So you’re me and

you’re in math class and– triangles, triangles,

triangles– I don’t know. The teacher keeps

saying words, and you’re supposed to be doing

something with trigons, whatever those are. But you’re bored and–

triangles, triangles, triangles. Sure you could draw your

triangles separately, but then they get lonely. They’re happiest when

snuggled up together into a triangle party. Everybody knows

triangles love parties. Sometimes they get together and

do these triangle congo lines. If you keep adding new

triangles on the same side, it gets all curvy and spirally. Or you can alternate and

it goes pretty straight. In fact, since all the

sides of the triangle are supposed to

be straight lines, and since they’re

all lying on top of some previous straight

line, then this whole line would have to be straight if

these were actually triangles. Since it’s not, it’s proof that

these aren’t quite triangles. Maybe they’ve been

partying a little too hard, but hey, at least

you’re not doing math. Speaking of which,

the teacher is still going on about types

of trigons, and you’re supposed to be taking notes. But you’re more

interesting in types of triangles, which you

already know all about. There are fat triangles,

and pointy triangles, and perfect

triangles, and cheese slice triangles which are

a kind of pointy triangle but are symmetric like a

slice of cheese or cake. Super pointy triangles are fun

to stack into triangle stacks. You can put all the points

facing one direction, but the stack starts

to wobble too much towards that direction. So it’s good to put some facing

the other direction before you go too far. You’ll notice pretty quickly,

that the skinnier the triangle, the less wobble it

adds to the stack. To compensate for

a big wobble, you can put just one not

so skinny triangle that’s pointing the other way. Or maybe you want to

wobble, because you have to navigate your triangle

stack around your notes. In which case you can even

alternate back and forth as long as you make the

triangles point towards where you want to go, a

little less skinny. The easy part about

triangle stacks, is that there’s really only

one part of the triangle that’s important, as far as

the stack is concerned. And that’s the pointy point. The other two angles can be fat

and skinny, or skinny and fat, or both the same if

it’s a cheese slice, and it doesn’t change

the rest of the stack. Unless the top angle

is really wide, because then you’ll

get two skinny points, and which side should

you continue to stack on? Both? Also, instead of

thinking fat and skinny, you should probably

create code words that won’t set off your

teacher’s mind reading alarms for non-math

related thoughts. So you pick two words off

the board, obtuse and acute, which by sheer

coincidence I’m sure, just happen to mean fat

angle and skinny angle. Of course, those are

also kinds of triangles. Which doesn’t make much

sense, because the obtuser one angle of a triangle is, the

more acute the other two get. Yet, if you make

an acute triangle with the same perimeter,

it has more area, which seems like

an obtuse quality. And then, can you still

call an obtuse equilateral triangle a cheese or

cake-slice triangle, because these look

more like [INAUDIBLE]. Point is, triangle

terminology is tricky, but at least you’re not

paying attention to the stuff the teacher is saying about

trigonometric functions. You’d rather think about

the functions of triangles. And you already

know some of those. There are sines, and cosines,

but enough of this tangent. The thing to pay attention to is

what affects your triangle how. If you start drawing the next

triangle on your triangle stack this way, by

this point, you already know what the full

triangle would have to be. Because you just continue

this edge until it meets this invisible line,

and then fill the rest in. In fact, you can make an

entire triangle stack just by piling on triangle parts

and adding the points later to see what happens. There’s some possible

problems though. If you start a

triangle like this, you can see that it’s never

going to close, no matter how far you extend the lines. Since this triangle

isn’t real, let’s call it a Bermuda Triangle. This happens when

two angles together are already more

than 180 degrees. And since all the

angles in a triangle add up to 180–

which, by the way, you can test by ripping one

up and putting the three points into a line– that

means that if these are two 120 degree

angles of a triangle, the third angle is off

somewhere being negative 60. Of course, you have no problem

being a Bermuda Triangle on a sphere, were angles

always add up to more than 180, just the third point

might be off in Australia. Which is fine, unless you’re

afraid your triangle might get eaten by sea monsters. Anyway, stacking triangles

into a curve is nice, and you probably want

to make a spiral. But if you’re not careful,

it’ll crash into itself. So you’d better think

about your angles. Though, if you do it just right,

instead of a crash disaster, you’ll get a wreath thing. Or you can get a

different triangle circle by starting with a polygon,

extending the sides in one direction, and then

triangling around it, to get this sort

of aperture shape. And then you should

probably add more triangles, triangles, triangles– One last game. Start with some

