The Brachistochrone

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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)