A kid born a few days before the battle honestly has a pretty fine chance of survival.

Now, onto the most interesting category of Big Three Kids in my opinion: those born less than sixteen years pre-the Pact. Firstly, like with the previous section, I do not believe it is possible for a child of Hades to be in this section without destroying the integrity of the story. Hades' protectiveness when it comes to his children is an integral part of the story, as well as the way that Hades tries to hide them from Zeus, another Hades kid in this age range doesn't make sense. Additionally, if we are to go off the idea that the prophecy was first stated in 1941 (which, as previously stated, makes the most sense with the wonky timeline) another ulterior motive for Marie to move to Alaska could be to escape the wrath of Jupiter, and another reason Gaea targeted Hazel, because she had the power to be the prophecy kid. But, she dies before Zeus really has the chance to track her down. (Yes, Alaska is beyond the gods, but do you really believe Zeus would have let that stop him if Hazel survived until 15? I doubt it). A Pluto OC makes slightly sense than a Hades OC but I think in both aspects Hades' characterization is that he cares about his children as best he can. I think it's in character for Pluto to have actually visited Hazel, but Marie didn't let him get close to her because of her resentment towards him due to Hazel's curse. Also, Hades' having three kids within four years is a lot, and with his less promiscuous ways, it contradicts the integrity of canon too much to have other young Hades kids when the prophecy was uttered and the pact enacted. Also, Hades tries to harbor Nico and Bianca, and if he had more children he tried to do that with, Persephone would've started a riot.

Now with the logistics of Hades OCs out of the way, let's talk about Zeus and Poseidon. Honestly, it doesn't make sense for there not to be Zeus and Poseidon kids in this age range because of their, as previously stated, adulterous and promiscuous ways. It can be argued, and I will argue, that the way in which Zeus demands Nico and Bianca to be handed over by a certain date has the implications that Zeus already had kids that had been "turned over". As tragic as it is, the canon heavily implies that Zeus euthanized murdered his own children. At least, that is how I've always interpreted it. (I doubt he turned them into trees or other plants, but it is possible, it is just for me the reason Zeus turns Thalia into a tree is because he wasn't the one to kill her, Hades was, and Zeus does not seem like the type of god to take that lightly.) Poseidon's under sixteen kids must've been killed before Zeus went after Bianca and Nico, because Hades seems to be the only one who Zeus is really grilling to hand over his children from the memories we see in The Last Olympian. Was Poseidon planning on harboring his children like Hades tried to, but Zeus got to them first? Did Poseidon just cross his fingers and hope for their survival without much aid? Did Poseidon turn them over to Zeus to avoid fighting? We can't be sure. As much as I'd like to believe the first one, especially since Poseidon seems to be a decent enough father to Percy (and Tyson and Trident though neither of them are half-bloods and therefore could not be the kid of the prophecy), Percy also is heavily implied to be his father's favorite, though whether that's because of his status as a forbidden child or because of Sally, it is unknown, so it is possible Poseidon just crossed his fingers and hoped his children were strong enough to survive. I don't feel like Poseidon would turn his kids over to Zeus, but honestly who's to say?

Clearly, I have a lot of feelings about Big Three OCs and just children of the Big Three in general. If you're really interested in the discrepancies in the timeline of The Pact, feel free to ask questions on it, because I personally haven't seen anyone talk about it but I think about it all the time. Also, if you've seen any posts on that topic, send it to me! I think about Riordan's wonky timeline a little too often to be healthy.

[emily-mooon]

Here’s a little wip I’ve been working on in between my homework!

Yes I am making a genderbent Jonathan design. I have a vision for her I must get out into the world or else I will (figuratively) explode