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Easier Way to Solve Quadratic Equations


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Mathematician Finds Easier Way to Solve Quadratic Equations

Here’s the secret.

 

A mathematician has derived an easier way to solve quadratic equation problems, according to MIT's Technology Review.

Quadratic equations are polynomials that include an x², and teachers use them to teach students to find two solutions at once. The new process, developed by Dr. Po-Shen Loh at Carnegie Mellon University, goes around traditional methods like completing the square and turns finding roots into a simpler thing involving fewer steps that are also more intuitive.

Here’s Dr. Loh's explainer video:

 

 

 

 

 

 

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There are easier ways to solve quadratics There are easier ways to solve long division.

 

It took me a long time to understand the reason it is taught these difficult ways is because long division as taught allows dividing polynomials by the same method, and quadratic equations allows solving certain differential equations by the same method.

 

The problem is that most people who use math in their life (jobs) will never need to factor a polynomial or ever solve any differential equation by any method.

 

There is a trade-school practical level of the population who could benefit from the easier methods. There are methods like Chisenbop which turn your hands into an abacus. Quick math counting (addition and subtraction on fingers). Why are teachers against this?

 

Spotter sees one miss, points index finger. Repeats until four fingers pointed (
Duddly DoWrong is on the stage). Shot 5 rings out... and buries itself in the berm. 5 misses. Fold four fingers in and point the thumb! The thumb is "5". Misses 6, 7, 8, &9? One finger, two, three, and four. Plus the thumb is 9! Tenth miss? Fold all finger on the first hand in and point one finger on the other hand (that is a mathematical carry).

 

Like if you just tried it.

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9 minutes ago, bgavin said:

Computer geeks can count to 31 on one hand in Hex.

We can, but usually use just the fingers to get to 15 (which is "F"), then carry to the next hand for the next hexadecimal digit (F+1=10).

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55 minutes ago, John Kloehr said:

There are easier ways to solve quadratics There are easier ways to solve long division.

 

It took me a long time to understand the reason it is taught these difficult ways is because long division as taught allows dividing polynomials by the same method, and quadratic equations allows solving certain differential equations by the same method.

 

The problem is that most people who use math in their life (jobs) will never need to factor a polynomial or ever solve any differential equation by any method.

 

There is a trade-school practical level of the population who could benefit from the easier methods. There are methods like Chisenbop which turn your hands into an abacus. Quick math counting (addition and subtraction on fingers). Why are teachers against this?

 

Spotter sees one miss, points index finger. Repeats until four fingers pointed (
Duddly DoWrong is on the stage). Shot 5 rings out... and buries itself in the berm. 5 misses. Fold four fingers in and point the thumb! The thumb is "5". Misses 6, 7, 8, &9? One finger, two, three, and four. Plus the thumb is 9! Tenth miss? Fold all finger on the first hand in and point one finger on the other hand (that is a mathematical carry).

 

Like if you just tried it.

Try it??? I'm still trying to understand it!!!

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Where's the Tylenol?

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10 hours ago, Sedalia Dave said:

In Naval Aviation on the flight deck. 1 fist is zero, Fingers pointing up for 1-5, Pointing to the side for 6-10, Pointing down for 11-15.

 

being a former-Army grunt, what kind of info  do these numbers mean to the flight crew?  or other ground crew?  

 

 

Edited by Cheyenne Ranger, 48747L
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40 minutes ago, Cheyenne Ranger, 48747L said:

 

being a former-Army grunt, what kind of info  do these numbers mean to the flight crew?  or other ground crew?  

 

 

 

When I was working the flight line we used those numbers for things line flap and Horizontal stab trim settings. when doing pre-launch checks. With a half a dozen or so jets all turning and burning no one could hear you scream. Two way radios are useless because a microphone picks up all the ambient noise.   They did make a mike that covered your mouth to block the noise but it required the a hand to hold it over your mouth so they were relegated to dedicated phone talkers.  

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That would be useful to someone who has difficulty with quadratics or even quadratics with terms of multiple digits but it stops short of solving equations with imaginary solutions.   Nor does it suggest methods for solving cubic, quartic, quintic and higher order polynomials.

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As a practicing engineer for 30+ years who’s also been adjunct faculty at an engineering, I can say with sincerity that I’ve never solved a quadratic, never used calculus, and never used a differential equation since earning my BSME.

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14 hours ago, Charlie Harley, #14153 said:

As a practicing engineer for 30+ years who’s also been adjunct faculty at an engineering, I can say with sincerity that I’ve never solved a quadratic, never used calculus, and never used a differential equation since earning my BSME.

I guess you are saying if not broke don't fix it......

 

Texas Lizard

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On 8/2/2021 at 4:29 AM, Charlie Harley, #14153 said:

As a practicing engineer for 30+ years who’s also been adjunct faculty at an engineering, I can say with sincerity that I’ve never solved a quadratic, never used calculus, and never used a differential equation since earning my BSME.

Yup!  The interesting thing was when introduced to calculus, in high school, they first taught Newton-Raphson interative process, and/or "least squares" (been a LOOOONG time!).  Then they got into using all those formulas I had a lot of trouble remembering.  Funny part of it is that digital computers essentially use N-R at high speed! :wacko:  But, you are right.  Once out of school in the real world of engineering, never used any of that.  Want answers to complex problems?  Just plug into a NASTRANS computer and you get answers (or whatever they use today).  Most useful part of math for deign work was geometry and trig. (Now if I can just remember how to use the sliderule sitting in my drawer... :P

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I've used exponentials, and simultaneous equations.

