
Love Begins

Andulka
Three Goblin Art
we're not kids anymore.

shark vs the universe
Jules of Nature
he wasn't even looking at me and he found me

ellievsbear
d e v o n

PR's Tumblrdome

@theartofmadeline
noise dept.

Janaina Medeiros
let's talk about Bridgerton tea, my ask is open

⁂

Product Placement

祝日 / Permanent Vacation
tumblr dot com
Monterey Bay Aquarium

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@totallynotloric
today was the first day of astrophysics!! here’s a general overview of what this blog will be like for a while: I’m gonna learn something in astrophysics, and post either a brief “space fact” which would be one or two sentences, or write a more in-depth post regarding said concept or idea, which would take longer. I’m aiming for at least one original post per day, maybe two or three! I’ll also reblog any interesting space pictures, physics facts, etc as i find them. Excited for a great year!
Lorien Legacy blog "sound off" (1 month time limit 26/07-26/08)
Hi guys! Since I’m rarely on nowadays, idk who’s who these days, so I’ve decided to do this thing, which is, if you are apart of the LL fandom or have an LL blog and want me to follow you, reblog/like this with the blog you want me to follow, so if you have a personal blog and don’t want me to follow that one, then reblog with the LL blog and I’ll just do it. And for those of you who I currently follow, please do so if you want me to continue following, cause I’m gonna unfollow any and all LL blogs that do not do this, cause I will consider them as inactive. And if you don’t want to do either of those, you can also just send me a PM or message me or whatever.
I will unfollow anyone who does not reblog this
Euler’s Identity//e^(i*π)=-1 PROOF
I’ve received several requests for the proof for eπ*i= -1, also known as Euler’s Identity, so here it is. If you have not taken calculus, you’ll have to trust me on a few parts, but you’ll definitely be able to understand. If you have any questions or I didn’t explain something right, let me know! The first part is a little confusing, so bear with me, but once we get past it, it’s significantly easier to get.
Before I do the proof, it’s important to explain what Taylor polynomials are. Taylor polynomials are polynomials used to approximate//estimate values for functions we can’t calculate by hand, such as sin and cos functions. Its general form looks like this (it’s intimidating, i know, but don’t worry):
where f’ is the first derivative, and Xo is the “starting point” (usually 0) and X is the point you’re trying to find a value for. Basically, each term is the nth derivative divided by n factorial, times x^n, and the Taylor Polynomial is all of these terms added together. This function goes on forever, or until you want to stop. The more terms you add, the more accurate your function is.
If you haven’t taken calculus, don’t understand, or don’t like math, you don’t need to worry about the formula or what it means, just that Taylor polynomials approximate functions.
The Taylor polynomials for e^x, sin(x), and cos(x) look like this:
meaning, these polynomials can approximate the functions above. We’ll need all of these for the proof.
If you don’t understand the above math, all you’ll need to know is the Taylor polynomials for e, sin, and cos, and that they are equal to those functions.
Now we’re going to do the actual proof. For this, we’re going to take the Taylor polynomial for eix and expand it:
Now, remember these powers of i:
since i^2=-1, we can substitute that value in every time we see an i^2, every time we see an i^3 we evaluate it and write -i, etc. Basically, we’re simplifying all the values of i. This leaves us with some terms having i in it, and other terms not having an i. We can group these terms separately, with terms not having i in one group, and terms having i in the other:
We can factor out an i from the terms on the right, since they all have an i:
Take a look at the two sets of terms we have remaining. The one on the left looks like the cos Taylor polynomial, and the one on the right looks like the sin Taylor polynomial:
because of this, we can substitute in sin(x) and cos(x) into the equation:
This general form is called Euler’s Equation. Since we are trying to find e^(pi*i), we plug in pi for X:
cos(π)= -1, and sin(π)= 0, so we evaluate and get:
This proof is kinda mind blowing and feels like math magic, but it’s real and it’s pretty cool. You’ll use it in differential equations classes. I hope you thought it was interesting and were able to understand it. If any of you have any questions, be sure to let me know!!!
i am the most obnoxious person i know
no you are a saint for making this thank you
THIS IS THE GREATEST THING I HAVE EVER SEEN
DEAD
THIS IS GOLD
Of course I had to get an alien tattoo to represent my loving desire for Lorien Legacies
Ah, that’s an awesome tattoo!
Trying to explain unit vectors to a non-math person.
FBI: You can’t just go around having your alien wars in random cities.
Garde: we have a permit.
*shows paper*
