Vladimir Arnold’s Rainbow Is a Masterclass in Simplification

(Submitted to #SoMe5 #3blue1brown) What's prettier, rainbows or math? Good news, you don't have to choose! In this video, following many cues from Vladimir Arnold's book Mathematical Understanding of Nature, I attempt to explain the rainbow in a self-contained way, without assuming any calculus or trigonometry. Arnold's approach is remarkably simple. Accessible to anyone with a bit of patience, really. Yet it can explain many of the complexities of the rainbow. In this video, we explain why the rainbow always appears at the same angle, why that particular angle, and why it appears to be lit from below but dark from above. If you persevere, there's also an Easter Egg at the end. Chapters: 0:00 (Vladimir Arnold) 1:25 (Mathematical Understanding of Nature) 3:43 (Our Story Begins on the Beach) 5:00 (Fermat's Principle) 6:52 (The Dragon) 7:34 (As a Minimization Problem) 10:55 (Thinking in Angles) 14:50 (Linear Approximation) 17:40 (Snell's Law) 19:05 (Proof of Snell's Law) 22:37 (The Rainbow Pt. 1: Reflection) 25:58 (The Rainbow Pt. 2: Diffraction) 28:10 (The Rainbow Pt. 3: Analysis) 33:13 (Somewhere Under the Rainbow) 34:24 (Thank You for Watching My Video) 36:12 (???) Attributions: Rainbow photo by ניר בן רש"י Pikiwiki Israel, CC BY 2.5, https://commons.wikimedia.org/w/index... Rainbow photo by Rhododendrites - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index... Rainbow photo by Johannes Bahrdt - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index... Prism work by Kelvinsong - Own work, CC0, https://commons.wikimedia.org/w/index...