The Brachistochrone, with Steven Strogatz

Steven Strogatz and I talk about a famous historical math problem, a clever solution, and a modern twist.

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).

Various social media stuffs:

[fenhirbr]

About your challenge... I do not love to be dunned and teased by foreigners.

[car-keys]

Just wanna say that all your videos are beautiful, well edited and animated, insightful, and a joy to watch. Thanks for the awesome content, 3Blue1Brown.

[MindYourDecisions]

Really neat! I wish I had this video when I took physics to learn the connections between different concepts.

[MegaAproductions]

I rarely ever comment on YouTube, but I wanted to say that your content is amazing and most importantly thought provoking!
Keep up the good work and thank you for the time you put into your videos!

[RexGalilae]

i have an excellent proof for this but this comment section is too small to contain it

[Larzsolice]

Do you challenge me because you think you've got an unusually clever solution, or because you think I'm Newton?

[Avose]

This channel has a superb standard of videos and never fails to present new insights into old problems. Thanks for all the effort!

[DweebsUnited]

The animation at 4:39 ~ish using a space filling curve is magnificent, and for such a one off display is magnificent

[Harinichandrasekaran-qgnt]

When I learn about Brachistochrone problem, I was very surprised and excited that this small question makes a whole new concept "Calculus of Variation." But this video takes me to next level of excitement. Really thought provoking and interesting.

[isaackay]

Holy crap, Strogatz! You mean the author of the book I loved in undergrad, Nonlinear Dynamics & Chaos! Loved my Dynamical Systems class in undergrad, but damn...it was a beast! Much much much respect for these mathematicians who pioneer the way in these fields, but even more so for those who can beautifully, eloquently, and effectively communicate these advanced concepts in math to plebeians like myself; such is the man you interviewed here: Steven H. Strogatz.

[theghostmachine]

Makes me feel special that I was subscribed to you before Vsauce. And I love that more people are tuning in, you need more exposure, your videos are simply the best math videos on the net.

[小刚-bj]

I find the final chanllage is actually solved in this video. stop the video at 12:34, note the velocity of piont P = √(2gy)(obtained at 8:00), so the angular velocity of P rotate around C is just √(2gy)/(D Sin(θ)) = √(2g/D). thus the curves in t-θ plane is always stright lines with slope √(2g/D).
besides, note θ=1/2 ∠POC (let O be the center of circle), so "P rotate around C with constant angular velocity" is equivalent with "P rotate around O with constant angular velocity", so the wheel rotate with constant rate.

[kennethgoodall]

This is amazing, honestly keep it up I need more insight into certain math problems and the history that surrounds them

[brikken]

I was really in doubt about this interview concept when you first presented it, but after just 30 seconds with talking and animation in perfect unison, I was convinced. Great job!

[c.j.awesome]

easily one of the coolest math ch. vocal, video quality, use of math language... everything real nice

[jesseacummins]

Glad you're posting more videos. These are some of the most beautiful on YouTube.

[pacolibre]

8 years later, and that challenge is still on my mind. Not solution, but it got me thinking about all sorts of other variations on the problem for different force terms.

[SliversRebuilt]

You're insanely intelligent, and an inspiration to me. I'm going to try this.

If there's one thing I think I've learned from your videos, it's that nothing consistent is off-limits and there is always a different reference frame from which to view your problem.

[chetan]

Strogatz, the chaos man. His Nonlinear Dynamics lectures made life much easier for me.

[formerlypie]

I must say, I love this channel, you are almost souly responsible for kindling my love of math, thank you