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#Mathematics for All
math1089 · 7 months
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Exploring Collatz-Like Functions: The Power of 3n – 1
The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe. Karl Pearson Be careful! Do not attempt to solve this math problem – it’s very tempting, but it leads to never-ending cycles. Here’s how it works: Start with a positive integer. If it’s even, divide it…
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dodecalemma · 6 months
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Grad school quote of the day:
“Lovely man. They shouldn't let him teach.”
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capricious-magician · 1 month
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"Mathematicians call them twin primes: pairs of prime numbers that are close to each other, almost neighbors, but between them there is always an even number that prevents them from truly touching. Numbers like 11 and 13, like 17 and 19, 41 and 43. If you have the patience to go on counting, you discover that these pairs gradually become rarer. You encounter increasingly isolated primes, lost in that silent, measured space made only of ciphers, and you develop a distressing presentiment that the pairs encountered up until that point were accidental, that solitude is the true destiny. Then, just when you’re about to surrender, when you no longer have the desire to go on counting, you come across another pair of twins, clutching each other tightly."
Paolo Giordano
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podcast-hemocytoblast · 10 months
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mathematician who ends up in the Distortion’s hallways and immediately starts crying not out of fear but out of frustration because they see some fractal or non euclidean bullshit that reminds them of that one fucking proof they can’t figure out
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doesephs · 2 months
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second coming? more like second succumbing to autistic men, shout-out to the OG mr will graham
for @moncuries aftg team thingymagig
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charlignon · 1 year
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Sorry to put maths on your dash this early in the morning, but the polls to make colours are fundamentally biased, because all values should be independent to get the full spectrum. But in a poll, all values are related by the simple relation that a+b+c... = 100%
It means that most colours will not be obtainable from such polls !! Example given in RGB, to get white you would need 100% R, 100% G and 100% B. That is not a result you can get from a valid poll.
In more mathematical terms, if you project your RGB/HSV/whatever space on a cube where values ranges from 0% to 100%, the result set would be restricted to the intersection of this cube with the plane x+y+z=100. It's called Maxwell colour triangle.
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On left, Maxwell triangle for a RGB cube. On right, Maxwell triangle on a HSL cube. Plot code based on this website
So here you have it. The result from these polls will inevitably fall in these. cw spoilers I guess
EDIT : the joke about gay being bad at maths was a bit unconsiderate as it vehiculate stereotypical ideas. English is not my first language, and sometimes I would just replicate some things that I read elsewhere, but I should be more cautious. I edited it, but I thought it was important enough to acknowledge
Also edited some sentences a bit for clarity. Oh and also also : this is not inherently a bad thing, and poll makers are generally aware of this. I just want to share a fun fact !
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chrisrin · 10 months
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because i'm SO curious...
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simplydnp · 4 months
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who's hand is in this picture?
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A Mathematically Rigorous Proof That I Spent Too Long Writing
welcome to university math: dnp hand edition
(no, don't leave, you'll be fine i promise)
to begin, we need a statement to prove. we have two options:
- the hand is dan's hand
- the hand is phil's hand
now, for most proofs in university math, you are told a true statement, and you must show why it is true using logic rules, definitions, and theorems. but, we do not know which of these statements are true, so we have to find out.
to prove that a statement is true, we must show that it is always true for the situation presented. to show a statement is false, we must present a single instance where the statement is false (also known as a counter example).
a quick not scary math example:
definition: a prime number is only divisible by 1 and itself.
statement: all prime numbers are odd
(this is false, because 2 is a prime number and it is even. you don't even need to check if there's any others, all you need is one single case where it isn't true to disprove it)
so now that we have a little background on proofs and how to prove and disprove them, we go back to our two statements.
the thing with this situation is, one of them must be true (unless you're gung-ho on someone else holding dan's face while phil takes a picture on his phone of dan in his glasses, in which case, i applaud your commitment, but in actuality this proof will cover that option too)
the full statement we have is: dan is touching his face or phil is touching dan's face
now, because this is Real Life and we have a picture where a hand is touching dan's face, we know already that one of these options is true (as mentioned above) but! using symbolic logic you could also come to this conclusion.
this type of statement is an 'or' statement, and if you're curious, you can look into 'truth-tables' and see why, but at least one of the options must be true.
