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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.
(Score: 2) by hendrikboom on Monday July 06 2020, @03:25PM (4 children)
It's not much different from the usual formula.
It just breaks it down to several steps instead of having to grok it all at once.
May be an easier way to *teach* the solution.
(Score: 2) by JoeMerchant on Monday July 06 2020, @07:32PM
To me, he's tweaked the A in Ax2 + Bx + C = 0 to always be 1 - and if you do that, then the classical formula simplifies quite a bit.
Then, he's broken it into a two step operation instead of condensing it into a single formula... it's a good presentation, the Khan academy style blackboard helps a lot.
🌻🌻 [google.com]
(Score: 2) by TheRaven on Tuesday July 07 2020, @09:24AM (2 children)
We were taught the formula and then taught the completing the square method [wikipedia.org]. If you complete the square with variables for the coefficients, you end up with the formula, so it provides a nice way of showing where the formula came from.
I really hated 'memorise the formula' lessons at school. If something can be reduced to a formula, I can write a program that solves it (and did, on a Psion Series 3) and a computer can then solve that category of problem. Understanding how the formula was derived from a sequence of basic algebraic steps was interesting and a useful skill, repeatedly applying that algorithm was not.
Calculus was the absolute worst for this. Here are a bunch of arbitrary rules that can't be created from first principles with the mathematical tools that you've got when you start calculus, apply them repeatedly by rote until you've gone from being 10,000 times slower than a computer solving these problems to only 1,000 times slower.
sudo mod me up
(Score: 2) by hendrikboom on Tuesday July 07 2020, @12:49PM
Yeah. Even if you understand limits, the process of proving the formulas for the derivative of sin and cos are not easy.
(Score: 2) by Immerman on Tuesday July 07 2020, @01:35PM
> If something can be reduced to a formula ... a computer can then solve that category of problem
Yes it can. And in math class *you* are the computer (= one who computes), as was always the case before the invention of mechanical and then electronic computers.
Having a terrible memory for details, I'm a big fan of understanding how the formula was derived. I found calculus-based physics far easier than algebra-based physics for exactly that reason - with calculus you can quickly derive the hundreds of specific physics formulas from a handful of core formulas. But after the first few dozen times you solve a particular class of equations you'd probably be well served memorizing the formula rather than re-deriving it from first principles. If you can manage it.
Calculus itself was a bear, but fortunately I had professors that allowed quick-reference sheets on the theory that we'd never again be expected to do all that from memory - and unlike physics it's not like you can quickly derive the integral/derivative formulas from first principles in a few seconds. Besides, the real challenge isn't remembering the formulas, it's figuring out which formulas and strategies will actually be relevant to the problem you're trying to solve. Especially once you start using calculus in other classes and for real-world problems, rather than just the straightforward exercises in the calculus book.