Rigging Newton's Method
Audience: high-schoolundergraduate
Tags: calculusnewtons-method
Newton's method is a powerful technique for approximating the roots of functions. But with a clever substitution we can construct functions where every value gets stuck in an endless cycle. Better yet, if you know integration you can find this function for yourself! This video is an entry to 3Blue1Brown's "Summer of Math Exposition #4". It is aimed at an early undergraduate audience, and was recorded in one take in the style of a live tutorial. This is also my first time making a maths video ... lots to learn :)
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I like this a lot as a follow up supplement to a lesson on Newton’s method. The idea of building your own weird example is fun and gives students something to think about while solidifying their knowledge of Newton’s method. Very fun and nicely produced. I think this is a novel approach to teaching newtons method and will be memorable for students.
I really liked this video. Great job with the subject and the implementation. Maybe the only downside might be “why someone should care” But when things are beautiful, you don’t need more incentives. Keep up the good work.
Really great.
I actually knew the Newton method a few years ago, but I’ve never thought of something like a cycle or a looped dance of points by applying Newton’s method. And that’s something unique in this video, which is represented at the beginning and proved in the end. The music also is a really great aspect and I believe the author arranged the music on purpose, though I don’t think the majority would find it related to Bach’s fugue or something, and just one note on each movement of point sound bad. There’re ways to improve, but overall impressive and inspiring.
The central result is surprising, and the proof is presented cleanly. But this video doesn’t give much intuition. It tells us the answer and walks through the calculations, but it doesn’t show where that answer comes from or how someone might come up with it.
Nice intro! Nice way to derivate the math too, combining handwriting with formal text. Cool example!
Really nicely done! Gives great intuition for newtons method and also integration. One thing I’m curious about is how one might find the function R(x) = 1 -1/x which satisfies R(R(R(x))) = x
Nice video, especially if it’s the first one !
0:15 sfx is distracting from the voicelines. Either make it quieter, the voice louder, (or get a better microphone).
0:36 Every one of the 3 points shown, or all points on the graph? Needs clarification that indeed this applies to all points, as later shown. Put some emphasis on this, it is impressive and should not sound like a random aside, it should be one of the guiding motivations/previews of the later video.
There’s a few retakes at words in the audio, for example 4:21. Just cutting these out would improve the flow notably
i really love the combination of animations and written presentation!