back to the proof at hand (bah-duhm-tss)
okay. now, proofs also must be 'general' in order to mean anything, really. these are statements of truth of the universe, not just for individuals. so, we will prove this generally.
we have 2 people involved, so individual 1 (dan, the owner of the face and potential face toucher) will be labelled as 'D' , and individual 2 (phil, the possible face toucher who does not own the face) will be labelled as 'P'. thus, this can be true for any such D and any such P.
so with our 'or' statement, in order to prove it, we pick one of the options and say that it is not true, and we have to show then that the other is true.
step 1: let's assume this is not P's hand. (assumption)
step 2: thus, it must be D's hand. (what we take from our assumption)
step 3: now, if it is D's hand, we look at what a hand on one's own face is capable of appearing like. (a definition or true fact about step 2)
the position in the given photo shows the hand with a thumb on the cheek, and a finger on the forehead. so, we find an example of a person with their fingers in the same position (or close to) and see if this supports our claim.
consider:
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now, with this image, you can clearly see how the subject's right hand has the thumb on the temple and index finger on the top of their head, however, it is a close enough position for our case.
from the view of the camera, the closest finger to the camera is the edge of the pinkie. in fact, it will always be the closest finger to the camera in this position, assuming the subject has all fingers and no additional appendages.
step 4: we now compare this to our photo (we verify if this holds to our claim or contradicts it)
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in our photo, the closest appendage to the camera is the edge of the thumb.
step 5: thus, it cannot be the case that D is touching their own face. (what the evidence says)
step 6: as we assumed it was not P's hand and have shown it cannot be D's hand, and as this is an 'or' statement both of these claims cannot be false, we can therefore conclude it must be P's hand. (our conclusion: re-stating the statement and assumptions and conclusion)
step 7: we verify that P is true (optional step but in beginner proofs you generally show why your case works)
to do this, i will show a picture of a person touching another's face, and compare it to our image.
consider:
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now, this image is not exactly the same, similar to above. however, P's left thumb is on the cheek, with their index on D's temple. the closest appendage to the camera (if it were in a similar perspective as our original) would be the edge of the thumb.
comparing it to our original:
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our comparison holds.
thus, we can conclude that the true claim in this statement is that P must be touching D's face, which, in particular means that:
phil is touching dan's face in the image
thank you for partaking in phannie mathematics. we now know. i am not sorry.
bonus:
phil has a hitchhikers thumb and dan doesn't so why was this necessary at all 🤡
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quirinah · 1 year
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they are having an argument over whether P=NP
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myfairkatiecat · 3 months
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So I was thinking about the whole elves-being-naturally-prettier-than-humans thing because that was always sort of weird to me when I FINALLY think I figured it out.
Humans used to know about the elves, and there are some things they still remember—hence myths about Atlantis and such. Reality is, humans and elves resembled each other in a lot of ways, but elves put themselves on a pedestal as better than every other species (that’s, like, canon, and better be addressed more fully at some point?) and that’s probably a part of the reasons humans “betrayed” the elves—they got sick of hearing that elves were better.
But it was just sort of implanted in their minds, though they weren’t fans of the idea, and elves didn’t go to great lengths to erase that idea from their minds. So humans remember myths and some things about elves, and Atlantis being the underwater city………and beauty standards.
It’s not that elves are naturally prettier than humans. It’s that human beauty standards are shaped around the natural looks of elves.
Thanks for coming to my ted talk
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cuubism · 9 months
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Zero [complex math verse]
cw for disordered eating eating disorder storylines can be very triggering so please mind this content warning as it applies heavily to the entire fic
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Hob is almost to his data structures section—running a bit late, as per usual—when he gets a call from Death. He picks up as he’s rushing up the stairs to the Comp Sci building.
“Hey, Hob,” she says before Hob can even tell her that he only has like thirty seconds to talk, actually. She sounds fatigued. “Can you go pick up Dream from the Maths building?”
Hob pins the phone between his shoulder and ear as he tugs open the door. “‘Pick him up’? Is he okay?”
“He asked me to come get him, but I can’t leave this patient right now.” Hob can imagine her leaning against the wall, hand pressed to her forehead. Why didn’t Dream call him?, Hob wonders. He’s usually much more available than Death, at this hour. “I asked if he wanted an ambulance, and he said no, but if you can’t go get him then—”
“Wait, wait.” Hob stops in the middle of the hall, stomach swooping. Someone walking behind him swears as they have to swerve to avoid hitting him, but he ignores it. “An ambulance? I thought you said he was okay.”
