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It annoys me unreasonably when a fancy map of political boundaries uses like a dozen colours and still ends up with two polities that share a border having the same colour. Like, "solving the four-colour problem" is an exercise we give to first graders, and you couldn't do it with twelve? Get out of my sight.
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pretty man pretty man pretty man
#wip#portrait study#formula 1#f1#f1 fanart#ln4#lando norris#mclaren#artwork#i love drawing moles ugh#started this in my graph theory class
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Discovering Jon and Martin’s Birthdays
It’s a wonder how much you can uncover about The Magnus Archives using only a bit of mathematics and a smidge of psychology.
Apparently I have too much time for both and can definitively say that I have revealed the absolute best and most accurate dates for both of their birthdays. Feel free to join me as we dissect piece by piece when these two were born and put to rest the age old question: What is Jon’s zodiac sign?
I’ll put the results in the tags as a TLDR if you’re not interested in reading my method and simply care about what star sign they are or what date to put in your calendar so you can go out for ice cream.
Statement Begins.
To find out the birthdays of Jon and Martin, we first must determine when exactly they joined the Archives. This will be important for the wider picture, as after all, the earliest possible birthday must take place after they start working there. We also must understand the Archive team’s speed in order to understand how to space out our statements and find that aforementioned number.
Gertrude Robinson passed away, according to her file, on the 15th of May 2015. This makes 15th May our earliest possible starting date. The next time the day’s date was specified was on 13th January 2016, when Naomi Herne gave a live statement. This is MAG 13, and our latest start date. Obviously, these numbers are nowhere close to the day we’re looking for, but they act as upper and lower limits. Our answer is somewhere inside.
In Jon’s supplemental notes for MAG 12, he states that Gerard Keay passed away late the previous year. Since Gertrude died after Gerard in early 2015, he must have died in late 2014. This confirms that MAG 1-12 was recorded to tape in 2015. We know that MAG 13, the next statement, was given live on 13th January 2016. This creates, at the very least, an almost two-week gap between archiving statements. This is likely due to the holiday season, so the time between 24th December and up to 1st January can be omitted. To recap, MAG 1-12 was recorded in 2015, and MAG 13 onwards in 2016.
The key to determining archival speed lies with Martin. Martin goes missing right before MAG 17 and reappears at the end of MAG 21. As he gave such a detailed account of those two weeks, our archiving timeline can be significantly accurate. MAG 19-20 were more than likely recorded on the same day, meaning three separate recording sessions took place in two weeks. However, it took a minimum of six weeks to record MAG 14-16.
So far, the timeline looks like this:
Now we have to figure out the left half.
Calculating the average time it takes to archive statements from MAG 13-22 (removing any outliers from our calculations), we can find a true average and apply it to the 2015 year. By March of The Magnus Institute’s 2016 calendar year, the Archive staff was able to archive 1.31 statements per week. I double-checked this number by doing the same with the statements recorded between MAG 22 and MAG 39. By multiplying the average amount of weeks it should take them by the adjusted number of statements recorded, it should equal the number of weeks it actually did take them. If the numbers are the same, the average is reliable. Hoping for the number 20, the number of weeks I had calculated... was 20.11. This average seems relievingly trustworthy and fits Elias’ complaint about the staff “barely getting through one statement per week.”
All we have to do now is multiply the first 12 statements by the 1.31 average to determine how many weeks it most likely took to do the recorded work of 2015. This leaves us with 15.72 weeks and makes the earliest and most probable start date somewhere around 5th September 2015. I will round this to 1st September as I am not expecting the team to start working on statements right out the gate, so these extra four days act as a buffer for everyone to get their bearings and find the tape recorder. Also, it’s convenient for Elias’ financials to start everyone on the 1st of the month.
Now is the fun part - the birthdays. We now know that Jon and Martin’s birthdays must fall somewhere between early September and the end of February. Since March kicks off the Archives living with the threat of Jane Prentiss, they have to take place before then. After that point, the team is far too stressed to have the carefree party heard in MAG 161. We also know that Martin’s birthday has to come before Jon’s, as the team mentions going out for ice cream at Jon’s party. This event has to be long enough in the past for Jon to forget about it, so their birthdays must be reasonably spaced out from one another in the allotted time. Likewise, an amount of time must have passed after their start date for the team to be close enough bond to want to celebrate Martin’s birthday.
