#<- enjoys math

[iguessthisisanewobsession]

Danny: So I may have did a bit of an oopsie daisy.

Jazz: … define a bit.

Danny: you know how you were telling me about the two main ways of conditioning?

Jazz: Yes?

Danny: And you remember how I said Pavlov’s dog sounded strangely familiar?

Jazz watching her brother pace: Danny?

Danny: Well, there’s this guy in my lit class who was very pretty and I heard he was vegan and you know that giant bag of vegan candy Sam sent?

Jazz: Please tell me you didn’t.

Danny: Not on purpose! You know how big that bag is! And I can’t just throw it way it’s good candy! So I just, kept giving him a couple pieces when I saw him! I didn’t even realize what I did until I passed him in the hall earlier and he nearly smiled at me and he never smiles!

Jazz: only you little brother.

Danny flopping on the floor dramatically: he just looked to the floor in confusion Jazz! Like visible confusion!

[poofpoofpurin]

happy bkdk new year

[aroaceleovaldez]

why are PJO characters most consistently measured in scales of Michaels?

Like. this is some of the most specific height information we have out of most characters, besides maybe Percy being an inch shorter than Jason. The Michaels Scale...

[mathysphere]

the counting for this was a pain, but boy do I like the look of little lines

A sine wave transformation bookmark, made for @badstitched's charity bookmark project: each variable in the top equation is color-coded to the aspect of the graph that it would affect.

The book's out now to anyone who donates $15 or more to one of a couple different literacy charities-- there's 27 bookmarks in total, all themed around different book genres (mine's in 'nonfiction'!).

Link Here for anyone who'd like to donate and get a nice PDF!

[chongoblog]

Have you heard of the Sum and Product Puzzle, aka the "Impossible Puzzle" because it initially seems like there isn't enough information to go on? I think I have the answer, and I'm mad about it.

I hadn't so I looked it up and here's Wikipedia's summary of it

There's also an explanation, but I didn't look. I wanna figure this out myself.

So let's break it down.

"P does not know X and Y" means that X and Y are not both prime. If they WERE both prime, then P would know the two numbers right away. So if S KNOWS FOR CERTAIN that P doesn't know X and Y, that means that the sum of X and Y can't be made up of two prime numbers. So, for example, the sum can't be 20, since if X and Y are 1 and 19, P would get 19 and be able to easily deduce the values of X and Y.

So we have a bound for the sum here, so we just need to find all numbers that can't possibly be the sum of two primes. I tried to get a good list of all numbers that aren't the sum of two primes through trial and error, but I after I found the first few I just let the OEIS do the rest of the work for me

So our possible sums are: 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, and 97.

Now that doesn't narrow it down a TON, but we can probably do something with this. Now that P knows that these are all of the possible sums, they know FOR CERTAIN what X and Y are. Very interesting. That tells me a lot about the product.

So let's say X is 4 and Y is 7. Then P is 28, and S is 11. Now, other factors of 28 include 2 and 14, which add up to 16 (not on the list), so we could just say that and call it a day, but there's something else that perplexes me. What if P is 24? The factors of 24 are 6x4, 8x3 and 12x2, which give us sums of 10, 11, and 14, and 11 is the only one on the list, so we have new X and Y values for S = 11 that could also apply. And since the S mathematician said he knew what X and Y were upon hearing that P knew, we can safely say S isn't 11, since X&Y could have multiple possibilities.

So, simply put, we need a value of S where there's only one possible P that could work for it. On one hand that still sounds like a LOT of guess and check work, but on the other, I feel like there's a way to find this solution without that.

Doesn't matter. I did the guess and check work anyway, granted it was actually easier when I got to the higher numbers, since most possible factors of P went over the sum of 100, which is one of our limitations. Easiest way to find these unique products is to find the largest prime number (lower than the sum) and use that as one of our two values.

So the conversation goes as such.

S sees that their sum is 17. Knowing that 17 can't be reached as a sum of two primes, S says "P does not know X and Y", which tells P that the sum is one of those numbers we saw up there. P's product is 52, he figures and he only knows two numbers whose sum add up to one of those numbers. So he says "NOW I know the value of X and Y". S hears that and figures that it has to be that one EXACT combination.

X and Y add up to 17 and multiply to make 52 which means that X and Y are 4 and-

...

GOD DAMMIT

[freakinnefor]

you’re so pass remarkable, cal…

[mathsuggestions]

Press random buttons on your TI-84 and see where it takes you.

[oneofthosecrazycatladies]

“You did good gettin’ off that boat when you did. St. Louis is dull as dishwater.”

Why don’t we talk about this line more? Actually, why don’t we talk about Louis and Lestat’s friendship more in general? Louis specifically says he confided in Lestat in ways that he’d never confided in anyone before except for Paul. They went on walks together. They sat on their bench. They had gumbo after the opera.

We focus so much on their rollercoaster romance after Louis becomes a vampire we forget about the lovely friendship they had when Louis was still human.

Loustat aren’t just lovers. They’re friends and lovers.

[statementlou]

hey some very smart people (my babes @captainrayzizuniverse and @goldcrumble) have cracked a 28 Clothing pattern check this out: Drop 1 and Drop 2 came out August and November last year and were both Collection 01 (labeled on the clothing tags); Drop 3 (this July) is Collection 02...

...which suggests a possible pattern of one collection consisting of two drops close together late in the year per year, which feels consistent with teasing items from the next drop in the promo for this recent one; so we would see Drop 4- the second half of Collection 02- in October or November, and then another long wait until the second half of next year for more?

[septune13]

its pathetic businessman griffith’s crush: former construction worker, current engineering student, himbo guts

[everyitachi]

[simplydnp]

who's hand is in this picture?

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:

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)

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:

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:

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 🤡

[gumibuki]

I haven't slept in almost 2 days, have random doodles I did while I had to deal with math

[trollhunters-eldritch-princess]

i think that it's really important how krel faces the majority of human racism during 3Below. he's visibly a latino and has darker skin than aja. krel also has the same quirks as her. but it's her quirks that are seen as cool and his that are seen as weird.

he's also a math genius, and it's constantly called into question how he is doing so well, with the racist man is season one claiming that he cheated solely because 'everyone knows people like him aren't good at math'. even the bounty hunter weaponizes this in the next episode.

there wasn't really a point to this post, but i think that it's really important that in a kid's show, the latino boy is shown to be accused of cheating simply because he doesn't 'look' smart, and the show explicitly calls this attitude out as wrong and does not give it any excuses. and the latino boy is given shades and dimensions to his character and allowed sympathy and rage for his losses. you know, the way all people should be allowed.

[rowanoftheunknown]

“I hope I’ll find all the pieces of my mind that fell out of my head over all those years, and that I’ll be able to put myself together again. I hope the echoes of pain will fade, and memories of sorrow will die, and that you’ll visit me here some day…”

“And I hope you have a happy ending of your own.”

[lover-of-mine]

I don't know who wrote the post about how all of Buck's past relationships have taught Buck the thing he needs to make his endgame relationship work, and like, they are very consistent with this thing where the next relationship somehow fixes something from the one before and while messing up something from the one after, and we all know Buck's endgame is Eddie. Buck has been being handed pieces of the puzzle since Abby. The one missing was his bisexuality. That's not missing anymore. Wherever goes down now, is about Buck getting comfortable in his own skin so he can finally be with someone who loves all of him. It's about Buck finally loving himself, so that he can actually understand what he wants from a relationship. So that he can reach the thing he actually wants, the family he has with Eddie.