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posted by Fnord666 on Monday July 06 2020, @03:09PM   Printer-friendly
from the math-simplified dept.

Math Genius Has Come Up With a Wildly Simple New Way to Solve Quadratic Equations:

If you studied algebra in high school (or you're learning it right now), there's a good chance you're familiar with the quadratic formula. If not, it's possible you repressed it.

By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University, there's actually been an easier and better way all along, although it's remained almost entirely hidden for thousands of years.

In a 2019 research paper, Loh celebrates the quadratic formula as a "remarkable triumph of early mathematicians" dating back to the beginnings of the Old Babylonian Period around 2000 BCE, but also freely acknowledges some of its ancient shortcomings.

"It is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorise," Loh writes.

[...] We still don't know how this escaped wider notice for millennia, but if Loh's instincts are right, maths textbooks could be on the verge of a historic rewriting - and we don't take textbook-changing discoveries lightly.

"I wanted to share it as widely as possible with the world," Loh says, "because it can demystify a complicated part of maths that makes many people feel that maybe maths is not for them."

The research paper is available at pre-print website arXiv.org, and you can read Po-Shen Loh's generalised explanation of the simple proof here.


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  • (Score: 4, Insightful) by VLM on Monday July 06 2020, @05:55PM (7 children)

    by VLM (445) Subscriber Badge on Monday July 06 2020, @05:55PM (#1017196)

    By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations

    I was put in the pipeline for smart kids where we skipped a grade of math and took college calculus as seniors, of the 50 of us about 20 made it thru in my year, and we had to derive the quadratic eqn not just apply or memorize it, and frankly it wasn't THAT hard, it was relatively lightweight and had few surprises, whereas this alternative looks worse with the WTF virtual z factor getting tossed in.

    I'm not saying its necessarily a bad idea, but it is more complicated to learn to derive than the original quadratic eqn.

    I'm not sure its useful to teach zero finding as a skill in and of itself as I've never needed the zeros of a quadratic in practice whenever I've needed a zero its something hideous so wolfram alpha or mathematica or some numerical method or whatever other option. So given that zero finding of quadratics is NOT, and probably never was, a practical vocational skill, the only point in learning the q-eqn is to learn how to think, and I think the classic q-eqn fits in better with the curriculum than the new eqn. I suppose they could just move the new eqn to a better location in the overall math education process and then it would be fine, but the kids would miss out on the nifty learning experience of the q-eqn.

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  • (Score: 2) by JoeMerchant on Monday July 06 2020, @07:39PM

    by JoeMerchant (3937) on Monday July 06 2020, @07:39PM (#1017260)

    I'm not saying its necessarily a bad idea, but it is more complicated to learn to derive than the original quadratic eqn.

    To me, he's just taking the one-step classical quadratic equation and breaking it up into two - perhaps simpler to execute - steps. It's harder to derive, perhaps simpler to execute, maybe gives a little more insight into what's happening with the parabola graph than the straight single equation does.

    I'd also swear I've seen this before, maybe he tweaked it a little, but the presentation with B/2 +/- U gives me a lot of deja-vu'

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  • (Score: 2, Interesting) by Anonymous Coward on Monday July 06 2020, @07:54PM (1 child)

    by Anonymous Coward on Monday July 06 2020, @07:54PM (#1017269)

    I've come to the opinion that success as a student is partly determined by raw talent but partly determined by how well your teachers can communicate in a way that's meaningful to you. My dad had his bachelor's degree in math, and in one on one discussions at home he could explain clearly. I breezed through math in school. My classmates who only had the mediocre teachers and their own parents who couldn't explain the material as well struggled. I didn't have more talent, I was just lucky.

    I'm not sure I can judge the educational value of this formula fairly, I learned the standard one decades ago. I would want a fresh set of eyes on the problem - not mine (someone biased towards the status quo just because it's familiar), and not the person who proposed using this one either (someone who at least appears to be biased in favor of doing something different just for its own sake).