Martin’s birth year is easy to determine. Martin tells us his age in MAG 56. His birthday could not have happened at this point in 2017, so his birth year must be 1987. In a Q&A, it was speculated that Jon and Martin have birthdays near each other (and one being slightly older than the other), so only 1987 and 1988 are our options for Jon’s birth year. Let’s look a bit closer at that.
Early ‘88 is closer to Late ‘87 than Early ‘87. At Jon’s birthday party, he says he’s turning 38. Martin is 29 at this time. The obvious conclusion to me is that Jon simply adds a decade to his age. (I find this the most hilarious yet believable scenario.) Jonny was also born in 1988, being 28 himself when that scene would take place. As Jon’s childhood details sometimes mirror Jonny’s, I am taking this as a sign of accuracy.
And by doing some additional work that I will not share here, I can reliably say that these are the best observed birthdays for Jon and Martin:
Martin - 23rd November, 1987
Jonathan - 2nd February, 1988
Also, this makes Martin a potential Valentine’s Day Baby. Do with that what you will.
Thanks for reading!
(Full timeline for those who are interested:)
#Jon: 2nd February 1988#Martin: 23rd November 1987#hopefully others care about this as much as I do#I was considering graphing a normal distribution and listing alternative start dates at varying levels of confidence#but the average was so accurate I didnt feel like I needed to anymore#this must be how Alex feels with his DPHW assignments#jons an aquarius#and he acts like it#martins a sagittarius btw#the magnus archives#tma#tma podcast#tma spoilers#tma jon#tma martin#jonathan sims#jon sims#martin blackwood#tma jmart#jmart#teaholding#fan theories#do not archive
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may be a longshot to find the actual original and if so im so sorry but i saw this in a tumblr post ages ago and saved it and now i cant find it anymore 😭
I couldn't find anything solid on this one, and I also stumbled on another version in this Reddit post from 2016:

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No, parents of the kid I tutor, I swear I didn't start telling your son about graph theory unprompted! He was the one who insisted on completing his multiple-choice matching question without crossing the lines over each other.
#this conversation didn't actually happen and i doubt the parents would mind anyway (they're family friends)#it just sounds funnier this way#but it just shows that a lot of kids naturally want to explore mathematical ideas even if they don't know that's what they are#he also told me he taught a couple of 9 year olds about algebra at camp#like the absolute basics but still#he's 13 for reference#graph theory
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The Three Branches of the Hamilton Fandom
(Psssst, historical hamliza art is coming your way soon!)
Ok so hey lol. Now, this is not saying that you have to be in a specific branch, but I’m just pointing out the big differences in the Hamilton fandom.
Meanings:
Musical external: It is the skin, the wall of the fandom. It is what most people will see first. It is outside of the more in depth fandom.
Musical internal: This is the rabbit hole of the fandom. It includes shipping, fanfics, animatics, theories, and much more. And even some facts!
Historical: One that tumblr is very familiar with. It includes of the actual events of Hamilton, and how it realistically/historically is.
#hamilton musical#historical hamilton#amrev#alexander hamilton#Hamilton graph#hamilton the musical#hamilton#historical lams#lin manuel miranda#szin#animatic#fandom#fan theory#analysis#idk what else to tag
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I’ve always headcannoned that elves look somewhat “uncanny” to humans. Like maybe at first glance an elf might just seem very beautiful, but as you take a closer look you can notice their facial structures are almost TOO anatomically correct, TOO symmetrical, their eyes a bit TOO big, their skin TOO perfect, their hair STRANGELY shiny, their posture WEIRDLY straight. So close to human but just slightly….. off.
#kotlc#The uncanny theory is the closer something non human gets to looking “human” the more uncanny or creepy looking it is#Like when it’s shown on a graph it spikes up the more “human” it looks#Then obviously it goes back to zero when it is a human
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Dragon Flyer Hierarchy (RTTE Headcanon and Theory)
Hello, everyone! Welcome to another HTTYD article! Sorry it took a while to write and put together since I was basically creating their lore from scratch.
Today will once again dive into the Dragon Flyers, this time concerning the topic of their hierarchy.
This is a continuation of my recent article which you can read here.
Now, be aware that this is a theory and headcanon on this end since the show doesn't really give us much background on the Dragon Flyers — even more so than with the Dragon Hunters — and we know very little about their ranks and hierarchy. This is just me taking a crack at how they function as a unit.
