top ten celestial bodies

best in the asteroid belt refer to me in a similar way as to how you would refer to the #1 dwarf planet

[bunniope]

in charcuterie city, you'll always be cheesed to meet your friends

[iamoutofideas]

I hate charcuterie city I want to go somewhere else

[bunniope]

this is all that's left.

[iamoutofideas]

this is all that's left.

[transfemininomenon]

dark souls 3 is ten years old ????

[transfemininomenon]

this isn't the gif i thought it would be .

[negativeresponse]

Feel Cold Yet ?

[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]

[spinchs-field]

accidentally wrote “never mill yourself” like yeah i don’t think anyone would do that unless they’re wheat or perhaps a rice

[spinchs-field]

what the fuck happens in Magic the Gathering dawg

[sakana-sister]

tkmiz

[sakana-sister]

this seems to be a followup to this tweet.. projecting her desires onto sumida..

[todreamofsadie]

england is a vile, miserable land. i hope harry kane dies alone.

[todreamofsadie]

bomb tottenham

[pokemon-npcs]

girlfriends...

[fishing-lesbian-princess]

These two even got a full art card when the remakes released

[pokemon-npcs]

Oh that's so cute!

[t00thpasteface]

me before i get my paycheck: i'm so excited to spend this on essentials and save the rest wisely

me as soon as that direct deposit hits: you know i've always wanted to learn the theremin

[contemptible-scoundrel]

it's not surprising, of course. to many, a dog being euthanized for attacking a person is a tragedy. poor thing was in a bad environment you see, it didn't deserve to die. and to many, every criminal should be put to death. they are inherently cruel and cannot change, any sentence more lenient than death is an injustice to their victims. why might a dog maul someone? well clearly the poor thing was a victim, it was circumstance that spurred it to violence. why might a person mug someone? clearly they have a corrupt soul, incapable and unworthy of empathy. they were spurred to criminality by their own sick nature. so to say, in their eyes, a human criminal is less human than a dog

[longhorned]

never join a local trans group in proximity to a naval base

[joeyclaire]

instead of “this person made good art so they can’t be a bad person” try looking at it like this: “this person made art so they can’t be a good person”

[contemptible-scoundrel]

I've noticed in recent years that, at least within mainstream usamerican culture, the sympathetic petty criminal archetype has largely fallen out of favor. you still have plenty of stories of noble nights, benevolent aristocrats, sympathetic mercenaries, but the idea of a thief with a heart of gold is increasingly rare. often petty criminals are just used as uncomplicated cannon fodder, so the protagonist has something human-shaped that they can kill or mutilate without remorse. you see this with dnd players often. the wicked king or the cruel dragon can be reasoned with, but a highway bandit robbing caravans to eat is perfectly fine to torture to death with sorcery

[pache-au-lait]

mahjong taught me that ridding 13 children of their parents makes one "peerless" and "distinguished"

[nyantara]

things that would exist if intellectual property wasn't a thing

so much cheap generic medication. reverse engineering compounds would be even more financially profitable.

fewer people dead of vaccine preventable illnesses in the global south bc the greatest barrier to distributing some vaccines like hpv is their ip

plant seeds and grafts that come from the plants instead of licensing them. don't invest so much in preventing cross contamination. more localised experimental breeding.

library of the world: every book and journal article in the world could be digitised and be searchable for every person in the world to read regardless of where they live. cheap reprint runs and local translations everywhere.

an online interface where every citation could actually lead to the text in question

freedom from the hell that is DRM software

everytime someone reverse engineered your shitty proprietary software we would all be freed from it instead of them getting DMCA'd

so much hardware would be opened up & therefore made so much cooler.

so many more songs that riff off and sample and interpolate shit from this decade instead of like 70 years ago and more analysis of music that didn't keep getting nuked off the internet

preserving movies and tv shows and games as long as someone, somewhere has the desire to host them

just go publish your fanfic/art/vid as is instead of all us pretending it isn't fanwork or begging the corporation for mercy / licensing

a world without ip lawyers. im getting chills just imagining it.

[currymaker]

ill be honest i dont really get queuing

[ntrider]

well this way instead of sitting in an empty lobby waiting for players to join you get to browse around until the queue has enough players to actually start a lobby and then they can all go play immediately

[currymaker]

picks you up and climbs my stepladder to put you on a high shelf

[ntrider]

HEY?????

[shroomgluggler]

in the future humans will have something called "sinus button " and pressing it will immediately drain your sinuses of all fluid so that it can be filled with other things like rocks, webs, paint, tar, freef (new fluid that will be so important in that time) and also dr papper

[noelle-ism]

#hope #hopepunk #positivity #utopia #dreamworld

[grimeclown]

Huge fat jiggly tits are so awesome . Though I may be alone in feeling this.

[grimeclown]

It could be massive. Heavy and swinging pendulously. Bouncing and all. This movement could bounce.