The Brachistochrone 

if we made a line if people around the planet, a lot of people would drown

So the perfect waterslide would also be a brachistochrome.

23:45 I love Michael having the idea to just stare at the camera instead of looking at his dream come true

Michael: “Adam and I are going on tour; we hope to see you there” Me: *super excited* Also me: *realises I’m 5 years too late*

"If all of us held hand with each other across the earth, that would be super gay"

oh so we need square wheels in Mexico City for all those fucking holes

0:41 It was an absolute pleasure to be featured in one of your videos, Michael! Thanks for showing me in the video.

Adam is so impressive Michael explained his thing and he immediately knew what to do, he started planning and building, and what do you know, it worked

You know a video is good when it gets 2.5 million views with a title "The Brachistochrone" and a curve as a thumbnail #NoClickbait

Vsauce as a toddler: O... O... Vsauce’s mom: He’s saying his first words... Vsauce: Or am I?

6:13 I'm studying physics for university entrance exams, and I casually re watched this video only remembering the brachistocrone curve, and when I saw that I just realized that this is Snell's law right before he said it I'm f*king proud of myself right now

At 23:39 Michael isn't watching the experiment, but rather he's staring at us🙂

When the smart kid and the creative kid in class get chosen to do a project together

Michael staring at the camera in slowmo kills me 😂

I know it's a pretty old video, but this is definitely one of my favourite things you've ever done, because of how it takes a mathematical proof and makes it real so even people who don't understand the math can look at it and get that it's true. I've rewatched this 4-5 times and will never get tired of it. lol You might say, brain candy videos like this, is a Tautochrone in that it brings mathematically-inclined people and those who are less-so together in something they can get and enjoy.

So does this mean that the Brachistochrone curve is the most difficult to run UP?

vsauce: *deep question* music: twaaaanhg boo doop doo

vsauce: today we are going to talk about the brachinstochrone. vsauce about 2 minutes later: and 7.5 billion people wouldn't even fill up the grand canyon.

Michael is like the adult that would rather be in the "children" group then sit at the table with the parents at family gatherings

How did Adam manage to bald so gracefully. Also when 2 exceptional people get together it's always a treat

The speed at which Adam figures out how he wants to build shit, is amazing.

"But what is...... rolling?" *music starts*

This is fun. I recall studying cycloids in college, and proving they were fastest with calculus. We also performed experiments in physics lab where we used gravity's acceleration to observe them. We even ventured into the topic of rotational inertia.

I love Michael and Adam's bit. It's so genuine! There's no acting, just actual conversations and genuine reactions.

Vsauce wedding: Do you, Vsauce, Michael Here, take this woman to be your lawfully wedded wife? "I do." "Or do I?" [Music plays]

"Do you have a favorite polygon" is the nerdiest thing ever said on this planet and I love it Personally I like apeirogons

22:00 EXCUSE ME WHAT THE HELL IS THAT HOLLYWOOD MOVIE ANGLE LMAO

@8:28 when Michael said "and he said...." RU-vid showed me an ad starting with "I don't have enough money" 😂😂😂😂. I'm dying 😂😂😂

Police: you're under arrest! Vsauce: or am I?

0:40 I'm in this picture and i don't like it

Michael staring into my soul during the second slowmo felt like I was being judged for existing.

A brachistochrone and a cycloid lining up perfectly feels like it makes perfect sense, and yet like a complete coincidence.

he lost his mind after isolation

23:39 Michael's deadly stare at the camera.

23:14 Michael looks like a proud father seeing his son (Adam) doing his science project infront of him.

@15:08 - Michael, question for you. The epicycloid drawn has seven points where it touches the circle and the hypocycloid has six. If the tracing circle were smaller or bigger, would the epicycloid always touch the stationary circle one more cycle than the hypocycloid? (Thats if you have a size that perfectly cycles around)

“Do you have a polygon around here?” Is the most Vsauce this I’ve ever heard

Vsauce: That's not just a circle Me: no... Sauce:That's a cirCOOL Me:NOOOOOOOOOOOOO

brachistochrone

25:34 Michel is the best this is why I watch vsauce

"If every single one of us held hands in a chain of unity around earth." A lot of us would drown.

