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Using Circles and Origami to Solve Equations | Lill's Method #SoME4

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Tags: geometrypolynomials

This video explores Lill's method, a forgotten visual method to solve polynomials. Instead of crunching formulas, the method involves geometry, sketching lines and circles, and even using origami to arrive at the solution. The video starts off with a general explanation of the method, followed by a proof, and also shows links to Thales' theorem for circles when solving quadratic equations. We then move onto a beautiful geometric method for deriving even the complex roots of quadratics, using a mixture of lines and circles, before doing a similar method for cubic equations. The method for cubics also involves some origami techniques, folding paper in a particular way to arrive at the solutions of the polynomial.

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6.17 Overall score*

71 Rank

12 Votes

8 Comments

Comments

6.6

This is a highly unusual technique that I had never heard of. The concept and the examples were well chosen but the visuals were extremely repetitive. It wold have been much more interesting to see how this could be done on paper or with actual origami. The voiceover became very plummy half way through. It’s unclear how useful this would be in the classroom because the technique is unorthodox it would not be immediately useful. It would be an interesting challenge lesson to ask students to find a way to draw a reflected line to hit the point, before giving them the origami idea. Overall it is a very interesting topic but the visuals and presentation are a little flat.

The results are interesting and surprising, and the explanation is perfectly clear. I would have liked to see the proof for the complex solutions, but otherwise it’s an excellent video.

6.9

Well done video. I admit that I don’t fully understand the math (yet), because this branch of math isn’t my strength. But after watching the video I definitely better understand why it’s important and how it can be used.

Connecting math to other topics like e.g. origami is always something I like to see. Math on its own can sometimes be a bit dry, so anything that makes it a bit more spicy is helpful.

3.3

The voiceover is a bit unnatural (text-to-speech?), and has some odd pauses/pacing. The animations were quite good and the explanation is not bad, though I would have liked to see proofs of the cases in the later half of the video.

I learned the technique presented here from the ‘Mathologer’ channel. If I had encountered it for the first time in this video, I would have struggled to understand it, especially due to the lack of engaging elements (AI voice in annoying). I don’t think this approach is stimulating for high-school students. You are very good with animations, but try to make your content more practical and include examples from everyday life.

5.1

I didn’t know about Lill’s method at all so the material was novel.

7.7

Amazing visual and an interesting topic. I didn’t know about this method. I think it got a bit too contrived at the complex roots construction because it wasn’t clear what is the point of everything we are doing.

The AI voiceover makes it sound bad and uninteresting however.

I expected more of the origami part in the title. It was actually just one fold.

Great visualisation. Thank you.