But... she hadn’t said that exactly, had she?
“He will be,” Death says, which doesn’t fill Hob with much confidence. But he turns around and heads back for the door, heartbeat picking up with each step.
“I’m going now, I’m not far.” The undergrads are just going to have to cope with not having discussion section today. He doubts they’ll be too unhappy about it.
“Thanks,” says Death, with relief. “Text me when you find him? And you should bring some food, if you have it.”
Oh.
Fuck.
Hob had been afraid something like this would happen. But he can’t exactly force Dream to pick up better habits. Horses and water, and all that.
“Yeah, yeah, I will, thanks,” he says, and walks faster.
Hob is going to be upset with him.
The thought circles Dream’s mind as he sits crumpled on the bench outside the classroom he’d been working in, head on his knees, hands clasped behind his neck. Nothing feels real. Everything is spinning and swaying. He might pass out. He might throw up. He hates throwing up. Hob is going to be upset with him.
It’s exactly what he was trying to avoid by calling his sister instead. Death will be upset with him, too, but she’s chastised him before. Dream is used to it. The same words coming from Hob will be a different matter.
He should have known that she would be busy, and would call Hob. Even if she could come to get him she would likely call Hob after. He should have known. He sits with his head pressed to his knees and waits for the inevitable.
Either Hob was very close by, or more time slips past Dream’s notice than he realizes, but it feels like only a few minutes before he hears Hob’s footsteps coming quickly down the hall. He doesn’t know what it means that he can recognize Hob’s footsteps. Or that Hob had known which classroom to go to. The one Dream always prefers to work in.
“Dream?” Hob crouches in front of him, trying to meet his eyes, but Dream can’t lift his head from his knees. It’s the only thing keeping the world from tipping over on him. Hob lays a hand on his arm. “Hey, love. What’s going on?”
“‘m dizzy,” Dream murmurs, voice small. He hadn’t realized how much his shoulders were shaking until Hob touched him. He thinks that’s distress more than physical shakiness. But Hob’s presence soothes him more than he’d expected. Even if Hob chews him out, he doesn’t want Hob to leave. He wants Hob to hold him. He just wants Hob to hold him.
“Okay.” Hob’s voice is quiet and calm. He brushes Dream’s hair behind his ear, though it’s not long enough for that to do much. “Sit up for me for a sec? I’ll help you.”
Dream is helpless but to follow Hob’s voice. He starts to sit up. His vision is still spinning. Hob wraps an arm around his middle and bodily lifts him up until he’s leaning back against the wall, then sits beside him on the bench, their thighs touching.
He meets Hob’s gaze. Hob is close enough that he doesn’t appear to waver as much as everything in the background. He looks beautiful, he’s a savior, an angel.
Dream’s brain is not working very normally right now. Not that it ever is.
Hob looks more concerned than angry with him. But Dream doesn’t have much time to study his expression before he’s turning to dig in his bag and pull out his water bottle. He uncaps it and hands it to Dream.
“Drink that. At least half of it. Slow.”
He goes back to digging in his bag as Dream sips the water carefully. Hob is very steady, underneath the concern. No panic. Good in a crisis, Hob. That’s interesting.
Hob watches him drink the water, then hands him a package of cheese crackers he’d pulled out of his bag. Despite himself, Dream laughs, weakly, as he takes it. “Do you always have food with you?”
“You’re not the only one who forgets to eat lunch, I just accommodate for it.”
‘Forgetting’ is… not exactly it, Dream thinks as he picks open the package and takes a cracker, eating it slowly. He still feels more nauseous than hungry, but he knows Hob won’t let it be until he eats it.
No, he has witnessed Hob skip a meal when in the throes of some engaging problem, but he always makes up for it later. Or by carrying around snacks, apparently. Whereas with Dream… it is not exactly forgetting.
He eats the crackers one by one, mechanically. Barely tasting them. Fortunately, the food cuts the edge of nausea in his stomach instead of exacerbating it, and he no longer thinks he’s in imminent danger of throwing up. Or passing out. That would certainly upset Hob.
“There you go, love,” Hob soothes him. “That’s better, isn’t it?”