 

Except for some PLL stuff, have not used much calculus. Well, not until I started to work on a wheeled upright "robot." Then I was suddenly deep into PID (proportion, integral, derivative) control. That is definitely calculus.

 

But the PID control was not for a job, was just doing it for fun.

Edited by John Kloehr
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3 hours ago, Trailrider #896 said:

Yup!  The interesting thing was when introduced to calculus, in high school, they first taught Newton-Raphson interative process, and/or "least squares" (been a LOOOONG time!).  Then they got into using all those formulas I had a lot of trouble remembering.  Funny part of it is that digital computers essentially use N-R at high speed! :wacko:  But, you are right.  Once out of school in the real world of engineering, never used any of that.  Want answers to complex problems?  Just plug into a NASTRANS computer and you get answers (or whatever they use today).  Most useful part of math for deign work was geometry and trig. (Now if I can just remember how to use the sliderule sitting in my drawer... :P


 Bet you wish you had a copy of this…

 

image.jpeg.fba114e2d45716385819689a1dbed045.jpeg

 

 A librarian in Fallon NV sold it to me for $5.00 after I renewed the checkout for the fourth time. 
 

 

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37 minutes ago, John Kloehr said:

But the PID control was not for a job, was just doing it for fun.


 Getting a PID controller properly set up is akin to black majic. 
 

 I am still looking for someone to properly tune one of our pedestals at work. The OEM of the controller refuses to provide any expertise because they didn’t build the pedestal. 

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I still have my Dad's K&E slide rule from his days at Annapolis.
He has "1937" engraved on it with his name.
Gen-yoo-ine ivory construction...  guaranteed to torque off a PETA type.

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9 hours ago, bgavin said:

I still have my Dad's K&E slide rule from his days at Annapolis.
He has "1937" engraved on it with his name.
Gen-yoo-ine ivory construction...  guaranteed to torque off a PETA type.

Have the ivory repurposed into inlays in a pair of grips or a rifle butt.

 

just a suggestion.  For a rifle butt I would not polish off the markings.

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On 8/2/2021 at 6:29 AM, Charlie Harley, #14153 said:

As a practicing engineer for 30+ years who’s also been adjunct faculty at an engineering, I can say with sincerity that I’ve never solved a quadratic, never used calculus, and never used a differential equation since earning my BSME.

I sympathize.  I was allowed to overspecialize in math and computer science, veterans could write their own curriculum. Then the job market stunk so I went to graduate school. In graduate school I studied everything except databases, I read the book and it was all too intuitive to waste 60-80 hours of my life. Years later I was was working for DEC, a now defunct computer company and I did a lot of things I enjoyed.  Then in 1983 I was offered a job working in databases,  OMG. I stayed in that group for thirty years, got promotions, bonuses and stock options.

 

now, what’s the point?  I think there were three or four things from all that education that I was able to use later, maybe twenty minutes of youthful studying that rose later in an aha moment to lead to a solution to a real problem.

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Semantics is also pedantic... for example, when I convert 105 Fahrenheit to centigrade for my Kiwi friend I do not go through the formula... just the result.
For 47 years in the computer business, I've been converting binary to hex to ebcdic to decimal without showing the work.

Shifting into the pedantic:  the 0x1F above is Thumb ("1") and four Digits ("F") which is decimal 31.
I have no interest in spoon feeding the lazy who can't figure out using five digits of the hand to represent 0x31, hence "do the math"
"Do the math" is a colloquialism I favor because it prods the lazy to do their own work and not be spoon fed.

I failed HS geometry because I refused to bother with "show the work".
My grade was based entirely on homework and "show the work", and not on getting As on every exam.
My HS teacher was pedantic as well. 

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4 hours ago, Marshal Mo Hare, SASS #45984 said:

Have the ivory repurposed into inlays in a pair of grips or a rifle butt.

I would never dream of doing that.
This would destroy a priceless precision instrument that is almost 100 years old, and long out of production.

My Dad engraved his signature on the rule, and it is a treasure to me.

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16 hours ago, Sedalia Dave said:


 Getting a PID controller properly set up is akin to black majic. 
 

 I am still looking for someone to properly tune one of our pedestals at work. The OEM of the controller refuses to provide any expertise because they didn’t build the pedestal. 

 

I can tune PIDs but when I'm done I never know how I did it.  I took a class from the ISA or IEEE on PID loop tuning and it was probably the best continuing education class I've ever had.  Went a long way towards demystifying the PID for me, but that stuff is still black magic.  The absolute worst is the customer who wants to tune the loop in during the factory test in the shop.  Before the thing is connected.  I cannot make them understand the importance of the load on the system.  So I always tune a super slow loop for those people. 

 

What kind of controller is it? 

 

On 7/31/2021 at 9:28 PM, bgavin said:

Computer geeks can count to 31 on one hand in Hex.

 

In hex?  I can do that but I coulda swore I was using binary.  I tried that for spotting but it didn't work out too well.  First time someone got 4 misses I forgot to convert it back to normie counting and the TO gave me an odd look.  Not enough people miss more than 5 targets to make it worthwhile. 

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