The Brachistochrone

  • Published: 21 January 2017
    Links to sources and to learn more below!
    Stan Wagon “Roads and Wheels” [PDF]:
    3Blue1Brown video, “The Brachistochrone, with Steven Strogatz”:فيديو.html
    Pile of people visualization originally from this Vsauce1 video:فيديو.html
    Online spirograph:
    The Brachistochrone
    Refraction of light:
    Feynman on The Principle of Least Time:
    cycloid as answer to brachistochrone:
    Music from:
    Roulette animations by Eric Langlay
    good relevant Wikipedia articles:'s_law
    Wolfram demonstration projects used:
    "Cycloid Curves" from the Wolfram Demonstrations Project
    Contributed by: Sean Madsen
    Additional contributions by: David von Seggern (U. Nevada, Reno)
    "Shaping a Road and Finding the Corresponding Wheel" from the Wolfram Demonstrations Project
    Contributed by: Stan Wagon (Macalester College)

Comments • 24 606

  • Syazaki Namura
    Syazaki Namura  15 ساعات قبل

    17:58 this is how you go faster in apex legend lol

    • Thanos
      Thanos  22 ساعات قبل


      • 506 independent VIDEO
        506 independent VIDEO  أيام قبل

        this is the amount of times he said the letter a 857 ^ | | |

        • Observ45er
          Observ45er  أيام قبل

          Question: What happens when the rolling cylinders have no/low rotational inertia.?.

          • Observ45er
            Observ45er  أيام قبل

            I'da put a pivot in the center of the circle on the band saw... no sanding.

            • Omega
              Omega  أيام قبل

              They teach these in GATEWAYS 2019 maths

              • Lancelot Xavier
                Lancelot Xavier  أيام قبل

                Less face more diagrams.

                • Guy Warner
                  Guy Warner  2 أيام قبل

                  Is a cycloid half of an ellipsis?

                  • Mabitent
                    Mabitent  2 أيام قبل

                    23:38 - Vsauce’s face XD

                    • gaming with a gamer
                      gaming with a gamer  3 أيام قبل

                      I like to use long words that I don't understand to make myself look more photosynthesis

                      • milo hook fish
                        milo hook fish  3 أيام قبل

                        Me: what's the fastest fastest route to school Micheal: hold up let me conceptualized the entirety of the universe for a sec.

                        • Tristan Harris
                          Tristan Harris  4 أيام قبل

                          25:34 when you step on a lego brick

                          • Caleb Gonsalves
                            Caleb Gonsalves  4 أيام قبل

                            tldr. Vsauce manipulates Adam to do his bidding and looks in your soul....

                            • Jay S
                              Jay S  4 أيام قبل

                              I want to build one too lol- unless someone’s got one i can buy?

                              • Sia SHETH [13F]
                                Sia SHETH [13F]  4 أيام قبل

                                Since there is only a gravitational force acting downwards, wouldn't the ball simply fall down? Assuming we don't have the curve ready before we investigate, what would be the horizontal force acting on the ball to make it take the shortest time path? (I need this to find a numerical way of solving the Brachistochrone problem with computer simulation - Excel - for my Math report) Any help would be appreciated!

                                • Bharat Kumar Gupta
                                  Bharat Kumar Gupta  5 أيام قبل


                                  • erik cyree
                                    erik cyree  5 أيام قبل

                                    are you vsauce or are we vsauce or is it only me who is vsauce?

                                    • Sam Garifalos
                                      Sam Garifalos  5 أيام قبل

                                      How do I calculate the radius of the circle when given two defined points?

                                      • Ant Hony
                                        Ant Hony  6 أيام قبل

                                        Dragged that out a bit

                                        • Abby Nicole
                                          Abby Nicole  6 أيام قبل

                                          It would be fun to slide down a brachistochrone curve next to the other lines at a park and experience it yourself

                                          • Holden Oddo
                                            Holden Oddo  6 أيام قبل

                                            your also really good at math

                                            • Dragon Fox
                                              Dragon Fox  6 أيام قبل

                                              It’s just beautiful to see two fully grown men obsessing over a circle that falls and it makes all the pains and sadness go away temporarily

                                              • AwesomePow
                                                AwesomePow  7 أيام قبل

                                                17:25 .25 speed. You're welcome. Edit: The whole video is almost as good too.

                                                • Boe Johnson
                                                  Boe Johnson  7 أيام قبل

                                                  This is gold

                                                  • Mudkip
                                                    Mudkip  7 أيام قبل

                                                    OMG THE OCTOPUS IS SO CUTE I NEED IT!!!!!

                                                    • Шоломицкий Артём
                                                      Шоломицкий Артём  8 أيام قبل

                                                      23:41 what's the name of music ?

