#triangle numbers

[storymaker14]

Bizzaro Right Triangles

Okay, we all know that, if you have a right triangle with sides a and b and hypotenuse c, that means a^2 + b^2 = c^2, right?

So you can have 3-4-5 right triangles, and 5-12-13, and 7-24-25, etc.

And technically, a 1-i-0 right triangle follows this pattern, too, which has made the rounds in the math meme community.

But I found something better and weirder. I found a whole family of better and weirder.

I'm gonna skip a bit of the beginning and start here:

cos x = (e^ix + e^-ix) / 2

That follows from Euler's formula; if you need a walkthrough, I can provide, but I want to start with the above. So then, it follows that:

cos (i*lnx) = (x + 1/x)/2 = (x^2 + 1)/2x

Which means that an angle of (i*lnx) radians in a right triangle will have an adjacent side of (x^2 + 1) and a hypotenuse of 2x. By Pythagoras, then, the opposite side must be (x^2 - 1)*i.

But please note: if x is odd, then the lengths of all three sides will be even, and thus can be divided by 2.

Which means -- are you holding onto your hats and shoes?!? -- means that the proportions of the right triangle with angle i*ln(3) radians... are 5-4i-3.

And for i*ln(5) radians, they are 13-12i-5.

And so forth, with all the familiar Pythagorean triplets sqrt(2n+1)-n-(n+1) showing up, just with one side imaginary and the hypotenuse and remaining side swapped -- so, (n+1)-n*i-sqrt(2n+1). They still fulfill Pythagoras, every single one.

Which I think is, pardon my directness, fucking terrific. But just as a little bonus, please note that this means the triangle with angle i*ln(2) radians, the proportions are 5-3i-4, which is just delightful IMHO.

[infamously-winking]

Silly Straw Page Fully Translated:

hbh grfwru ri d gliihuhqw nlqg/ zkr zdqw wr pdnh klv sdwlhqw eolqg = “eye doctor of a different kind/ who wants to make his patient blind”

Qeb alzqlo pxvp/ qeobb pfmp x axv/ tfii jxhb qeb sfpflkp/ dl xtxv = “The doctor says/ three sips a day/ will make the visions/ go away”

Ixvvb hdwhu/ edeb eloob/ zrxogq'w gulqn/ xqohvv lwv vloob = “Fussy eater/ baby billy/ wouldn't drink/ unless its silly”

215 858 117 450 110 628 19 211 120 2256 216 951 25 256 27 532 212 506 18 1317 110 1137 221. 658 23 1330 210 231 118 929 112 2043 = “Twisted out of shape after the kill, the ghosts of his family are haunting him still.”

we’re not talking about that last cipher enough…

[jellyfishtoenail]

[lavernius]

More old art that never got posted!

[brixbraxium]

I love how in Deltarune you have like all of this symbolism and allusions and whatnot for Noelle Angel, and you have a bunch of explicit textual stuff that kinda only really makes sense under Eldritch Angel (The idea that The Angel is its own character, not a 'role') with Alvin's dialog, And then for Player Angel you have This Door.

And yet somehow this actually does put Player Angel on equal footing with the other theories because like man wtf would this mean otherwise. Like what

[stellabyystarlight]

happiest and most triangful birthday to the trianglest triangle boy 🫶📐(haha i said triangle 3 times)

[h4unted-d4rling]

I love the idea of a humanoid Bill Cipher. Like human body with the cool ass suit but the one eyed triangle head. Easily the hottest design. Otherwise, I want the triangle. I know what I am. Again, I am NOT a coward.

[elizabethzoopzoop986]

How I THINK the tbhk characters would feel about imaginary numbers

Hanako- “isn’t this math why are there letters” ass kid

Nene- ????? So confused, they give her a head ache

Kou- thinks that the one 3D graph he was shown was cool looking, does not get it

Aoi- Gets them, does not like them, I think they light a rage in her soul more than they should

Mitsuba- why would I have an opinion on a math concept???? What??

Akane- Enjoys math and imagery numbers more than one probably should (got sad when the teacher said to ignore them because we don’t go into 3D in highschool(and honestly disappointed in himself that he thinks there so cool and fun))

Teru- can use them, understands them, thinks they’re difficulty is overhyped. Does not think about them after they are one the test

Tsukasa- “WHAt????!?!?? Can I eat it!!?!!?”

Natsuhiko- “How are numbers even imaginary… what does that even mean??”

Sakura- could learn them and use them, but does not care to bother herself with that

[noosphe-re]

[leafix-arrts]

I forgot this was supposed to be an art account

[swan2swan]

When this first came out, I thought it was a funny joke. A little fun with the fandom. And of course, Kiersten was just being silly. We joke here, right?

Now, though, this is Beyond Hilarious and is actually Kind of Ominous.

[indycinders]

This was so cute 👉🏼👈🏼

It's my canon now this was their first kiss.

Template below if you'd like to try uwu

[aroaessidhe]

2024 reads / storygraph

Road To Ruin

start of a postapocalyptic fantasy series set in an Asian-inspired desert world plagued by dangerous storms

follows a courier who transports romantic letters between a prince and princess, who helps the princess escape across the wastes towards the prince’s safe haven

but they’re pursued by bounty hunters, and accidentally uncover some ancient secrets. and also she’s in love with both of them

dinosaurs, magical motorbikes,

bi MC, start of polyam triad

[plotbunnybreeder]

In Scripturam Veritas

An unknown number texts Derek in an obviously drunken post-breakup ramble. He never expected their texts to lead to friendship or feelings. Just his luck to fall for someone that might not even live in the same state.

Then his scattered pack members come home from college for summer break with a whole other pack in tow.

OR

Isaac and Cora start dating, and Scott wants to be a proper Alpha and have their two packs officially meet. It's Stiles' job as Emissary to help the McCall Pack make a good impression on the historied Hale Pack, but it's hard to speak formally when the Hale Alpha is the physical embodiment of his perfect type.

Who he's been unknowingly texting for the past couple of months.

[object-vault-9]

Week 128

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