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Links to sources and to learn more below!
MY TWITTER: www.twitter.com/tweetsauce
MY INSTAGRAM: www.instagram.com/electricpants
THE CURIOSITY BOX: www.curiositybox.com/

Stan Wagon “Roads and Wheels” [PDF]: web.mst.edu/~lmhall/Personal/RoadsWheels/RoadsWheels.pdf

3Blue1Brown video, “The Brachistochrone, with Steven Strogatz”: www.youtube.com/watch?v=Cld0p3a43fU

Pile of people visualization originally from this Vsauce1 video: www.youtube.com/watch?v=C6eOcd06kdk

Online spirograph: nathanfriend.io/inspirograph/

The Brachistochrone whistleralley.com/brachistochrone/brachistochrone.htm

Rolling:
www.animations.physics.unsw.edu.au//jw/rolling.htm
teacher.pas.rochester.edu/phy121/LectureNotes/Chapter12/Chapter12.html

Refraction of light:
www.physicsclassroom.com/class/refrn/Lesson-1/Refraction-and-Sight
www.funscience.in/study-zone/Physics/RefractionOfLight/AtmosphericRefraction.php
www.walter-fendt.de/html5/phen/refractionhuygens_en.htm
micro.magnet.fsu.edu/primer/java/particleorwave/refraction/
astro.unl.edu/classaction/animations/telescopes/snellslaw.html
demonstrations.wolfram.com/FermatsPrincipleAndSnellsLaw/

Feynman on The Principle of Least Time: www.feynmanlectures.caltech.edu/I_26.html

cycloid as answer to brachistochrone: sinews.siam.org/About-the-Author/quick-find-a-solution-to-the-brachistochrone-problem-1

Music from:
www.youtube.com/jakechudnow
and
www.audionetwork.com

Roulette animations by Eric Langlay www.youtube.com/c/ericlanglay

good relevant Wikipedia articles:

en.wikipedia.org/wiki/Brachistochrone_curve
en.wikipedia.org/wiki/Tautochrone_curve
goo.gl/SlRDhK
en.wikipedia.org/wiki/Cycloid
en.wikipedia.org/wiki/Snells_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)