sort of asterisk, then go around a triangle it up. Shade out from the

obtusest angles, and it’ll look pretty neat. You can then extend it with

another layer of triangles, and another, and if you

shade the inner parts of these triangles,

it’s guaranteed to be an awesome triangle party. And there’s lots of other

kinds of triangle parties just waiting to happen. Ah, the triangle. So simple, yet so beautiful. The essence of

two-dimensionality, the fundamental object

of Euclidean geometry, the three points

that define a plane. You can have your

fancy complex shapes, they’re just made

up of triangles. Triangles. Dissect a square into triangles,

make symmetric arrangements, some reminiscent of spherical

and hyperbolic geometry. Triangles branches into

binary fractal trees. Numbers increasing exponentially

with each iteration to infinity. Triangles, with the

right proportion being a golden spiral of perfect

right isosceles triangles. Put equilateral triangles

on the middle third of the outside edges of

equilateral triangles to infinity, and

get a snow flake with the boundary

of the Koch Curve. An infinitely long perimeter,

continuous yet nowhere differentiable. With a fractional dimension

of log four over log three, and– uh oh, teacher’s

walking around, better pretend to be doing math.

1:02

Illuminati

Nice doodle btw Vi

Dangit, Vihart, you've got me drawing fractals!

Now I can't finish this drawing, since I have an infinite amount of triangles to go…

How long will it take you to find the Illuminati in the video? ❔ Hint. It's at 1:02 If you find it you get money! If you don't… You get attacked by the Illuminati. ? AHHHH!!!! The only way to save yourself then is to type a shape. This shape. ➡️▶️ Or this shape. ◀️ Any type of triangle! ⏩⏪⏫⏬⏭️⏮️⏯️◀️▶️⚠️??????????????? Ready… GO! ?

Woah.

DEATHLY HALLOWS

3:24 Aperture Science, we do we must because we can.

I love the Illuminati, Triforce, and other stuff. Just perfect.

In the end, you should have started "You're assuming I'm a human what I gotta do to get it through to you I'm superhuman…"

This should have been released on purim instead on Chanukah.

My teacher showed me this video and I️ asked what the hell is the relevance to trigonometry

1:08 my favorite kind of triangle ⚡️

0:56 illuminati confirmed

I love the illuminati and Harry Potter triangles

vi, i didnt know you liked Harry Potter!

"There are signs, and cosigns, but let's get off that tangent" I'm dying!

1:12, did anyone see the Illuminati and the deathly hallows!?

Your mentality is great.

Signs and cosigns…

Can not make an emoji because my keyboard is weird <Insert sad emoji>

I heard hamentashen and got excited.

Triangles: equalateral, scalene, isosceles, right angle, obtuse, acute, and reflex to name a few

Why….. Did i subscribe?….

Btw, the thing she said it looked like at 2:00 was “Hamantash,” a type of pastry

I find your lack of Sharpies disturbing!

Are you Jewish?!

Who cares about the illuminati I see the elder wand

Someone understands the beautiful ways of the triangle

OMG Vi Hart before sharpies?! What is this parallel universe!?

You…did…a..skech…of…THE DEATHLY HALLOWS?!

I JUST REALIZED TRIANGLES CAN BE MADE FROM CIRCLES AND CIRCLES CAN BE MADE FROM TRIANGLES HOLY MANN

Triangles are my favorite polygon!

I wanna share my method for trisecting any angle…

Illuminati Confirmed 0:55

"Everyone knows triangles love parties !"

THIS PARTY NEVER STOPS ! TIME IS DEAD AND MEANING HAS NO MEANING ! WELCOME, ONE AND ALL, TO WEIRDMAGGEDON !