"Dragon-skin Meritocracy": A 300(?)-Years-Old Hierarchal System
The first part of this article will dive into my theory of what I call "Dragon-skin Meritocracy" — a system of hierarchy based on the merits of one's achievements via the possession of certain dragon skins from dragons that they slay. They are forbidden from purchasing any dragon skins to boost their own status, career, or reputation. Even leaders or individuals with wealth or influential families must adhere to this dictate.
Each Tribe in the Barbaric Archipelago has its own customs, cultures, rules, traditions, etc, concerning the etiquette of dragon skins and the art of dragon-slaying. In fact, I even hazard to guess that there are differences even between the Tribes in the Inner Isles vs those of the Outer Isles, as what those of the Inner Isles view as a top-tier dragon to hunt might not be what those of the Outer Isles view as a prestigious dragon to hunt, simply due to exposure to different dragon species that those of the Inner Isles aren't accustomed to.
(You can look for my previous article on the use of dragon skins here)
Aside from the fact that they look aesthetically pleasing to wear and give the user anti-fire protection, it's also a show of one's prowess and status as a man and warrior.
As Hiccup had even said in the first film:
"Killing dragons is everything around here. A Nadder head is sure to get me at least noticed. Gronckles are tough. Taking down one of those would definitely get me a girlfriend. A Zippleback? Exotic. Two heads, twice the status. Then, there's the Monstrous Nightmare. Only the best Vikings go after those."
As such, in Archipelagoan society, there is a hierarchy or meritocracy that is based on what dragons you kill, and how many of them. And it's also based on how difficult these dragons are to kill.
Again, the achievement hierarchy concerning dragon skins differs from tribe to tribe, from region to region — heck, even family to family.
However, I'm going to try to create some sort of hierarchy that the Dragon Flyers might plausibly employ, since it's an organization and must have some semblance of order. (You can find the article here.)
Thus, I created this chart below:
From this chart, you'll see the following:
Flyers wearing Zippleback + Nightmare skins are Elite Flyers.
Flyers wearing yellow dragon skins are Senior Flyers.
Flyers wearing Nightmare(?) + Nadder skins are Junior Flyers.
Flyers wearing brown/poor-tanned dragon skins are Rank-n'-File
I'm only basing this on what I've seen on the show, where the ones showing the most experience and ferocity in battle were those wearing Zippleback and Gold-skins, respectively, while those below them seem to be not as experienced and are more prone to express fear and cowardice. Naturally, there are exceptions, but strictly based on what we've seen, that is my diagnosis concerning the Dragon Flyers and their hierarchy based on the dragon skins they wear. It's likely that Netflix intentionally did it this way, but I haven't a clue.
Those who wear those brown-skins (I can't tell if they're poorly tanned Nightmare skins or Gronkle-skins or what) seem to be more greenhorns than anything. Those without the pauldrons and Nadder-wing skirts appear to be more rank-and-file than the others. In contrast, those with those items seem to be slightly above them in rank — similar to how a Private First Class or Corporal is above a rank-n'-file Private.
The Hierarchy
Now, it's VERY possible that it's just a random configuration of minions without any order of hierarchy. It's possible that the hierarchy is the following:
Krogan > 12 Flyer Disciples (Dawn of Destruction & Wings of War) > Other Flyers > Dragon Hunters
Here is a graph I made which showcases this hierarchy, as I see it.
Of course, this is in Krogan's own eyes, as he deems himself and his Flyers to be above Viggo and the Hunters. In contrast, Viggo would likely have viewed himself as equal to Krogan, despite having no choice but to work with him, as his organization has mostly been absorbed or scattered.
Furthermore, the Flyer hierarchy is further divided into the following:
Krogan's Disciples > Squadron Captains > Veteran Flyers > Junior Flyers > Regular Flyers > Recruits
If you're wondering who I mean by "disciples," it's the 12 Flyers who were personally trained by Krogan and were his BEST warriors in "Dawn of Destruction" and "Wings of War". "Disciples" is what I call them, as a result.
Also, by popular vote, they'll be called "The Deadly Dozen" from now on.
Underneath them are the Squadron Captains and Veteran Flyers who lead the pairs and squads of regular Flyers. After them are the Junior Flyers, who are essentially like the Corporals or Privates First Class of the unit. Underneath them are the Regular Flyers, who are the mainstay of the force; their experience, equipment, and abilities vary. And finally, we have the Recruits, who have recently joined and have only basic training and have little combat experience.
Let us start with Krogan's Disciples, shall we?
