The Brachistochrone ─ Vsauce

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/R...

3Blue1Brown video, “The Brachistochrone, with Steven Strogatz”: https://www.youtube.com/watch?v=Cld0p...

Pile of people visualization originally from this Vsauce1 video: https://www.youtube.com/watch?v=C6eOc...

Online spirograph: http://nathanfriend.io/inspirograph/

The Brachistochrone http://whistleralley.com/brachistochr...

Rolling:
http://www.animations.physics.unsw.ed...
http://teacher.pas.rochester.edu/phy1...

Refraction of light:
http://www.physicsclassroom.com/class...
http://www.funscience.in/study-zone/P...
http://www.walter-fendt.de/html5/phen...
http://micro.magnet.fsu.edu/primer/ja...
http://astro.unl.edu/classaction/anim...
http://demonstrations.wolfram.com/Fer...

Feynman on The Principle of Least Time: http://www.feynmanlectures.caltech.ed...

cycloid as answer to brachistochrone: https://sinews.siam.org/About-the-Aut...

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/Brachis...
https://en.wikipedia.org/wiki/Tautoch...
https://en.wikipedia.org/wiki/Roulett...)
https://en.wikipedia.org/wiki/Cycloid
https://en.wikipedia.org/wiki/Snell's...

Wolfram demonstration projects used:

"Cycloid Curves" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/Cyc...
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/Sha...
Contributed by: Stan Wagon (Macalester College)