One of the Most Powerful Math Techniques No One Knows Who Invented It
Audience: high-schoolundergraduategraduate
As someone who teaches mathematics to college students (or sometimes high school students I know), I've always been wishing to share something students cannot easily find in the textbook so that they can use it for problem-solving and learn mathematics in more interesting way. I believe this is one of such things that (I am pretty sure) many high school students, college students, high school math teachers, or even college math professors will find interesting to learn. I haven't seen many people who know about this property - I exchanged an email with Grant, and hopefully he remembers this very interesting ratio property of a cubic function I shared with him via email. The goal for this video is to share a ratio property of a cubic function that is very easy to remember and use for a lot of math problems involving a cubic function but still not many people know of. I wish many people get to know this ratio property of a cubic function. According to my experience, it helped me a lot when solving a polynomial equation. So, why don't you check this out? This is a very cool technique I am pretty sure a lot of people would love to learn. Thanks a lot!
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Simple, straightforward, clean.
This is definitely the best submission I watched in SOME4. As a high school math teacher, I’ve never seen this, but I now can use this to teach my students very usefully. This fits perfectly to the goal of SOME4
This is such a cool property of cubic functions that I had no idea about. This video helped me understand the geometry of cubic functions so much better. I will definitely use this trick in my upcoming math endeavours. The motivation, novelty, and memorability of this video are all on point. I would suggest including a short segment, before the proof of the ratio property, where you show why all cubic functions that have both a local minimum and a local maximum technically fall under the form of (x-a)^2(x-b) + c. It is super important to talk about rigid transformations and dilations in this case to show that the ratio relationships shown do not change.
I only watched math videos as I am a high school math teacher. Content-wise, this one is the best. I skipped many videos looking at their thumbnails as I already knew them, and they were already well-known even in Youtube. But, looking at this video’s thumbnail, I was curious what it was about to give out, and watching the video, I found this very very interesting as I haven’t seen it before, but still, I believe people find it useful the most among all the pieces I watched in SOME#4. I also like the transition of the video, starting with the well-online-structured presentation and went on to the actual person showing an example in the classroom with the blackboard. I voted this the highest and the best.
Outstanding. Simple but much needed formula for high school students or even a lot of teachers. Excellent entry
Very useful, simple, easily grasping, and something I’ve never seen before. One of the best and most useful piece
This is the most excellent entry for the goal of 3Blue1Brown Some - something really new to people but highly useful for students and teachers at the same time. Easily followable. I give this the best
This video should be rated no.1. Clear and concise, to the point, and superb quality. Quality 10/10. Length 9/10. Easiness in understanding 10/10. Overall 10/10 PS. I really like classroom work at the end
Clear and concise explanation, complete with a simple to understand proof. Visuals were good too.
One or two more example problems to illustrate the range of applicability of this property would have made it even better.
One place where I struggled was understanding the example problem at the end. I understood how it was easy to get x=2 knowing this property, without having to calculate the derivative. And that was the point of the video. But from there, how do we get that minimum integer K=33 would give one positive and two complex roots? It could be trivial for students and teachers working on such problems but maybe a small intuitive explanation would help people like me.
It is a lovely idea that might be useful for a small subset of problems. The explanation is clear and the board-work is gorgeous. It doesn’t tackle a general topic, so it might not be something I show my students. However, this is important to me as I can learn from the way it is explained.
I learned this for the first time in my life - I believe I can teach this method to my students coming to tutoring center. What a lovely formula
This entry was perfect fit to the spirit of SoME#4 described in the website. Kudos to whoever made this. I will remember it and use it.
Such a well-made video. Yes, a beginner can definitely follow this exposition as it is easy to remember. Interestingly, I’ve taught cubic function quite a lot to my students, but never seen this before.
The analytical reasoning was developped to a better extent than the geometrical one (i.e. solving of the equation was done thoroughly, whereas the proof that B is at the internal division point of (2beta+alpha)/3 was just asserted). It’s a well packaged piece of knowledge and the addition of an example at the end is a real positive (pun intended). Thank you!
The best video!
This is an amazing one. I will definitely show this to my students. Can be used to a wide range of polynomials
As a former math teacher, I always find myself delighted when I got to know something really new. This video explains it very well with great visuals. I also like the transition to a classroom example as that was what Grant said as a purpose for SOME4. Something that is helpful for students in the classroom. This is that one.