I wish I was this creative when doodling in math class

1:06 DEATHLY HALLOWS!!!!

1:09 I only just noticed the deathly hallows and the triforce.

ILLUMINATI CONFIRMED1:13 Harry Potter fans will know

So many cool triangles, serpinski, triforce, deathly hallows, illuminati

This was my first Vi Hart video, I watched it when I was 8, I was like SLOW DOWN OMG, lol my journey into Vi Hart world had begun

t r i a n g l e sThanks, Vi.

I’m floating on a triangle high right now. Don’t worry, though. It’s all natural.

Onward

3:25 is that a cake I see? Beside the aperture logo? Hmm

Cake saighn!

1.08 omg the deathly hallows

You don't need to pretend, you would melt any teachers mind with this anyways

TRIANGLEE PARTTYYYY!

When she made the stack at some point on the side there was the triforce

I have triangles ….

I guess u're a bit obsessed with triangles.. Am I right?

So I take it that you prefer squares.

Triangle party.

Lol thought I was the only one who did this

3:24

PORTAL 3 CONFIRMED

This is maths, but it isnt maths,wtf?

TRIFORCEEEEEEE

INSTRUCTIONS UNCLEAR

DREW A RECTANGLE….

trianglesTRIANGLES

1:00 pause

1:08 the deathly halos and sirpinski

“There are signs and cosigns, but enough of this tangent”

This is why I subscribed.

Sell a notebook full of these doodles

3:25 YES PEOPLE KNOW PORTAL!!

4:20 ok, I got it, triangles makes you wet

Damn, this girl really likes triangles….

I saw the Deathly Hallows sign…

Somebody tried watching this in 0.5x speed? ? Especially around 3:23

Who needs Rick and Morty?

0:56

illuminati confirmedwhat if we made a koch snowflake but every triangle is a serpinski's triangle?

so a Bermuda triangle is a triangle with more than 180° because a triangle with 180° is impossible and the Bermuda triangle is not real. But on a curved surface, all triangles have more than 180°, so Bermuda triangles are possible on curved surfaces. Vihart said she doesn't think the Bermuda triangle is real. Therefore, Vihart must believe the earth is flat. Vihart = Flat earther, confirmed.

Stop it! I’m accidentally learning!

i don't know how i got here but i instantly subbed 😀 have you tried to create triangle structures with code?

i really see that math youtuber has 1f*cking million sub, and view wow the end of word is coming?

How about a sphere? Or a circle?

Just sayin, are you a jew?

I get what you did with the sine, cosine, and tangent joke.

Always

1:10 did anyone else see the Deathly Hallows symbol?

i love how this slowly developed into a slam poem and i didn’t even notice

“There are signs and cosines but enough of this tangent”… It’s taken me years to get this pun. You’re absolutely amazing.

The Hypotenuse song

"signs, cosigns, but enough of this tangent…" (sine, cosine, tangent)

ME:

smirksI see what you did there… (Like this comment if you're watching this in 2019)I learn more from this than I have in ant lesson.

2019 anyone?

And the moment you mention aperture STILL ALIVE blares in mental speakers for the next… half hour of class

Why is no one talking about the face on the demonstration triangle?!

4:21

Thank goodness, my anxiety levels were going off the roof after you started talking too long.

I was about to hyperventilate.

2:01 "Point is…" omg I saw what you did there nice

Seriously? Pen spinning can’t cut it for ya?

So what is your point?

We watched this in class!!

When you were doing the explanation on how you made your triangles curve around your notes, did anyone else see the deathly hallows symbol and the triforce symbol?!

UwU

Edit:

When ViHart mentions Aperture labs and the cake, and you realise that you play the same games as her:

She's almost as nerdy as me!!!

who also needs 0.75 speed to understand this video?

This is why triangles are my favorite shape and that I am going to be a math teacher when I get older

Hilarious!! ?? by the way good art skills

1:09 Is that…

the deathly hallowsI love your voice

too…

many…

math puns…That was…poetry.