[HN Gopher] A new way to make quadratic equations easy
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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.
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