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## The Brachistochrone - VideoRolls.com

## By: Vsauce**Published: **2 years ago

273, 711 Likes 3, 098 Dislikes

BRAIN CANDY LIVE TICKETS: http://www.braincandylive.com/tickets

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://tune9.net/watch/Cld0p3a43fU

Pile of people visualization originally from this Vsauce1 video: https://tune9.net/watch/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://tune9.net/watch/jakechudnow

and

http://www.audionetwork.com

Roulette animations by Eric Langlay https://tune9.net/watch/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)