    I also agree that teaching these skills in school may not be that useful. I've heard the argument, "If you can learn advanced math, you can learn anything". But school should be about more than drilling facts into a kid's skull, it should be about teaching critical thinking and fostering a life long interest in learning. There have got to be more engaging things to learn, in and out of mathematics.

    • (Score: 2) by VLM on Tuesday July 07 2020, @02:56PM

      by VLM (445) Subscriber Badge on Tuesday July 07 2020, @02:56PM (#1017673)

      My classmates who only had the mediocre teachers

      Its worth pointing out that my wife could handle math so she did STEM degree so I eventually met her at a STEM employer and eventually married etc. Meanwhile my SiL couldn't handle math, so she went for a K12 educator degree instead of STEM, and she's been teaching math to the next generation of STEM students for more than a quarter century. So the sister who knows math designs and implements the call center queuing statistical analysis formulas in your PBX firmware, but doesn't teach anyone math, whereas the sister who couldn't learn math is teaching math. Hmm.

      Given the extreme income disparity between something like a BSEd vs BSCS or BSEE, I would think anyone who can pass calculus is almost certainly not teaching kids math, which in the long term would seem to be a problem for the next generation of calculus learners.

      I'm not sure if its good or bad news that the district curriculum is so detailed and specific that she's practically reading prepared materials to the kids or showing approved multimedia all day rather than actually teaching in the traditional sense of 1 on 1 learning. In a similar sense I don't know anything about playing Rugby, but given an authoritarian micromanaged enough school district curriculum I could "teach" rugby by word for word reading of the school district issued mandatory rugby textbook, and accidentally some kids might learn rugby from "me" in the sense that they heard me create a live audiobook presentation of the textbook they probably wouldn't read on their own without me crack'n the whip on them.

  • (Score: 0) by Ethanol-fueled on Tuesday July 07 2020, @02:02AM (2 children)

    by Ethanol-fueled (2792) on Tuesday July 07 2020, @02:02AM (#1017461) Homepage

    Working with zero crossing (and hell, any threshold crossing) is everywhere in electronics. Sure, you can MATLAB it all away, but it helps to have a more intuitive understanding of the underlying math mechanisms.

    But that's why that level of education is shit in America. The worst travesty of lower-level American education is that basic vectors are taught separately from complex numbers and when complex numbers are first taught there are no real-world applications taught with them. So students before the internet had their "what the fuck is this used for"-isms for complex numbers just like you had with root-finding in general.

    • (Score: 0) by Anonymous Coward on Tuesday July 07 2020, @02:23AM

      by Anonymous Coward on Tuesday July 07 2020, @02:23AM (#1017468)

      If only they would start with the axioms of set theory and get straight onto tensor calculus then we could derive the math test and solve it before it was even written. Bastards.

    • (Score: 2) by VLM on Tuesday July 07 2020, @02:43PM

      by VLM (445) Subscriber Badge on Tuesday July 07 2020, @02:43PM (#1017662)

      Working with zero crossing (and hell, any threshold crossing) is everywhere in electronics

      Yeah but it never ends up as a quadratic eqn, or never seems to. Sure would be convenient, but...

      Its always stuff like IC=beta(Vcc-Vbe)/RB or Is*exp[(VBE/VT)-1] or worse. Just plop it into SPICE or similar simulator and solve/simulate for zero voltage or whatever.

  • (Score: 2) by Nuke on Tuesday July 07 2020, @04:27PM

    by Nuke (3162) on Tuesday July 07 2020, @04:27PM (#1017746)

    I was put in the pipeline for smart kids where we skipped a grade of math and took college calculus as seniors, of the 50 of us about 20 made it thru in my year, and we had to derive the quadratic eqn not just apply or memorize it, and frankly it wasn't THAT hard

    Agreed. IDK what age of kids you are referring to, but we derived it in second year at UK grammar school which means most of us would have been 12 years old. Seemed perfectly logical to me. I never forgot the formula, and we used it in hundreds of school excercises. I'm old enough that it was before calculators, and we were not allowed to use Napier's Bones - I mean slide rules - either.