DO NOT STARE DIRECTLY INTO THE APERTURE

// 28 // she/her // 95% Silly Meme Posts™ // Hate to break it to you, pal, but that wasn't a read. I had no idea what I was going to do.

[dylandude120]

Happy TTYD remake week!!

[kesia-stupid-arts]

This dialogue dude!!!

[weirdplutoprince]

Well, well, well. If it isn't the consequences of someone else's actions that I am directly impacted and severely affected by

[dosmeow]

I’ve been seeing a lot of Scooby Doo on my dash lately. My friend discovered what he describes as “Shaggy eviscerating an ape”

[mevil]

[shittysawtraps]

jigsaw influencer: it must feel good as fuck to survive a saw trap and know that you’re going to live your life to the fullest ⭐️ use code SAWTRAP to get 15% off on blue apron until 8/31

[furryprovocateur]

they should allow you to report posts for being gauche or passé

[girlswater]

[gemologie]

DISCRETION

[lamortwrites]

Women being described as handsome >>>>>>>>>>>>

[lamortwrites]

TARGET AUDIENCE REACHED

[catchymemes]

[paper-mario-wiki]

[pharmersonly]

me when i engage with something that i know is gonna piss me off: wow that pissed me off

[contemptible-scoundrel]

tch... so it's an alliance out of necessity, huh...?

[coelii]

[actualized-animal]

every chapter of deltarune has a secret npc who only appears if you leave and re-enter the room 1225 times while you have a bagel in your seventh inventory slot and the npc is a sentient doorknob and when you talk to them the music cuts out and they’re like “who’s that whispering in the trees, it’s two sailors and they’re on leave, pipes and chains and swinging hands, who’s your daddy, yes i am” and then within four hours there’s a thirty minute long video on youtube titled “ASGORE IS FRIEND??? DADDY THEORY EXPLAINED” and it already has 100,000 views and then a year later people call the next chapter disappointing because it was focusing too much on developing the main characters instead of explaining the doorknob guy

[fleetwood-mac-andcheese]

[itsbasil]

you put those tags on this post where they belong

[girlnephew]

[ryanthedemiguy]

I don't think this is possible????

[physicallyimprobable]

Hello Ryan I am here to help. So the first step is pretty easy: Three cheeseburgers are worth 18, so each one is worth 6. If these are dollars, that's a steal!

From the second equation we get that cheeseburger plus fries-squared is five. Subtracting cheeseburger, which is six, from both sides, we get that fries-squared is negative-one. Math fans will know that there are two solutions to this; either fries are the "imaginary unit" 𝒾 or they are its negative, -𝒾. We'll do the rest of the problem with 𝒾, keeping in mind that at the end we should also take the complex conjugates as solutions.

Finally, we have that cup to the power of fries, minus cup, equals three. Replacing fries with 𝒾, and moving a cup to the other side, we get that cup-to-the-𝒾 is equal to cup-plus-three.

Now, the weird part about this is the cup-to-the-i. The problem with this is that complex exponentiation is technically not a thing. That is to say, there is no one function which is mathematically equal to "input-to-the-power-of-𝒾". In fact, there are infinitely many such functions.

Fortunately, due to reasons that take about six pages to explain (trust me I've done it), there is one particular function that many people have agreed is "the most reasonable one". This is not a mathematical notion, but a human preference. Seeing as this question was presumably written by a human, I am comfortable with using this function.

So, what function is this? Well, given a complex number r∠θ written in polar form (if you don't know what that means don't worry), where -π < θ ≤ π, then (r∠θ)^𝒾 = e^(-θ)∠ln(r).

Applying this to our problem a value r∠θ will be a possible solution for cup if e^(-θ)∠ln(r) = r∠θ + 3. Splitting this into real and imaginary parts, we get two equations: e^(-θ) cos(ln(r)) = r cos(θ) + 3 and e^(-θ) sin(ln(r)) = r sin(θ). We can graph these equations on Desmos:

The possible values of cup are the intersections between the red, green, and purple. There are infinitely many of these which have an angle of around -π/3, and there are two weirdos: One which is a complex number very close to -2.98, and one which is somewhere around -25. The possible values for cup are all of these infinitely many solutions, and also all of their complex conjugates.

[sharkgirldick]

They were right, 99% of people can't solve it.

[peelerofpotatoes]

i've actually been working on some formulae to give all possible solutions to complex exponentiation problems recently, so here's my take on this:

let the value of the glass = z, for z ∈ ℂ:

z^(±i) = 3+z

let z = r·e^(iθ) for r,θ ∈ ℝ, -π < θ ≤ π

∴ z = r·e^i(θ+2πn) for all n ∈ ℤ

∴ (r·e^i(θ+2πn))^(±i) = 3+r·e^i(θ+2πn)

distribute powers (apologies for the use of ∓):

r^(±i)·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

convert to the same base:

e^i(±ln(r))·e^(∓(θ+2πn)) = 3+r·e^i(θ+2πn)

split into real and imaginary components:

re: cos(±ln(r))·e^(∓(θ+2πn)) = 3+r·cos(θ)

im: sin(±ln(r))·e^(∓(θ+2πn)) = r·sin(θ)

in effect, all this changes is the restriction on the domain of theta to be between -pi and pi, so you can just ignore that constraint.

[inthefallofasparrow]

[skopostheorie]

[iwantwings44]