Hob could have gone into the medical field instead if he wanted to, Dream thinks, somewhat deliriously, swallowing his final cheese cracker. His bedside manner is very good.
Or perhaps this is just because it’s Dream.
The thought makes him want to cry, but he doesn’t. He just stays still as the world starts spinning a little less, and Hob takes the water bottle and empty snack package back and shoves them in his bag, then tugs on Dream’s arm.
“Alright, why don’t you lie down.”
“This is a public hallway,” Dream complains, albeit weakly.
Hob sighs in exasperation. “We’ve slept on classroom tables before. Besides, this is a university, everybody’s seen weirder shit in public than this. Lie down.”
Dream acquiesces, and Hob guides him to lie down on the bench, his head on Hob’s lap. It’s pleasant, like that, and the world spins less and less. Hob pets his hair, and Dream closes his eyes.
“Are you going to make me go to A&E?” he murmurs, after a few moments of quiet.
“Depends how you feel in twenty minutes or so.” He sighs, and there’s a shake to it. “But I think you’ll be okay, love. Just give it a moment.”
Dream will be okay, until Hob decides he’s recovered enough to chastise him for his behavior. For now, he just lies there quietly and enjoys the settling feeling of Hob’s hands in his hair.
Hob doesn’t ask him what he did to himself, or why. Perhaps he’s judged Dream too tired or incapacitated to talk about it right now. He just keeps steadying Dream, quietly, his hands ever-moving.
When several minutes have passed, Hob asks, “How are you feeling, darling? Do you want to go home?”
Darling. Hob calls him such sweet things when Dream is nothing but difficult to him. “I would like to go home. Please.”
Hob helps him sit up, bracing an arm around his shoulders. But the room, thankfully, has stopped spinning. He gets Dream to his feet, and Dream doesn’t sway. Hob picks up both his bag and Dream’s from the floor and slips them over his shoulder. He wraps an arm around Dream’s waist. And silently, relieved to be standing again, Dream follows Hob home.
~~
Dream’s flat is closer to campus, so Hob takes him there, gets him settled on the couch and makes tea and pushes a box of biscuits into Dream’s hands, and all this before even telling Dream off for his behavior. Dream is not a child, he knows perfectly well how much sustenance a body needs to sustain it, he knows that it is unwise to go without eating, so why doesn’t Hob tell him so? Chastise him for his foolishness?
Dream sits curled up on the couch. Turning the box of biscuits over and over in his hands, unopened. Finally, Hob sits beside him with his own tea.
“Do you want to talk about it?” he asks.
Dream can’t manage to get himself to open the biscuits. He sets the box in his lap, but picks up his tea as a compromise that will hopefully ease Hob’s worries. It does not work, based on Hob’s expression as he watches him do it. Dream sips his tea anyway. Hob’s put a lot of honey into it. Correctly deducing that Dream hasn’t had enough sugar or anything else today.
Instead of responding, he tears up.
Hob puts both of their mugs back on the coffee table and pulls him into his arms.
Dream presses his face into Hob’s shoulder. Tucks his hands in against the warmth of Hob’s body, pressed between his back and the couch. Crawls halfway into his lap. Hob wraps his arms around him and holds him close. Dream feels like his soul is pattering around and only staying contained by the boundaries created by Hob’s body. He doesn’t know what that feeling is.
Hob strokes his hair, murmurs against the shell of his ear, shh darling, it’s okay. Dream is a pathetic cowering creature soothed by Hob’s touch. That feeling. It’s fear. He’s scared. Scared of himself. That he can lose such control while grasping so tightly for it.
“Thank you,” he finally manages, something he should have said earlier, but means more than he can say, “for coming.”
“You could have called me, you know.” It’s not accusatory, but a little hurt. “It’s okay if you’d rather have Death, just—”
“It is not that. I—” He pulls back to see Hob’s face. Hob wipes the tears from his cheeks. “Death has told me her feelings on the matter before. I was… apprehensive to hear yours.” Death, also, has seen Dream at lower points than this. She can hardly think less of him. The same is not true of Hob.
Hob looks sad to hear this. “My feelings are that I’m concerned. Did you eat anything today?”
“…No.”
“What about yesterday?”
Dream thinks. He must have, surely? “I think so.”
“I can make you stuff, you know,” Hob says. “Whatever you want. I don’t mind.”
This is the last thing Dream wants. For Hob to think this is somehow his fault.