Adam kinda looks like Adam from Mythbusters.

Okay guys, I just wanna throw this out there, this is my understading of the video. I will just try to go in order of the points discussed in this video. The center of a disc produces a roulette that's just a smooth straight line while rolling on one, but as you can see in the video a rolling disc (let's call it a circle) draws a straight line in the horizontal dimension, but only one point on the circunference of a of the circle contacts that straight line at a that exact coordinates, because the center of the sphere always points to a singular and unique point on the circumference if pointed in a single direction (radius), and the "place" of that radius is always being changed is a single straight direction (in this case to the right), by rolling. We can observe this 2 dimensional graph because we live in the 3 dimentional world, but the perception of the point on the circumference is that it is not moving what so ever compared to the center of the sphere, to him, the center of the sphere is always a fixed distance, and he is always on the same coordinates of the 1 dimensional circumference. Now just replace the circle with a sphere and the straight line with time. The path time draws is always attributed to a single point of the sphere, there is always only one istant in time and it is always moving forward (rolling), we perceive this because we can perceive that the point on the circumference is following a straight line in the 2 dimensional world, but to itself it is described by a single coordinate, (a 2d object on a graph is x=1 y=2 but a 1d object is just x=1, it describes itself), but we know that that a 1d object can follow a straght line if it's described by a 2nd coordinate in the second dimension. So even though we see the distance getting larger between two points, for the 1d object the points are always the same, so if x=1 and y=2, we get a geometrical straight line from any other point with x = 1 and y != 2, but the perception of a 1d object isn't changed, it is still only 1, is still the same "thing", it has not become 1 and 2 together. So we can fixate two separate and distinct points in the 2d world, that are the absolute same in the 1d world. So if we say that these points are the same point, from our percpective of the 2d world, the statement if false, but from the perspective of the 1d world this statement is true. Knowing this, we who live in the 3 dimensional world, perceive that even though a single point is the same for us, it is never the same for the 4 dimensional world, and so we perceive...time. A 2d object doesn't experience the passage of time, because it cannot observe things changing, it can only observe the 1 dimensional world, which is always the same, it is never chaning, it is the same thing, it is always the same coordinate x=1. But it can perceive the 3d world like we perceive time, because by chaning the value of coordinates you get different points. And this is why discs (circles) are such good wheels, it always follows the shortest path from 2 single points on a road, being the road 1 dimensional, it doesn't matter where the road goes ( we only know where it goes because we describe it in 2d, otherwise it would always be the same road and lead to the same place), but only a single point of the wheel is touching the road at a time, unlike a poligon, who will always have 2 (imagine a square wheel and it's two vertexes), more ditance between the points = more time; but if you make the numbers of vertexes infinite, the distance bewtween them becomes infinimetly small, approaching 0, so on a circle it is 0, zero time, the best time, the best wheel. So if we draw a sphere on a 2d graph and a cube on the 2 graph, in which the x axises is time, the shortest amount of time (length of the lineitself if you measure it) is always a straight line, which is only drawn by a perfect circle that is tangent to the X axis, only a single point whill ever be adjacent to it at a time, which makes a square wheel work only if you bend the 2d world (side note after reading my whole comment: we are assuming here that these 2d objects have 0 mass, and and objects with 0 mass can only move trough the axis if it is tangent to it because it enables it to roll; a square in this example will never move because you need mass to generate force and you need force to slide it on the axis, actually rolling it would require an upward motion as well, but that would require the axis itself to bend, to not be straight), and we can do that, because we can observe it, we just draw a curved line, that is longer. We can recreate this 1d road in our 3d world by bending it's 2nd dimension, creating the road at 2:22, in which the square is tangent to the road, only a single point is touching it at a time. This is not true for a prolate because it goes in the negative "mass", two points of the line connect to a single point in time, which is for us, impossible. We cannot build a road for a prolate wheel, because we cannot bend the 2d space (in this case time) to accomodate the fact that point is always tangent, we would have to remove the space where the point is travelling on the road, but we cannot "remove" space, negative space -> negative mass -> impossible. So really x = time and Y = mass. In the same way, a curtate is also impossible because it does not even touch the time axis. But what happens when mass = 0? Light. Light is the perfect wheel of our 3d world. Light will always travel the shortest distance. A straight line. Light is always tangent to the dimension of time, making the two points the same, so the distance between the points is none, and since speed is the distance / time ( 0/0 ), the speed is impossible, there is no speed, it is the speed limit, making it impossible to achieve the speed of light ( it is the only thing with 0 mass ), or go beyond it by the means of removing the space we need to travel (negative mass). Further on, we cannot bend our 4th dimension, time, we cannot create the conditions for two points in time (the 2 vertexes of a square) to connected the same thing at the same time. In order to do that we would need to "bend", accomodate for this by problem by bending the 3rd dimenion, a thing that we cannot do because we do not actively observe it, we see in 2d, a picture at a time. Now a cyclode is what happens when instead of focusing on the point touching the time axis which is ever changing, we focus on a single point that is moving; we draw a cyclode. Again this wouldn't be possible with a poligon because there would always be a side of the poligon that has two tangent points at one time, creating a parallel to time (parallel times). Now in this amazing video, Adam and Micheal built a 3d version of the cyclode by doing the reverse of what we did in order to build it, by attaching the pencil on the disc they drew the tangent path of the disc (which was in fact rotating for it to happen) on a 2d plane, and later projected that tangent in which time is always costant ( X axsis), so theoretically speaking, it doesn't matter from which point in space the balls starts from, because this "shape" of the road in our 3d world makes it so that they reach the end of this road at the same time, because the tanget touches time on Y = 0 whichever the point in space is , in fact the shot from the side (2d view) they made later on, shows the balls merging into one, they become the same thing, they overlap each other. Light is just that, it has 0 mass, it is the same thing everywhere, is has the same constant speed, and is for us, the costant of universe, because on the graph it is just a straight line, it is the axis itself. But an object living in a dimension higher that us, would perceive and observe the dimension we call time, and it would be able to bend it like we bend the 2d one, unlike the 4th dimension which it cannot bend, because it does not observe it, like us with time. That is why we cannot even imagine what a being living in a dimension higher than us would see like, because a 1d object only knows itself, a point, a 2d object can see every point in a straight line, while we perceive the plane (like looking at a graph from above, perpendicular, like you look at it on your screen right now), and an object in a dimension higher would perceive all of this, plus it's version of our "plane". This is why, in intersellar for example, it is shown as every point in space in every point in time, like we see every point of the line on the graph where the X axis is time, making you able to basically "travel in time", because you have access to that dimension, like we have access to the line on a graph. Anyway, I spent two hours on this, I'm way too high.

