Stories
Slash Boxes
Comments

SoylentNews is people

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.


Original Submission

 
This discussion has been archived. No new comments can be posted.
Display Options Threshold/Breakthrough Mark All as Read Mark All as Unread
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
  • (Score: 0) by Anonymous Coward on Monday July 06 2020, @05:08PM

    by Anonymous Coward on Monday July 06 2020, @05:08PM (#1017152)

    This whole topic is about "When A is One," the whole thing can be simplified to -B/2 +/- u. (and then it goes through additional steps to find C, and so it's not a one-step process any more.)

    It ignores A. At least, it ignores A until the very, very end, and then it says "Oh but we can take B to be b/a." And that means that C=c/a, and his initial part is -b/(2a) +/-u (2), which leads to "their product is C when..." b^2/(4a^2) - u^2=c^2/a^2, and so, obviously it gives a valid u. GoTo Wtfbbq.

    Continue the solution, add u^2 and subtract c^2/a^2, you have b^2/(4a^2)-c^2/a^2=u^2, take the square root ("obviously"), and you get u=sqrt(b^2/(4a^2)-c^2/a^2) = sqrt((b^2-4c^2)/(4a^2)) = sqrt(b^2-4c^2)/2a = u. Remember the original "simplification", -B/2 +/- u, and whalla! You have... did I commit an arithmetical error? it doesn't look simple when a != 1. Something looks wrong because I have -4c^2 instead of -4ac, which is the original form of the equation.It makes sense that you will have a -b, but you can't get an a into that sqrt() here.

    heh. This is _much more_ complex than the original formulation, I feel. This is only "easier" when a = 1:

    (-b +/- sqrt(b^2-c))/2

    Retarded Genius strikes again.