FBI: This just says “We can do what we want.”
Loric News!!!! *0*
Public bathrooms are such a godless place. Ppl do the most bizarre stuff
one time i walked into a mcdonalds bathroom and their was shit on the wall with actual hand prints like a scat version of the shining and it took everything i had not to vomit after the immediate 180 i did
Last week I really had to pee walking home from the bus stop so I jumped into the park bathroom a few blocks from my house (in a pretty upscale area) and there was a chick in goth lolita dress smoking crack in the men’s room.
after i saw the remake of annie, i went into the bathroom and this guy at the urinal was whipping his dick back and forth while singing uptown funk and his friend was urinating beside him and laughing the entire time
My dad and I stopped at a truck stop in Northern California (or Southern Oregon, it was a long time ago and I don’t remember) when I was 12 or so and I ended up needing to go to the bathroom while we ate, so I was directed towards the back of the building. I walked in and saw a woman laying in a clawfoot bathtub, immediately shreiked and turned around apologizing, to be greeted with 10-15 truckers, including my dad, laughing their asses off. …It was a blowup doll.
okay that story beats the ones i had
Let me tell you a story about Dairy Queen and the time I closed an Allsup’s.
With my ass.
Many moons ago, when I was but 14, I, my father, and several others were going on a fishing trip to southern Colorado. Now, like good Texans, we loaded up at 5:00am to make the twelve-hour trip in a single day because, you know, that’s what you do in Texas.
Several hours later, we found ourselves in Childress, the very gateway to the Texas panhandle, a surreal place a thousand Tumblr posts could be written about. There, we had a proper breakfast at Dairy Queen, certainly a Texas institution. I recall quite clearly having a basket of disappointing chicken strips and unpleasantly greasy fries. It was a bland, unsatisfying meal, but I was 14, still sleepy, and really quite hungry, so I ate it regardless.
Not long after, I felt a sensation like one my young body had never felt before.
To say that I was in discomfort would be putting it mildly. I was cramping, I was sweaty, I was fairly sure I was one hard bump in the road away from shitting my pants and forever ruining not just my pants and my pride, but the back seat of my father’s friend’s harvest gold metallic 1999 Ford F350 Super Duty.
This day, the prairie tan upholstery of the harvest gold metallic 1999 Ford F350 Super Duty would be spared.
Mercifully, as we entered one of the many smallish towns on the way through the panhandle, we stopped for gas at an Allsup’s. Then and there, I was making my final stand. Every muscle in my body clenched desperately, holding in the terrible burden foisted upon it by a meal of grease, batter, and regret.
Like all Allsup’ses, it was a liminal space, a place that had no real business in the real world and was, instead, a small, dingy realm within its own flimsy walls, a pocket dimension with a spinning rack of country music cassettes and CDs from artists I’d never heard of and a Blue Bell freezer that was likely only ever 1/3 full no matter how long the early days of that Texas summer might drag on.
It was here, in this space between spaces, an outpost in the first real steps into the panhandle, that I would commit one of the gravest crimes of my life.
Stealthily, as though smuggling some secret only slightly less terrible than the grim truth my life had become, I made my way to the back of the dingy, unpleasant gas station. Thankfully, it had an indoor restroom that didn’t force me to ask for a key, one of the few saving graces of the little mess of a place.
I would, in short order, rob it of even that marginal virtue.
With my stealthy power-waddle into the lav, I locked the door behind me, my body and mind already relaxing, knowing that relief was at hand and soon my suffering would be over though I didn’t know at what could that relief would come, I couldn’t have known. The restroom was not overly dirty, but just the same I mouthed a hushed “fuck” as a churning growl from ominously low in my gut warned me there was no time for the gossamer security of a paper ass gasket, this was happening then and there, the process had already begun, the die had been cast.
Hurriedly fiddling with my belt buckle as I approached the toilet, the promise of relief quickly gave way to desperation. In seeing the finish line so close, my body was quickly losing the will to struggle across. The time of choosing had come, and it was not mine, not my body’s, this was Dairy Queen’s battle; it had been from the moment that overly-dense, overly-greasy shadow of a meal had touched my lips.