                                                      • Kaera猫
                                                        Kaera猫  8 أيام قبل

                                                        What is this, a crossover episode?

                                                        • Dan Frederiksen
                                                          Dan Frederiksen  9 أيام قبل

                                                          Not to be a spoil sport, ok maybe a little, bit the spin of the roller might change the fastest curve a bit away from the cycloid.

                                                          • Chiara J
                                                            Chiara J  9 أيام قبل

                                                            Are we not going to talk about how Michael is just staring into the camera 23:39

                                                            • raz or
                                                              raz or  6 أيام قبل

                                                              song name?

                                                              • R.I.P Peep
                                                                R.I.P Peep  9 أيام قبل

                                                                But what is... *raises eyebrow* rolling?

                                                                • ALL THINGS TO ALL MEN
                                                                  ALL THINGS TO ALL MEN  9 أيام قبل

                                                                  This video earned you a new sub...very entertaining and informative!

                                                                  • nora :D
                                                                    nora :D  9 أيام قبل

                                                                    Someone make a water park race ride inspired by this

                                                                    • Ben Perfetto
                                                                      Ben Perfetto  9 أيام قبل

                                                                      “How did they get this paper to stick on the plexiglass?” Asking questions leads to higher intelligence. That’s why this guy is so smart.

                                                                      • Nova RL
                                                                        Nova RL  9 أيام قبل

                                                                        This is how those pesky criminals outrun the cops. 🤔

                                                                        • Joshua Rogers
                                                                          Joshua Rogers  11 أيام قبل

                                                                          Ok am i the only one who noticed the mandelbrot bulb at 15:17?

                                                                          • Joshua Rogers
                                                                            Joshua Rogers  11 أيام قبل

                                                                            Michael: 14:55 There is a special name for epitrochoids and hypotrochoids traced by points on circumferences, analogous to disks rolling on straight lines, they are called- Me: Flowers.

                                                                            • ALE C.
                                                                              ALE C.  11 أيام قبل

                                                                              7326666666.67 in the cone of humans

                                                                              • Anne Reilley
                                                                                Anne Reilley  11 أيام قبل

                                                                                Must be nice for them to be with someone that they don't have to dumb things down for.

                                                                                • 413X V4N D3 KU!13N
                                                                                  413X V4N D3 KU!13N  12 أيام قبل

                                                                                  Is that rule still in effect if point B is 30cm to the right of point A and only 1cm lower than point A, or wouldn’t it work in real life due to friction? I would love to see that in real life.

                                                                                  • ryuzakilawlight
                                                                                    ryuzakilawlight  12 أيام قبل

                                                                                    Sorry this isn't brian candy it's confusing the shit out of me. If light always follows snell's law.. how DOES it do it.. how DOES light know which path EXACTLy to take.. it's not sentient so what gives????????????????

                                                                                    • Messi Best
                                                                                      Messi Best  13 أيام قبل

                                                                                      0:01 Is This How You Science?

                                                                                      • Tarek Hedar
                                                                                        Tarek Hedar  13 أيام قبل

                                                                                        At 18:00 you can see that the disks was faster than Michels eyes ;)

                                                                                        • Miguel La Baguette
                                                                                          Miguel La Baguette  13 أيام قبل

                                                                                          1:35 ah.. that music... it gets me every time 😂

                                                                                          • Thor
                                                                                            Thor  14 أيام قبل

                                                                                            What would be the fastest with no gravity

                                                                                            • William Hough
                                                                                              William Hough  14 أيام قبل

                                                                                              If all of humanity held hands across the equator Most of us would drown

                                                                                              • Gonzalo! Hi
                                                                                                Gonzalo! Hi  15 أيام قبل

                                                                                                Does vsauce love classrooms with protractors

                                                                                                • Gonzalo! Hi
                                                                                                  Gonzalo! Hi  15 أيام قبل

                                                                                                  Actually this wouldn’t happen he doesn’t specialize in law

                                                                                                  • Audrey Chavarin
                                                                                                    Audrey Chavarin  16 أيام قبل

                                                                                                    Micheal is the kinda guy to question the existence of God and come up with a definite answer

                                                                                                    • Piyush Lovanshi
                                                                                                      Piyush Lovanshi  16 أيام قبل

                                                                                                      What does VSAUCE means, virtual sauce???

                                                                                                      • Fox Tear
                                                                                                        Fox Tear  16 أيام قبل

                                                                                                        When the brachfhhkx curve is 100 billion kilometres high and you let this disk fall, will it reach near light speed?

                                                                                                        • Itsgilbert
                                                                                                          Itsgilbert  16 أيام قبل

                                                                                                          Wait, so then is a 400m track a brachistichrone with the stagger in a race?

