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This discussion has been archived.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, @08:32PM (5 children)

    by Anonymous Coward on Monday July 06 2020, @08:32PM (#1017299)

    I always did long square roots. The nice thing about knowing how to do it that way is that I usually found it faster than remembering which scales to use on the slide rule, it can be used for arbitrary sizes, and to arbitrary precision.

  • (Score: 0) by Anonymous Coward on Monday July 06 2020, @08:52PM (4 children)

    by Anonymous Coward on Monday July 06 2020, @08:52PM (#1017309)

    There's nothing to remember on the slide rule, what you need to remember is that half the log is the square root. Then it's obvious that you need to find two scales, one with two decades (two cycles) against the other with one decade. Line up 2 with 4 for a quick check and bob's your uncle!

    • (Score: 0) by Anonymous Coward on Tuesday July 07 2020, @12:06AM

      by Anonymous Coward on Tuesday July 07 2020, @12:06AM (#1017408)

      There's nothing to remember on the slide rule

      what you need to remember is that half the log is the square root. Then it's obvious that you need to find two scales, one with two decades (two cycles) against the other with one decade. Line up 2 with 4 for a quick check and bob's your uncle!

      So you do need to remember something to get the right scales, usually the A and B, and then double check your work. And then hope the numbers you need aren't off the end of the scale or your graduations are enough to provide you with the needed number of decimals.

    • (Score: 2) by fyngyrz on Tuesday July 07 2020, @01:54AM (1 child)

      by fyngyrz (6567) on Tuesday July 07 2020, @01:54AM (#1017460) Journal

      There's nothing to remember on the slide rule, what you need to remember is that half the log is the square root. Then it's obvious that you need to find two scales, one with two decades (two cycles) against the other with one decade. Line up 2 with 4 for a quick check and bob's your uncle!

      My little Picket (an N1010-ES / TRIG) has fixed A and D scales; D is the square root of A (and of course A is the square of D.) Direct readout from 1 to 100, somewhat less precision from 100 to 10000, etc.

      But... you do have to remember that. 😊

      --
      Math puns are the first sine of madness

      • (Score: 1, Funny) by Anonymous Coward on Tuesday July 07 2020, @09:08AM

        by Anonymous Coward on Tuesday July 07 2020, @09:08AM (#1017547)

        Is it A and D? No wonder I'm usually better off doing it by hand.

    • (Score: 2) by fyngyrz on Wednesday July 08 2020, @02:55PM

      by fyngyrz (6567) on Wednesday July 08 2020, @02:55PM (#1018209) Journal

      Also, in case anyone cares, cube roots and cubes can be found using the K and D scales.

      --
      All generalizations are false.