With no small desperation, I threw myself at the seat, and it was perhaps in that forced desperation that the morning came to a head. The sound my body made was unreal as a daisycutter of shit blasted out of me, still several inches above the seat. In that moment, time itself lost all meaning, I became part of the liminal space of that Allsup’s and the forsaken dungeon that I had doomed its lavatory to be. I couldn’t bring myself to straighten out enough to actually sit down, in part for knowing the seat had been lost to what had poured out of me and in part because the pain of my cramping gut wouldn’t allow it.
When it was over, I felt a mixture of emotions that seemed wholly fictive, like something no true human could ever experience. In the immediate aftermath, relief ruled over all other sensation, the pain was gone, the fear was gone, I was left purified… And then I saw at what cost.
Indeed, I was purified, but what I was purified of had found its way into the world and found, in turn, terrible purchase. It had not just dominated the toilet. It was on the walls, it was on the floor, it was even on the underside of the sink. The spread was so wide, so even, and so dense that it seemed no human ass could have created it, it seemed the work of evil, and yet there I stood, staring at it in horror, at my creation.
Amazingly, as though shielded by Providence itself, I was saved from a similar fate. Somehow, miraculously, I was no more sullied than had it been a regular, uneventful trip to a restroom. As I transferred every bit of evil within me into that Allsup’s restroom, it lost whatever dignity it had that I might retain my own, something I am grateful for to this day. Careful to avoid touching any, you know, shit, I tidied myself up and debated for a moment trying to clean the restroom with the minimal tools at hand, but I knew it was a lost cause, there was no way a damp bit of single-ply could solve anything I had done.
Leaving that forsaken lavatory to stew in my misdeeds with a similar stealth, I made my way out of the restroom and out of the Allsup’s together, finding my way back to the renewed security of the prairie tan and harvest gold metallic Ford F350 Super Duty. Shortly thereafter, my father found me, asking if I’d gone in to use the restroom yet, if I’d seen its unbelievable horror.
Using my exhaustion to my advantage, I looked up from my book, undoubtedly looking tired and befuddled.
“Nnno? I was gonna go in, but I used the restroom at breakfast and I just want to get through this chapter, why?”
It was an expert lie and, by God, somehow it worked. Somehow.
Other parts of the story go on from there, but they don’t relate to public restrooms, where this story does pick up though is a year later.
By sheer coincidence, my father and I were making another trip through that part of Texas. By sheer coincidence, our journey took us through the same town in the panhandle. As I saw familiar scenery move past the window, I felt a hot wash of guilt work up through me from below.
And that’s when I saw it.
The Allsup’s.
Not just closed, but boarded up, plywood over its windows, black plastic covering its door. My stomach dropped and my eyes went wide.
It was then that I told my father the terrible truth of that day a year before.
He was strangely proud I had closed a gas station with my ass.
that had me enthralled from start to finish and i am determined to get everyone on tumblr to read the story of how your ass is responsible for the closure of a business.
OH MY FUXKING GOS INM CRYJNF
@sirarmeyeth
Talk about a yarn expertly woven.
Say what you will about how Harry Potter increases in complexity and darkness as it progresses but I think JKR sets the tone of the series pretty well when she has Dumbledore play ding-dong-ditch with a baby in the first chapter
This is maybe the most important paragraph in all of Harry Potter.
The gatekeeper’s parents
I came across this statement “The gatekeepers don’t have parents because it is possible that they were never actually born … even if that thought does rather make my head spin.” by Anthony Horowitz in an interview (you can find the whole article here) and that supports that one theory about the gatekeeper’s I have.
So, you remember that Past Matt said he believed all the gatekeepers were born at the exact same moment and past Matt is always right. But Scott and Jamie are twins and that means they can’t be born at the same time. Therefore they just kind of appeared somehow on earth when they were needed most.
But Pedro and Matt knew their parents, how does that make sense? Well, about Pedro, he grew up in a small village and his parents died when he was still pretty young. It’s well possible they just took him in as a baby and never had the opportunity to tell him about it. It’s more difficult with Matt. He had a deep and important relationship with his parents. But it’s still possible he was just adopted. Think about it, he was eight when his parents died. They probably thought he wasn’t ready to know yet. And that doesn’t make their death less awful or anything. They were on an emotional basis still Matt’s parents just not biologically.
Another thing that always confused me was that woman in the Dreamworld. Past Scar met her once and than all the gatekeepers did in the end. Still, she never played an important role and Anthony Horowitz never really explained her. Each of the gatekeepers saw her as their mother. Doesn’t it make sense if she actually was their mom and the librarian was their father.