"The Deadly Dozen": Krogan's Elites

So then, who are these "disciples," in detail?
In Wings of War, Krogan says this to Viggo after the latter questions him:




Viggo: I haven't seen your Flyers in quite some time. Shouldn't they be preparing?
Krogan: Those are twelve of my most fearless and gifted warriors. I doubt they'll have much of an issue.
<><><><><><>
As they are Krogan's elites and are close to him, they will possess the highest place in this hierarchy as Krogan's lieutenants, with Krogan possessing the top-most position as their Chief. As a result, they will be ad hoc and de facto leaders who will be in charge of important and secret projects or missions. They'll also be given limited carte blanche authority at these times, so long as they obey any direct orders from Krogan.
The foremost of whom is the Flyer Leader, who appears to be the Chief Disciple among the "Deadly Dozen", similar to how the Witch-King of Angmar was the Chief Lieutenant of the Nazgul, Sauron's servants. He was charged with hunting down the Riders in "Dawn of Destruction" and "Wings of War", and was later in charge of protecting one of the secret Singetail Nurseries in "Family Matters".
That being said, aside from these times, they'll most often act as Krogan's personal entourage, who accompany him whenever and wherever he goes anyplace, or to hunt down anyone he wants.
These Flyers would prove to be the Riders' greatest adversaries capable of besting them in air-to-air combat. However, later in the war, the Riders would end up on top as the numbers of the "Deadly Dozen" dwindled — either because of war attrition or because of reassignment to other bases or missions — or were replaced by regular Flyers who had less training and teamwork abilities than their predecessors.
By the time Krogan's and Johann's forces attacked Berserker Island, the "Deadly Dozen" would lead their fellow Flyers into battle to intercept the Riders and provide close-air support to their ground forces.
The "Deadly Dozen" is definitely a force to be reckoned with, and were Krogan's fiercest, most experienced, most loyal, and most fanatic warriors under his command, and were warriors whom the other Flyers respected and wished to emulate.
Squadron Leaders / Veteran Flyers: Backbone of the Dragon Flyer Warband
As such, whenever Krogan's Disciples were absent, the squadron leaders and veteran flyers were next in command. These two groups were the backbone of Krogan's Flyers and were essential to the command structure.
Based on what we see in the show, these Flyers often wear Zippleback or golden dragon skins. The Gold-skins, interestingly, are the only Flyers with a one-horned helm, possibly indicating some senior NCO-esque rank, as these guys are purposefully distinct from the other Flyers. They are usually tough, cruel, and experienced.
Squadron leaders were responsible for leading their squads on patrols and missions and for ensuring that their unit was battle-ready and prepared to fly at a moment's notice. It's possible that this position is less of a rigid rank and was more of a fluid position that interchanged hands frequently, depending on the mission and circumstances.
Veteran Flyers, as their name implies, are those who have accumulated a lot of experience and were essentially the NCOs of the Thunderband. They were the wing leaders of every pair of Flyers — the Senior Flyers, if you will, accompanied by their wingman.
As you can see from the pictures above, the Gold-skin Flyers seem to hold this position more often than not. This seems to imply that they are often veterans or have some commanding ability.
However, this doesn't seem to be restricted to just them, as we see in the photo below. As such, it can be speculated that either anyone who is senior can be a wing leader, or such a position doesn't even exist and pair groups are more of a teamwork-oriented unit than having a true hierarchy.
For example, look at these two Flyers as they take down Stoick in "Darkest Night".
Or these two Flyers when the Twins were chasing their tail in "Dawn of Destruction".
So it's very possible that in pair-units, it's more of a fluid, teamwork-focused unit with a dash of hierarchy, similar to the Riders' command structure (albeit less flexible since they have to obey Krogan's commands to a T).
On to the next group!
Junior Flyers: The Runner-Ups
Junior Flyers are those below the Veteran Flyers and often fill the wingman roles in the pair-units, and would probably be similar to the corporal or sergeant ranks, in contrast to the Goldskins' senior sergeant or ensign ranking. The one above is one of those "Deadly Dozen" Flyers prominently shown in Seasons 5 and 6.
Junior Flyers are often portrayed wearing one pauldron, white markings, Nadder wing skirts, and Nightmare tunics. This implies they have some status in the Flyers organization, since Nightmare and Nadder skins are impressive skins. (However, as Hiccup mentions that slaying a Nadder only "gets you noticed", it's probably more of an expected minimum requirement in order to even start ascending the hierarchy.)