“If you’re forgetting I can just come get you whenever I’m eating,” Hob continues. He’s only growing more distressed at Dream’s silence.
How can Dream tell Hob, who cares so much and wants to help, that he does this on purpose? That he doesn’t forget that he’s hungry, but rather ignores it? Or worse, relishes in it? That he has done so for a long time. That it makes him feel sharper. In control of himself.
That once broken, habits are, it turns out, very hard to pick up again. Even when that habit is eating.
“It is not so simple, I’m afraid,” he says, ducking his head.
“No, I guess it wouldn’t be.” Hob bites his lip, looking away. “Why, then? I want to help you, but I don’t…”
“It makes me feel better,” Dream says. “Until it doesn’t.”
Like today. He pushed too far. But it’s only when he does go too far that the reality of what he’s doing comes back to him. It’s easy to forget, when he is used to it.
Ironically, he knows from experience that it will be easier to eat better in the next few days, now that he’s shocked himself back to reality. It will be easier, until he slips again. He doesn’t know how not to slip.
When he finally looks back up, Hob is already looking at him again. He looks sad. Dream doesn’t want him to be sad.
Hob takes Dream’s jaw in his hand, strokes his thumb over Dream’s lower lip. “You scared me, seeing you like that.”
Dream should probably apologize for his behavior. Instead, all he can do is lean in again to press his forehead against Hob’s. He knows Hob wants to fix it, to offer solutions, but all Dream really wants is his touch. Hob’s touch fixes more for him than anything else.
“I’m gonna stay over,” Hob says, cradling the back of his head. “And we’re going to have dinner.”
It is, in fact, almost dinnertime, Dream realizes. No wonder he felt overcome, after having nothing until now. Hob will insist on him having something, he knows. It still feels… strange. To be having something.
He tucks his face into Hob’s neck. “Very well.”
“Will you eat some of it?” Hob asks, petting his hair again, tugging the short strands between his fingers. Dream thinks it must be soothing to him to do so.
“Yes,” he says. “However. I don’t want you to think that this is your responsibility to fix.” Or that you can. Hob is very very good at taking things apart and fixing problems, but if he digs his hands into this one he is going to get his fingers jammed in the unsteady gears of Dream’s brain. He is only going to get hurt in trying.
“Maybe not,” says Hob, and, like he heard what Dream didn’t say, continues, “but I can feed you one meal so let’s start with that?”
Does Hob understand how much comfort he brings? Can he possibly?
“I love you,” Dream murmurs, almost unintelligible for how close he’s pressed himself to Hob’s body.
Hob kisses his head. “I love you, too, my darling.”
He bundles Dream closer so their limbs are all tangled together. Dream loves that, how he can feel each pressure point where they touch. “Will you tell me more about it? When you feel up to it. The more I get how you feel, the more I can help you.”
As a child, Dream’s favorite number was zero. Some mathematicians would insist zero was not actually a number, but rather the absence of one. That was exactly what Dream liked about it. The nothing defined by the everything around it. Zero was foundational, and yet it was not even properly there at all.
Sometimes Dream felt like zero. The less he ate the more he felt it. It was easier to be nothing than to let the everything in.
“You are insistent upon trying to help me,” Dream says.
“Yup.”
“Because,” Dream realizes, with a hard swallow, “you love me.”
“Exactly. You get it.”
Dream twists their fingers together and squeezes. If Dream is zero, Hob is like infinity, so boundless that he can’t help but let it engulf him.
Perhaps one day Dream will be able to explain it all to him in better words than that.
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math1089 · 2 years
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Finding Square of Numbers – Part 3
Finding Square of Numbers – Part 3
The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver. I. N. Herstein Welcome to the blog Math1089 – Mathematics for All. Glad you came by. I wanted to let you know I appreciate your spending time here at the blog very much. I do appreciate your taking time out of your busy schedule to check out Math1089! Squaring…
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humantardis38 · 3 months
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why must everybody be a Spock? “I’m so Spock, where my Kirk?” whatever sure, but the real question is where are the Kirk’s? Do Kirk-stanners exist?? if so, marry me??
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rhodesmusic · 11 months
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lipshits-continuous · 6 months
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Fuck ÷, all my homies hate ÷
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only-lonely-stars · 1 year
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Because I'm curious:
Please rb for greater sample size!
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