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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: 2) by looorg on Monday July 06 2020, @04:25PM (3 children)

    by looorg (578) on Monday July 06 2020, @04:25PM (#1017121)

    I was wondering the same thing here. I guess I was though the "guessing" method of factorization as a substitute for the formula. Even tho I dispute that there is actually any or much guessing involved, it might be a semantic matter really. But The thing about factorization is that a larger problem is broken down into smaller and simpler problems and at the base level they are so small there is really no guessing involved. You can just see the solution if you can do plus and minuses in your head. If I have to do more calculations then I might as well just use the formula.

    "So, we can try to look for numbers that are 1 plus some amount, and 1 minus the same amount."

    Trying? Looking for ... Isn't this just other words for guessing? Sounds just like what you do normally when you use factorization to solve the problem.

    What I can agree with him on tho is that I do wonder why they even teach the formula in high school (or equivalent) instead of using factorization. I guess they want to sell the pupils some calculators instead of just using pen and paper and a tiny amount of brain power.

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  • (Score: 2) by Immerman on Tuesday July 07 2020, @01:43PM (2 children)

    by Immerman (3985) on Tuesday July 07 2020, @01:43PM (#1017627)

    >What I can agree with him on tho is that I do wonder why they even teach the formula in high school (or equivalent) instead of using factorization.

    Easy - because when you're solving real-world quadratic equations the answers will almost never be integers, and the "guessing method" is basically useless when the roots are long decimals. To say nothing of when the roots are complex numbers, which actually crops up in a lot of situations (AC circuit analysis for example gets radically easier when representing the problem into the complex plane)

    • (Score: 2) by looorg on Tuesday July 07 2020, @01:50PM (1 child)

      by looorg (578) on Tuesday July 07 2020, @01:50PM (#1017631)

      I don't suggest one should be cut, my suggestion was that they should teach the factorization method before the formula. There is also a pedagogical difference in that the factorization method is probably easier to understand then being told inserts the values here and hit calculate and then the magic box tells you the answer. Naturally in most text books etc the numbers will be picked such as that they are nice and easy to understand. In real-world examples you rarely have that but then nobody expects you to crank those numbers by hand either, at least not these days.

      • (Score: 2) by Immerman on Tuesday July 07 2020, @03:25PM

        by Immerman (3985) on Tuesday July 07 2020, @03:25PM (#1017698)

        Did they stop?

        Seems like I, and everyone I've tutored over the years, got the basic factorization first. It's just that it's only a brief conceptual step of "reversing the FOIL method" to figure out the solution, which is very rapidly skipped over in favor of the quadratic formula, since manual factorization is mostly useless in the real world.

        If it weren't for the fact that there is no general formula to solve for cubic and higher-order equations I'd question the value of teaching mostly-useless manual factorization at all. As it is though, manual factorization is an unavoidable evil in solving higher-order polynomial equation, and comes in handy for symbolic solutions in trig, calculus, etc., so at least the practice doesn't go completely to waste.