Similar to the Zippleback and Gold-skin Flyers, they seem to be experienced, ruthless, and tough warriors. Unlike the former two, however, the Junior Flyers seem to be far more expressive and more likely to express fear or uncertainty if something doesn't go the way they expect.
Which leaves us to our next layer in the hierarchy.
Regular Flyers: The Rank and File
The rank'n'file. The wings on the sky. The wannabes. The grunts. The minions. Whatever you wanna call them, this what makes up the Regular Flyers, the second-lowest part of the hierarchy, who are given no command positions, few protections, and fewer distinctions and trophies to set them apart as warriors.
Often portrayed as Flyers who lack pauldrons and even shields, they are often given menial tasks and missions that those further up the hierarchy can't be bothered to do. In fact, they can be called the apprentices, disciples, or even squires to the Flyers of the Upper Ranks. Their wish is to be recognized and gain much fame, wealth, and glory for themselves and rise up the hierarchy. Their ultimate ambition is to become a part of the "Deadly Dozen," their Chieftain Krogan's personal retinue.
However, even then, they're not the bottom-feeders of the hierarchy. There's one more group of Flyers.
Ranker/Fledgling Flyers: The Snubs of the Litter
The Fledglings. These are basically the greenhorns, "boots", or "Shinies" of the Flyers. They just passed their Flyer Cadet Training School exam and are easily recognizable by their distinct lack of everything aside from a helm and a vambrace made of Monstrous Nightmare skin. Other than that, the rest of the outfit looks badly tanned and not as quality as the others further up the hierarchy. They're also noticed for their distinct expressive natures, easily showing their lack of experience and emotions too easily — particularly fear and uncertainty.
Due to their bottom-most rank, and derisively called "Stubs" (basically wings that haven't come out and developed yet, practically meaning "flightless bird") or "Shedders" (as in discarded scales) by the more experienced Flyers, they are basically given all the unwanted tasks, chores, errands, and assignments as a form of hazing. Despite this, they are proud to be a part of the force and look up to the Higher Echelons, and look down on those beneath them, such as the Riders and the Dragon Hunters, often using them to feed and clean the Singetails in their place.
Dragon Hunters: The Grunts and Footstools of the Organization
While not strictly a part of the Dragon Flyers, the Dragon Hunters are the grunts who do the heavy labor, patrols, security, garrisoning, as well as the capturing, feeding, and cleaning of Singetails. They also serve as walking target dummies for Flyer training. They do all the dirty or unwanted work for the Flyers, who view such work as beneath them (which is usually the case since they're always high up in the air 😎).
Flyers always outrank the Hunters in status, similar to medieval knights and men-at-arms.
Often called "Tuskies" in a derogatory manner (viewing them no better than boars), Flyers aren't afraid to look down on them with disdain or indifference; they [the Flyers] often throw all the unsavory jobs to them, particularly when it comes to caring for the maintenance of the Singetails. They view them as clumsy, unreliable, vulgar, noisy, and stupid, and make it a point to never get close or communicate with them anymore than necessary except when giving orders. They don't hesitate to use them as fodder against the Riders and dragons, and even enjoy forcing them to act as target practice for them.
Neither side trusts nor likes each other. Nonetheless, their mutual fear of Krogan drives them to work together for the sake of his plans. They often use the Hunters for ground-to-ground and ground-to-air combat, while the Flyers provide cover for the Hunters in close-air support.
Conclusion
In conclusion, this is my idea of what the Dragon Flyer hierarchy might've been like.
Again, keep in mind that I could be totally wrong and that Netflix had no rhyme or reason or purpose for the Dragon Flyer designs or outfits. Meaning that the Flyers could be much more fluid than I expected.
However, I personally feel that my theory and headcanon is plausible, even possibly correct. Even if the canonical hierarchy is literally just consisting of Krogan, the "Deadly Dozen," and everyone else below them, with the Dragon Hunters being at the very, VERY bottom.
What do you guys think about this? Like the hierarchy? Or think that there's anything I'm missing or should add? Or perhaps got your own thoughts? Let me know what they are! 🤓
Thank you for reading, and I hope you have a wonderful weekend. I plan in the near future on posting an article with some fanedits on what I think the Dragon Flyers could look like if they were a large organization, and what ranks they would have. Look forward to it!
Long Live the Night!