Vsauce made me both the smartest guy in my school for knowing ridiculous things that no one my age ever thought about, and the dumbest by academic standards because I spent all of my time studying Brachistochrone curves rather than what was actually in my exam papers.

Me: "Hey Michael you wanna roll outta here for a bit and grab food?" Michael: "Sure but what is... rolling. *side tangent for 20 minutes*"

Seeing Michael on the square wheeled tricycle brought great joy to me

One thing that I find interesting about brachistochrome experiments that’s never brought up is that if they tried the three-different-starting-points drop with the really deep curve they made earlier, the wheel at the highest point would hit the bottom first. The brachristochrome is truly neutral.

3:25 was that a threat

Vsauce: Do you have a favorite polygon? CGP Grey: Hexagons are the bestagons.

Smart kid: the quickest way to get to an object is a straight line Quiet kid:

FUN FACT: The brachistochrone curve also works in reverse too! To reach orbit rockets must follow the fastest path to space before their fuel runs out. Rockets launch vertically to get above the atmosphere but then pitch down to fly horizontally above the earth’s surface. How do they know when to start pitching and at what rate? The Brachistochrone! 🚀

Its amazing to me how he takes the idea of a ring of 7.5 billion people into a wild theory in only 30 minutes

Vsauce: When you do this to a shape and follow the line it's a Me: Brachistochrone? Vsauce: Roulette. When you do THIS though, and then you follow the line it's a Me: Brachistochrone? Vsauce: Cycloid. Ah but now I want you to build THIS, and then follow the line, then it's a Me: Brachistochrone? Vsauce: Cyclogon. When you get from one point to another as quickly as possible, then it's a Me: Cyclo-something? Vsauce: Brachistochrone

Michael and Adam working together is the perfect example of "the scientist comes up with an idea and the engineer makes it work"

hearing michael yell "BRACHISTOCHRONE!" is just the best thing ive heard all day.

