[HN Gopher] A new way to make quadratic equations easy ___________________________________________________________________ A new way to make quadratic equations easy Author : jbredeche Score : 36 points Date : 2021-11-25 15:31 UTC (2 days ago) (HTM) web link (www.technologyreview.com) (TXT) w3m dump (www.technologyreview.com) | Supposedly wrote: | I'm surprised that people consider this worthy of begin published | on a semi-serious blog post https://www.poshenloh.com/quadratic/ | . | CyberRabbi wrote: | "Completing the square" may seem like an arbitrary and hard to | remember math trick but it is the algebraic analogue of something | that is very intuitive in geometry. The Greeks solved quadratic | equations by visually completing the square. | saulrh wrote: | The B/2 term places the center of the parabola, which you can | verify by either inspecting the derivative or fiddling with a | graphing calculator. Then, because the parabola is symmetric, the | zeros must be a pair of points mirrored across the center, with | the distance from the center determined by the vertical offset | (the C term) versus the narrowness (the A term). Which I | definitely agree is an easier way to deal with the problem! But I | think that, if you're going to do it that way, it might be easier | to work from geometric intuition instead of an algebra trick that | represents but obscures the same relationship. | finite_jest wrote: | I don't think this is new at all. This looks like just a standard | proof of the quadratic formula. | | I believe most people probably have seen a variation of this in | high school. Depending on your preferences, this might be a | slightly better or worse presentation than what you have seen | before. | | The fact that they couldn't (or haven't) publish it in a journal | also supports this. [1]. (The ArXiv pre-print [2] is dated | December 16, 2019) | | [1]: | https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=%22A... | | [2]: https://arxiv.org/pdf/1910.06709.pdf | jimhefferon wrote: | I think there is a different standard way in Europe, compared | with the US. Dunno about other places. | cperciva wrote: | Leaving aside the fact that this isn't new -- it's how I was | taught to solve quadratic equations in the 80s -- if you look | closely he's still completing the square. | finite_jest wrote: | Surprisingly, the article seems to be written by a smart | mathematician, not a crackpot or a social scientist. [1] | | This kinda reminds me of that medical researcher who | rediscovered trapezoid rule in 1994, and called it "Tai's | Mode". [2] | | To be fair, this is slightly better as it is supposed to be | pedagogical, but it is still quite dishonest to pretend that it | is new. | | [1]: https://en.wikipedia.org/wiki/Po-Shen_Loh | | [2]: https://fliptomato.wordpress.com/2007/03/19/medical- | research... (It's 459 citations now according to Google | Scholar, btw :-)) | coyotespike wrote: | I learned this technique while reviewing high school math to take | the GRE, and really enjoyed it. I find it elegant and easier to | derive than the usual formula - I prefer not to memorize | equations. And with just a little practice, it was easy to work | through manually on my whiteboard (no scratch paper allowed). | | Of course it is not some big discovery in fundamental knowledge - | but it is a helpful pedagogical advance and I am happy Po-Shen | Loh has advertised it. | [deleted] | codeflo wrote: | I just hand-derived it both ways to make a comparison, the | standard way was from memory. | | So. The standard way to complete the square uses a trick to | rearrange the equation so that one can use the formula (a+b)^2 = | a^2 + 2ab + b^2. | | This uses a different trick to rearrange the equation to make use | of (a+b)(a-b) = a^2 - b^2. | | Frankly, I don't see how this is any easier. If anything, I think | it's harder to do from memory because you need to introduce a new | variable in a very specific way to make the simplification work. | The standard way feels a lot more systematic. | jiggawatts wrote: | Three pop-ups or overlays when attempting to read the article. | | If this is the new standard for the web, I want to get off the | ride. | jstx1 wrote: | This is neither new, nor easier. It can be interesting to think | about and deriving the same results through different methods can | help with understanding. But I really doubt that there will be | any students who can understand and use this who at the same | would struggle with the regular formula for the quadratic. | KolenCh wrote: | It is 2019-new https://arxiv.org/abs/1910.06709 | rackjack wrote: | Should have (2019) in the title, I think | threatofrain wrote: | This is a modestly interesting simplification, but I think it's | notable that they are dealing with _monic_ quadratics. | prof-dr-ir wrote: | From 2019. | | And, dare I say it, still a waste of time. In my not-so-humble | opinion you either know enough algebra to understand that, for | non-zero a, 0 = a x^2 + b x + c <=> 0 = x^2 + b/a x + c/a <=> 0 = | (x + b/2a)^2 - b^2/4a^2 + c/a <=> (x + b/2a)^2 = (b^2 - 4 a c) / | 4a^2 or you need to improve your basic algebra skills - not | search for a better derivation of this particular formula. | sedeki wrote: | The result is called "the PQ-formula" in Swedish and is taught in | schools. ___________________________________________________________________ (page generated 2021-11-27 23:00 UTC)