The Brachistochrone

Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resources directly to growing science channels here on YouTube! https://www.curiositybox.com BRAIN CANDY LIVE: http://www.braincandylive.com Links to sources and to learn more below! MY TWITTER: http://www.twitter.com/tweetsauce MY INSTAGRAM: http://www.instagram.com/electricpants THE CURIOSITY BOX: https://www.curiositybox.com/ Stan Wagon “Roads and Wheels” [PDF]: http://web.mst.edu/~lmhall/Personal/RoadsWheels/RoadsWheels.pdf 3Blue1Brown video, “The Brachistochrone, with Steven Strogatz”: https://www.youtube.com/watch?v=Cld0p3a43fU Pile of people visualization originally from this Vsauce1 video: https://www.youtube.com/watch?v=C6eOcd06kdk Online spirograph: http://nathanfriend.io/inspirograph/ The Brachistochrone http://whistleralley.com/brachistochrone/brachistochrone.htm Rolling: http://www.animations.physics.unsw.edu.au//jw/rolling.htm http://teacher.pas.rochester.edu/phy121/LectureNotes/Chapter12/Chapter12.html Refraction of light: http://www.physicsclassroom.com/class/refrn/Lesson-1/Refraction-and-Sight http://www.funscience.in/study-zone/Physics/RefractionOfLight/AtmosphericRefraction.php http://www.walter-fendt.de/html5/phen/refractionhuygens_en.htm http://micro.magnet.fsu.edu/primer/java/particleorwave/refraction/ http://astro.unl.edu/classaction/animations/telescopes/snellslaw.html http://demonstrations.wolfram.com/FermatsPrincipleAndSnellsLaw/ Feynman on The Principle of Least Time: http://www.feynmanlectures.caltech.edu/I_26.html cycloid as answer to brachistochrone: https://sinews.siam.org/About-the-Author/quick-find-a-solution-to-the-brachistochrone-problem-1 Music from: https://www.youtube.com/jakechudnow and http://www.audionetwork.com Roulette animations by Eric Langlay https://www.youtube.com/c/ericlanglay good relevant Wikipedia articles: https://en.wikipedia.org/wiki/Brachistochrone_curve https://en.wikipedia.org/wiki/Tautochrone_curve https://goo.gl/SlRDhK https://en.wikipedia.org/wiki/Cycloid https://en.wikipedia.org/wiki/Snell's_law Wolfram demonstration projects used: "Cycloid Curves" from the Wolfram Demonstrations Project  http://demonstrations.wolfram.com/CycloidCurves/ 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  http://demonstrations.wolfram.com/ShapingARoadAndFindingTheCorrespondingWheel/ Contributed by: Stan Wagon (Macalester College)