I find myself coming back to this video. I love how it starts out with Michael completely in charge, introducing the topic, then you can see the wheels start to turn in Adam's head, he figures it out, and then he takes over. And then Michael takes control back over to take things to the next level. Their skills compliment each other so well

Just imagine Michael being your maths teacher

1:34 the "intellectual shit is about to go down music"

In my years in a BS in astronomy, I never had Snell's Law explained to me in such understandable terms.

I wish I had a math teacher like them in school. I’d have never hated math or be bad at it.

I'd like math only if Micheal was my teacher.

23:39 Please don't look at me like that Michael.

"Adam...do you have a favorite polygon?" Is the most Vsauce thing I've ever heard, and it warms my heart ♡

8:08 this vidoe was shot when 3b1b had ~100k subs. Today, it has ~6mil. How time flies.

Superb explaination. Brachistochrone can be my next password.

Video title: *How Do We See?* Intro: *Hey, Vsauce! Michael here! I am in a video. Or am I?* *15 minutes later* Vsauce: *And that is why cereal is soup.*

Love watching them nerd out. We need more videos like this.

Michael: Do you have a favorite polygon? CGP Grey violently enters the chat

23:39 Most people: watching the three spheres fall Me: focusing on Michael staring in the background

Him what’s the fastest way to slide? My brain: Boat on blue ice

I love how in the slow mo shots it looks like Michael is just staring down the camera

It took me less than a second realising that Adam is the man who keep appearing in mythbusters jr.

teacher: what is the fastest to route to point A to point B everyone: a straight line Michel: a brachistochrone

Adam: “I’ve got some protractors here.” Michael: “oooo”

"I told Adam all of this, and I told him that it would be really fun to have a cycloid curve we could roll things down, and he said..." ~gets an ad for Manscaped~ "Have your balls thanked you yet?" yes this actually happened to me and it is indeed the funniest thing that happened to me all day

The fun that these guys were having brought me such joy.

Michael: Whats your favorite polygon Adam: *laughs hysterically*

This Brachistochrone should be a water slide

Vsauce is the only youtuber who can completely switch the subject in a matter of moments and still have it make complete sense.

"If you do it in software, it's perfect!" those words must have spoken a few times just before various planets exploded

9:05 is so wholesome “I got some protractors there” “Oh oooh” “You’ve got a compass extension” “I’ve got all sorts of things” “I feel so guilty this is a dream of mine come true”

Police: “You’re under arrest!” Vsauce: *Pulls out unicycle* “You know, cough drops make you cough more”

These videos are legit timeless

The sound of the knife on the acrylic made me physically recoil

"in theory, theory and practice are the same thing but in practice..." Is one of the best quotes I've ever heard

23:38 I love how Michael stares into our souls in the slow mo

I absolutely love how excited Adam gets about this idea

I love how the thumbnail is so simple yet so affective to tell everything about the video

1:34 When the music stars you know shit is getting real...

Michael stares into our eyes because it's the fastest way into our souls ; a brachistochrone

I love how frantically and excited Adam works.

What about a ring of 8.0003B people?

14:16 Micheal (sees his wife): eh See some acrylic: I L I K E T H O S E C U R V E S

Can't look at this guy the same way after watching him and idubbz

That was a treat to watch for so many reasons, thank you!

This should be a TV series. Great vid! 👍🏼

People forget that Michael's first channel was called "Pooplicker888". What a hero

people like adam savage who can make almost anything from scratch amaze me

"I just wanna curve to roll things down.." Me too, Michael. Me too..

15:24 Am I the only one who sees the main island of the Mandelbrot set there?