#and they are not big images

[coraniaid]

top 5 mathematical identities :)

I wish Tumblr supported LaTeX.

OK, not trying to overthink this too much.

There are lots of fun identities involving binomial coefficients (or their q-analogs), or related integer sequences like the Catalan numbers and Motzkin numbers. But I think I have to go with the Chu-Vandermonde identity: who doesn't like a good convolution formula?

Of all the trigonometric identities I've ever had to learn, this is certainly not the most useful in practice or the hardest to prove or, arguably. the most inherently interesting either. I think the half-angle formula for tan is surprisingly pretty though.

Let S be a finite set of real numbers. The maximum-minimums identity relates the largest element of this set to the smallest elements of every (non-empty) subset of S.

or, more concretely,

Perhaps not classically beautiful, but certainly enormously useful, the Sherman-Morrisson-Woodbury identity in linear algebra gives a formula for computing the inverse of a rank-k update of an invertible matrix by doing rank-k updates of the inverse of that original matrix. It's valid whenever the matrices are suitably conformable and when both the required inverses exist.

I feel like I have to include something due to Euler here, but -- rather than one of the famous ones involving π or anything to do with topology -- I'll go with some analytic number theory. The pentagonal number theorem gives a series expansion of the Euler function, valid for any complex x in the unit circle.

or, expanding both sides,

That takes us into the world of q-series and we can generalize it further to get Jacobi's triple product formula or various identities due to Ramanujan or MacDonald's identities for affine root systems or other increasingly exotic and strange things ... but this identity is the prototype for all of them.

[nemfrog]

"The Big Dipper as it is today (left) and as it will look in 50,000 years." Dream of stars. 1940.

Internet Archive

[mildmayfoxe]

GET WEIRD! // shop

[aaronstveit]

if you’re cold, she’s cold. let her in your window

[incredubious]

(asl+uta) she's addicted to setting him up for failure

[bigskycastle]

the covers i was allowed to do for the "a year in hyrule" planner project (preorders closed now)

[delicourse]

i miss them a little if im gonna be honest

[animatedtext]

[willowser]

HMMMMM bakugou being just. the absolute picture of sin.

he works overnight and comes home early in the morning, around 3 or 4 am or so, and you greet him and give him a kissy and ask how it all went. and even though it's still dark outside and he's been working for twelve hours—he's still coming off patrol, right ? so he's still got some energy left, and he eats something and takes a shower and winds down as you fall back to sleep.

and it's not until much later in the day that he wakes up, early afternoon, and you're kind of tiptoeing around so that he can get his much-needed rest. you slip into the closet of your bedroom for something and you think you're gonna get in and out without a sound, but his hearing is so attuned to just about anything and everything at this point.

so rough and raspy, he grunts out, "what're y'lookin' for?" and you whip around real fast and he's just—

half sitting up in bed, bare back leaning against the headboard. an arm behind his head, so that his bicep is tense and round and stone-solid. stretched like that, his obliques are more prominent, taut and rippling up the side of his ribcage. he must have gotten hot while passed out, as he usually does, because the comforter is all askew; one of his legs is bent, the fine hair a dark gold in the waning day; the other is hanging off the bed, lightly swinging as he watches you, and the blanket has come down enough that you can see the bulge of his thigh muscles beneath his stupid tiny black boxer briefs.

and he's just so. man. in every single way.

(his hair is flat on one side, too, and his eyes are still a little puffy from sleep—but you think that adds to it, all in all)

[cinnamontoads]

date with kaz

[nemfrog]

As the ancients saw it. The book of stars. 1920.

Internet Archive

[fashionsfromhistory]

Brooch

Marcus & Co. (New York City, New York)

c.1900

This exquisite brooch is one of the few extant examples of plique-à-jour jewelry made by the New York firm of Marcus & Co., whose reputation at its prime rivaled that of Tiffany & Co. Herman Marcus (1828–99), a German–born and Dresden–trained jeweler, arrived in New York in 1850 and worked for a number of prestigious firms before establishing Marcus & Co. in 1892. Following his death, the company continued under the direction of his two sons, George Elder Marcus and William Marcus.

The brooch is a superb example of Marcus & Co.’s work in plique-à-jour enameling, in which the "cells" of color have no backing, allowing light to shine through the transparent enamel, thereby creating the effect of stained glass. One of the only jewelry firms of its day to succeed at this challenging technique, Marcus & Co. followed the lead of such innovative French designers as René Lalique. The sensitive 3-dimensional sculpting of the sweet pea blossoms and leaves, as well as the naturalistic coloring of the enamels, reflects the Art Nouveau aesthetic that prevailed at the turn of the century. Indeed, close parallels can be drawn with the brilliant naturalistic work of Louis Comfort Tiffany, whose oeuvre is so well represented in the Met’s collection.

The MET (Accession Number: Accession Number: 2016.107)

[boojangs]

Enid: Wednesday, go apologize to Thing or I won't help you.

Wednesday:

Enid:

Wednesday: Yes, querida.

Enid: Wednesday, I made a black cat costume for you.

Wednesday:

Enid:

Wednesday: Yes, querida.

Enid: Wednesday, I made us matching snoods!

Wednesday:

Enid:

Wednesday: Yes, querida.

Enid: Wednesday, please get rid of your creepy crime board.

Wednesday:

Enid:

Wednesday: Yes, querida.

Enid: Wednesday, please hold me in your-

Wednesday: Yes, querida.

[jarrows]

recently i reread a bunch of my favorite sherlock holmes stories (norw my beloved) and felt compelled to create my own diagram for 221B

[imethirdperson]

What I like most about farcille is that I think its a perfect encapsulation of Ryoko Kui's signature mixture of the cozy and the horrific. Overall Marcille has this clean pristine aura that she breaks only for Falin's sake. She's uppity, rigid and idealistic almost childishly, then she shows this immense drive, gets her hands dirty, and bends and bends. Dungeon Meshi is about how all beings become objects of consumption, and Marcille wouldn't have arrived at that conclusion if Falin hadn't died. She also wouldn't have if she hadn't befriended her in the first place. The course for Marcille's life was set when she was just open-minded enough to follow the weird girl to the cave in the woods. Forever cursed to eat wildlife

It's that contrast between cleanliness and filth that interests me, the interactions between the comfort and the horror, the uncanniness of the familiar and the familiar in the uncanny.

Every bit of Marcille's characterization points to a type of immaturity (the picky eating, the detached romance obsession, the failure at foreseeing the obvious consequences of her actions, the ridiculous plans to equalize all lifespans, the death crisis). Even in her dream she appears as stuck in childhood due to her loss trauma. Her development throughout the manga consists of coming to terms with grime and disgust, learning where food comes from, learning her limitations, coming to terms with death and decay... And it's all powered ironically by her drive to save Falin

[chloesimaginationthings]

im sorry but your mike/fnafsb vanessa dynamic reminds me vaguely of the fuckass deviantart hot yaoi base so i wasted like 30 minutes of my time doing this

my brain loves to continuously shit out horrible ideas and for some reason i decide to do them

This is a greater compliment than you can even imagine