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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: 0) by Anonymous Coward on Monday July 06 2020, @03:17PM (1 child)
It's not so much about math as showing you're superior. Point scored.
(Score: 2, Informative) by Anonymous Coward on Monday July 06 2020, @03:35PM
His major contribution: to search for the roots of a quadratic equation is to search for two numbers with a given sum and product; because if x0 and x1 are the roots, then the quadratic equation can be written under the from of x2 - (x0+x1)x + x0x1 =0. Oh, wow, amazing!
His next contribution: translate the equation (variable substitution) so that the average of x0 and x1 is the origin of the axis, massage a bit the terms and, voila, you get to the well known formula of the roots of a quadratic equation.
Gotta tell yah, he's genital. A math twat, as it comes.
(Score: 4, Insightful) by Snotnose on Monday July 06 2020, @03:24PM (11 children)
It's a simple formula. The only hard part is finding the square root. But in school it's always an integer and it should only take 2-3 guesses to figure it out.
Can you tell I did college before calculators were a thing?
I came. I saw. I forgot why I came.
(Score: 5, Funny) by Anonymous Coward on Monday July 06 2020, @04:32PM (1 child)
And in the era of BLM, everyone should be proud of their roots, even when some of them are imaginary!
(Score: 0, Offtopic) by legont on Monday July 06 2020, @06:13PM
Not really. Those math founders were mostly slave owners and their work is still used to torture children.
"Wealth is the relentless enemy of understanding" - John Kenneth Galbraith.
(Score: 2) by progo on Monday July 06 2020, @05:53PM (7 children)
"The only hard part is the square root." Slide rule works fine. We've had those for millennia too. How do you get simpler than this?
Other than "I did it differently" I don't see the point of this "new" method.
(Score: 2) by LVDOVICVS on Monday July 06 2020, @06:35PM
Slide rules were invented around 1620, so only four hundred years ago.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @08:32PM (5 children)
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)
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
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)
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
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
Also, in case anyone cares, cube roots and cubes can be found using the K and D scales.
--
All generalizations are false.
(Score: 4, Funny) by PartTimeZombie on Monday July 06 2020, @10:07PM
My gods I hated quadratic equations.
It didn't help that my fifth form maths teacher was completely unengaged and didn't really help.
Also, Robert Smith sat beside me and spent the whole year drawing cartoons. Then the bastard got 94% in the end of year exams.
Nice bloke though. Couldn't stay mad at him.
(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.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(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.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @03:35PM (9 children)
I've been taught this method in high school, around 1995, albeit with factorization through the discriminant (b^2 - 4ac). Even wikipedia [wikipedia.org] already knows about it.
So what's new here? Have other high school really been teaching this factorization by guessing?
(Score: -1, Troll) by Anonymous Coward on Monday July 06 2020, @03:48PM
Didn't you read the history? For thousands of years nobody was smart enough, not the Babylonians nor the Greeks nor Albert Einstein. We are indeed fortunate to live in this time where $chineseImport at $majorUniversity benevolently casts out elegant proofs and solves problems we didn't even know we had. Where can we find more $chineseImports to elevate our existence?
(Score: 2) by KritonK on Monday July 06 2020, @04:23PM (1 child)
It is an easy way to factorize a quadratic equation, without having to remember the formula for the determinant or how to use it to calculate the roots of the equation. It is equivalent to the determinant method of calculating roots (the author proves this at the end of the article), but, unlike the determinant method, it is easier to do the calculation in your head.
As for the guess-and-check method, it's the first time I hear about it, too, but I think that he refers to cases where the equation is obviously in the form of x2 -(a+b)x + ab, which is equivalent to (x-a)(x-b), so the roots are a and b. When a and b are not obvious, one may be tempted to identify them by guessing, to avoid calculating the roots using the determinant. The author eliminates this guessing part, by describing how to calculate a and b simply, from their sum and product.
(Score: 3, Insightful) by stormreaver on Monday July 06 2020, @07:48PM
The sum-and-product method described in the article was part of my College Algebra (MTH 135) class back in the early 1990's (1992, if I remember correctly). This is neither new nor novel.
(Score: 2) by looorg on Monday July 06 2020, @04:25PM (3 children)
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.
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.
(Score: 2) by Immerman on Tuesday July 07 2020, @01:43PM (2 children)
>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)
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
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.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @06:11PM
>> Have other high school really been teaching this factorization by guessing
The new way of teaching math (one program is called Jump Math) is for students to explore how they feel about numbers by picking one digit to become their Best Number Friend. They then get to role play that number for the whole semester, exploring how it interacts with other numbers by interacting with the other students. I wish I was kidding, but things like memorizing the times-table are no longer in the curriculum.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @07:40PM
In my kids' algebra class they teach factorization by guessing first with easy-to-guess problems like x^2 + 5x + 6, then they move on to problems that are harder to guess and the use of the formula. That's how it was taught to me too, 150 miles away and 30 years earlier.