— Noctus Fury
#noctusfury#httyd#httyd articles#httyd lore#httyd theories#httyd headcanons#dreamworks dragons#race to the edge#dragon flyers#flyer leader#krogan#hierarchy#military ranks#meritocracy#httyd dragon flyers#rtte dragon flyers#httyd krogan#dragon flyer leader#httyd flyer leader#rtte krogan#dragon hunters#rtte dragon hunters#httyd franchise#httyd article#httyd theory#httyd headcanon#charts#graphs#httyd charts#hierarchy charts
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Symmetry: The beauty of Mathematics
Listen, symmetry isn’t just aesthetic. It’s the backbone of mathematics, the reason your equations behave, and honestly, the only thing keeping some functions from spiraling into utter chaos. And here’s the truth: symmetry isn’t just about looking pretty; it’s about mathematical harmony, balance, and the deeply satisfying moment when everything aligns perfectly, just as it should.
The Y-Axis Mirror Selfie (a.k.a Even Functions)
2. The Rotational Drama Queens (a.k.a Symmetry about the Origin; odd functions)
3. Group Theory Symmetry : the reason your Rubik's Cube works and why physicists don’t spiral into existential despair when studying quantum particles.
Cyclic groups, Dihedral groups and Lie groups
4. Polar Coordinates—aka the Art Students of Math
Polar graphs SCREAM symmetry. Roses? Circles? LEMNISCATES?
the bottom line : Symmetry is how we recognize order in chaos. And symmetry isn’t just confined to math. You see it in biology (DNA), art (da Vinci’s Vitruvian Man), and even in the way we naturally find faces with symmetry more attractive. It's everywhere, from the humble parabola to the complex eigenfunctions of quantum systems. So next time you plot a graph, take a second to appreciate the sheer elegance of its symmetry. Or lack of symmetry—because asymmetry can be just as hot.
#math#mathematics#mathblr#symmetry in math#even functions#STEM#academia#math academia#fun with graphs#math graphs#graph plotting#polar coordinates#group theory#group theory symmetry#math elegance
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I made a graph about mouthwashing plot and I think it’s worth to show you guys
#matematic#mouthwashing#mouthwashing swansea#mouthwashing curly#mouthwashing jimmy#mouthwashing daisuke#mouthwashing anya#graph#no one will understand this#theory#i made this graph and i am proud of it#people will understand#no they wont
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Edwin: *monologuing about confusing feelings*
Monty: *kisses him*
Edwin: "That was unexpected"
Monty: "I have feelings for you too"
Edwin: "I wasn't talking about you"
Very funny but oh so awkward
#and the cats looking at all this as well of course#anyway at least Edwin is being honest with himself and has realised that he's got feelings for Charles#of course charles has feelings for crystal#but I'm 99.9% sure charles is bi and also into edwin#but also jealous as fuck of edwin and monty#oh this show puts the concept of a love triangle to shame#you need graph theory to make a diagram of these idiots#i love them#also charles is fucking hot so can't blame edwin and crystal for wanting that#tbh the cat king being the cat king (aggressively flirting) while in charles' form had me going 🤤#anyway that was enough oversharing on tumblr for today#dead boy detectives#dead boy detectives e5#edwin payne#charles rowland#dbd monty#monty#edwin x monty#edwin x charles
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this should probably not be possible
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Mace Windu would've fucking loved graph theory. Legitimately. Math nerd in a modern AU. he's obsessed with finding graphs with higher toughness. he's gonna find a graph of toughness 3 if it kills him.
Alternatively he can be the Václav Chvátal of his world and introduce the concept itself
(this post is about shatterpoints)
#mace windu#star wars#i am taking graph theory right now if you didn't get that#it's cool#mathematics#graph theory#shatterpoint#math history
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graph theory question:
is it possible for a connected graph to have two vertices that are the unique farthest vertex from each other but their distance is not the diameter of the graph?
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The infinite diamond lattice consists of layers of graphite sheets Manuel, Paul & Xavier, Antony & Therese, Stanislaus & Arokiaraj, Andrew. (2016). A CLASS OF PERFECT DOMINATION PROBLEMS ON DIAMOND LATTICES. International Journal of Pure and Applied Mathematics. 109. 115-123. 10.12732/ijpam.v109i7.15.
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The Four Color Theorem is a theorem in Graph Theory which states that for every collection of contiguous non-overlapping regions on a plane, no more than 4 colors are required to color the plane so that no two adjacent regions share the same color.
Below are 108 examples I made in Photoshop:
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