                                                                                                          • Ali-A
                                                                                                            Ali-A  17 أيام قبل

                                                                                                            September 20th: we gonna storm Area 51 Micheal: or do we? [music starts playing]

                                                                                                            • Sir Bennyboi
                                                                                                              Sir Bennyboi  17 أيام قبل

                                                                                                              Whats is rolling? *vsauce music plays*

                                                                                                              • Nini T.
                                                                                                                Nini T.  17 أيام قبل

                                                                                                                Now I know what to do if I am in the mud and have to run to a ball in the middle of the asphalt! I feel so relieved 😅

                                                                                                                • Koopa #56
                                                                                                                  Koopa #56  17 أيام قبل

                                                                                                                  One of those slomos Micheal was staring right at the camera ...... 🤨

                                                                                                                  • Kannao
                                                                                                                    Kannao  17 أيام قبل

                                                                                                                    How To Basic

                                                                                                                    • Andrew Gotts
                                                                                                                      Andrew Gotts  18 أيام قبل

                                                                                                                      One small problem. With the three curves the release mechanism lets the verticle one go first and straight line last. I think you can see the vertical one starts a moment before the other ones. Slightly fudged results.

                                                                                                                      • Ahmad Mesto
                                                                                                                        Ahmad Mesto  18 أيام قبل

                                                                                                                        2:23 I finally learnt how to ride my bicycle

                                                                                                                        • Elijah Atchley
                                                                                                                          Elijah Atchley  19 أيام قبل

                                                                                                                          I wonder if you make a large enough one, where terminal velocity comes into play, the cycloid still wins? The cycloid will reach terminal velocity first but has longer to go....

                                                                                                                          • 21131 91125
                                                                                                                            21131 91125  20 أيام قبل

                                                                                                                            They should make this a toy. It would be so cool and I’d probably buy one.

                                                                                                                            • battousai9795
                                                                                                                              battousai9795  20 أيام قبل

                                                                                                                              You could totally make more of those and sell them !

                                                                                                                              • Connor Mc 519
                                                                                                                                Connor Mc 519  20 أيام قبل

                                                                                                                                Walks into house DO YOU HAVE A POLYGON

                                                                                                                                • Tomas Arseneault
                                                                                                                                  Tomas Arseneault  20 أيام قبل

                                                                                                                                  This guy is 10 times my age and thinks a billion times faster it was harder to follow his test (not talking about micheal)

                                                                                                                                  • trentong1113
                                                                                                                                    trentong1113  20 أيام قبل

                                                                                                                                    How do you know how large the radius of the circle youre tracing should be?

                                                                                                                                    • Switchy Box
                                                                                                                                      Switchy Box  21 أيام قبل

                                                                                                                                      "Where are your feet?"

                                                                                                                                      • Christopher Martin
                                                                                                                                        Christopher Martin  21 أيام قبل

                                                                                                                                        I am from Osceola Mo

                                                                                                                                        • Logan
                                                                                                                                          Logan  21 أيام قبل

                                                                                                                                          I had no idea what they were building, almost the entire time

                                                                                                                                          • Van Frankenstein
                                                                                                                                            Van Frankenstein  21 أيام قبل

                                                                                                                                            Fun watching you nerds! :P

                                                                                                                                            • Will Kleespies
                                                                                                                                              Will Kleespies  22 أيام قبل

                                                                                                                                              If you notice, most videos have 10% of people that dislike the videos compared to the people that liked them. Vsauce has 1% people putting a thumbs down compared to thumbs up...Those are the Troglodytes that don't understand and are haters. I love the videos thanks for the cool content!!!!

                                                                                                                                              • ANormalSmile 23237
                                                                                                                                                ANormalSmile 23237  22 أيام قبل

                                                                                                                                                This is also a video for people with OCD

                                                                                                                                                • Shilonious Monk
                                                                                                                                                  Shilonious Monk  22 أيام قبل

                                                                                                                                                  Worst channel on YT

                                                                                                                                                  • Randomness
                                                                                                                                                    Randomness  22 أيام قبل

                                                                                                                                                    A what

                                                                                                                                                    • someonedifferent YT
                                                                                                                                                      someonedifferent YT  22 أيام قبل

                                                                                                                                                      I did it What did it take 3 plexiglass and 5 years of knowledge

                                                                                                                                                      • TheDeltaW Gaming
                                                                                                                                                        TheDeltaW Gaming  22 أيام قبل

                                                                                                                                                        Micheal was so proud of his Cir-cool pun.

                                                                                                                                                        • Wally Meerschaert
                                                                                                                                                          Wally Meerschaert  23 أيام قبل

                                                                                                                                                          It's a pendulum! It also shows how a boat tacks.