[No Spoilers] Made this “A Dance with Dragons” thumbnail in photoshop and Illustrator. What do you think about it? / via
My brother demonstrating how to pick up girls in a club ;)
They should make the series into a Netflix show! It should be titled “Lorien Legacies” and each season can be a different book. Season One can be “Lorien Legacies: I Am Number Four” and the second season can be “Lorien Legacies: The Power of Six” etc… -meerkatpawz
this is a fucking good idea netflix
More Lorien Legacies Friendships I want
Some of these are really weird or unlikely, but bear with me
John and Marina:
They’re basically the only ones who know what they’re doing half the time
They hugged once and I cried
Basically the Dad Friend and the Mom Friend
Can you imagine what would happen if they fought? A constant stream of strained politeness and passive aggression
Ella: “Mom and Dad are fighting again
John helps her cook and Marina sketches him while he trains
For Christmas, John gets her an apron that says “Kiss the Cook” and she gets him a fanny pack
They send each other letters even when they live near each other because yeah it’s slow but it’s nice for John to be staying in one place long enough to have a constant address
Marina sends him little dried flowers
All around incredible 10/10
Five and Daniela:
(this was originally Sarah but you know how that turned out)
Literally the fiercest friendship you have ever seen in your whole life
Daniela actually sits and listens to Five’s whole story (from the very beginning, not just the Eight thing) and, of course, Nine’s testament and decides “You know what? You made a mistake–a hella big mistake–but you’re trying to make up for it. I get it, you’re trying”
From that moment on Five latches on like there is no tomorrow
In the middle of a battle a mog sneaks up on Daniela, but never gets past Five
You want to take out the medusa girl? Good luck getting past Five cause he’s made of metal and flying and COMING RIGHT AT YA
They go out for Starbucks and frozen yogurt all the time
The Garde check Daniela’s Snapchat story to find dozens of selfies with Five
“Apologizing is hard, I get it, but just say it, Five. Five. Are you listening to me? Get back here right now!”
She calls him Cinco
The unstoppable force
Could totally kick your ass
Nine and Sam:
I know I’ve talked about this one before but I need more
Nine gets him into trouble all the frickin time
These kids can’t even go to the grocery store without something going wrong
You know that list going around the internet called “How to get kicked out of Walmart”?
They’ve tried all of them
You can and should make a sitcom about them
HOWEVER it mainly began when Sam started getting nightmares about his torture and Nine relates and they support each other and I’m crying now excuse me
“GOODE MOVE YOUR ASS” “OH MY GOD”
–90% of their interactions
Got lost in Ikea. Found hours later eating meatballs in the fake dining rooms with no clue as to how they got there
Mark and Six:
The unstoppable duo of death and over-competitiveness
At first Mark is kindof really intimidated because he’s seen what she can do, and she’s the first Loric that he’s met (besides John, but he was never scared of him)
Then he beats her at checkers
Then it is on
Constant competition to prove superiority in any situation
Making smores? “Hey Six I bet I can fit more marshmallows in my mouth than you can.” At the library? “Mark I can totally stack more books than you can AND THEN stand on top of it.” “PROVE IT, LORIC!” Literally just walking down the street. “CARTWHEELS NOW GO DO IT”
Non stop
People start taking bets. It is glorious. Five keeps track of it all. Sam looses all of his allowance every time.
They’re super great sports about it though no matter who wins because they respect the frick out of each other
Loser buys ice cream for the winner
Adam and Ella:
Kinda awkward but once they get to know each other more their friendship works out really great
They know what it’s like to be treated like actual Mogadorians, so they’ve experienced quite a bit more than the others, and it brings them a little closer together
Ella sometimes picks up on his thoughts and when she picks up on his little sassy bits she bursts out laughing
Sometimes in the middle of important meetings but she can’t help it because it’s just hilarious
“Hey, uh, sorry I almost killed Setrakus Ra even though I knew you might die.” “Don’t worry about it. I was trying to get everyone else to do that for days.” “Dude that’s hardcore.” “I know.”
Whenever Ella’s in a crappy situation (You know, teen party gone wrong stuff, after the war is over) that she doesn’t want the rest of the Garde to know about, she can call Adam and she knows he won’t tell
Secret handshakes and acting cool with sunglasses
Ultimate sibling relationship
And that’s all for right now! Feel free to add on to any of these if you like them!