(Score: 0, Flamebait) by Anonymous Coward on Monday July 06 2020, @03:39PM (1 child)
Clickbait title, a page-long summary full of airy prelude and zero meat.
(Score: 2) by DannyB on Monday July 06 2020, @05:54PM
This could give us a real reason to change the math books for the next school year.
A reason that is much better than the usual reason college math books are rewritten and reprinted. Specifically, to ensure that the previous year's textbooks cannot be used in this year's class, and thus you must purchase a NEW textbook, and old textbooks have no re-sail value.
Or maybe, math books are rewritten every year because of all of the changes to the cosine function or how square roots work this year vs last year.
Maybe the English literature books are rewritten to keep up with all of the changes Shakespeare makes to his text.
Maybe the History books are rewritten because we have always been at war with . . .
NO CARRIER
It's interesting that high school textbooks, in the very same subject areas, but usually paid for by taxpayers, do not get rewritten every year.
It's just one of those things.
Which things?
Don't bother me with details, just one of those things. You know.
Young people won't believe you if you say you used to get Netflix by US Postal Mail.
(Score: 0, Disagree) by Anonymous Coward on Monday July 06 2020, @03:58PM (13 children)
From TFS:
The quadratic formula is unwieldy? Please.
What's unwieldy about:
x=(-b +/- sqrt(b2-4ac)/2a
it's actually a pretty simple formula, especially as compared with other formulas -- Newton and Liebniz should take turns smacking TFA's author about the head and face. He certainly deserves it.
Based on the comments (no, not going to read TFA), it sounds like the "simple" version involves factorization with interpolation. I'm all for factoring quadratics when the roots are integers. However, using the simple formula is especially useful when the roots aren't integers.
I went to school when calculators weren't allowed in math class, and especially not during tests. Perhaps the rise of calculator use has kept folks from being able to do simple arithmetic/estimation?
Arithmetic is *not* difficult. Nor is Algebra. As Heinlein rightly observed [goodreads.com]:
(Score: 2, Insightful) by shrewdsheep on Monday July 06 2020, @04:22PM (2 children)
x^2+px -q = 0 =>
x = -p/2 +- sqrt(p^2/4 - q),
ah..., the memories. This was Germany btw.
Seems the author needs some cultural awareness.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @09:39PM (1 child)
WRONG!
It's (-b + sqrt(b^2-4ac)) / 2a. Learn to speak English numbnutz
(Score: 2) by gawdonblue on Tuesday July 07 2020, @09:08AM
Aren't there 2 roots?
(Score: 0) by Anonymous Coward on Monday July 06 2020, @04:37PM (1 child)
So how do you classify a brilliant mathematician who leaves messes about the house and fails to bathe?
I've met a few such fellows.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @04:43PM
Mathtards. There are corridors filled with them at most universities.
(Score: 5, Insightful) by Thexalon on Monday July 06 2020, @08:11PM (2 children)
My experience is that the people who hate math the most passionately are those who focused on developing skills of persuasion rather than developing knowledge, and can't stand the fact that a wrong answer in math is still wrong no matter how persuasively you try to argue that it's right.
Which correlates rather strongly with the people who want to believe that the most fundamental findings of science are, well, just, like, your opinion, man.
Unfortunately, these kinds of people also have a strong tendency to find their way into being in charge of businesses, governments, and other institutions, largely because the people they need to convince to put them in charge are just as ignorant as they are.
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @10:09PM
I disagree on two axes:
1. I had the misfortune - long story - of attending a religious university and had mathematics and computer science professors that were technically brilliant but still devoutly religious. Being unable to understand math is unrelated to being irrational about bearded sky gods, vaccines, or the shape of the earth.
2. Some portion of the population is just plain stupid. I grant that. But many other people who are terrible at math just had a bad educational environment as children. If you spend a long time with someone and decide they're not too bright, that's fine. But if you are only acquainted with someone with poor math skills, you have to find out if their problem is innate stupidity or lack of opportunity. I have two anecdotes. First, one of my neighbors dropped out of high school at 16 to work construction. In his late 20s he decided he wanted a more interesting job so he got his GED, then his bachelor's degree, then a PhD in biochemistry and now he does cancer research. Second, one of my brothers had an elementary school teacher that beat the kids when they got a math problem wrong. (Hooray for religious schools.) He was traumatized by the abuse and barely passed math classes for the rest of his schooling - he could learn the material, but when it was test time he would freeze up. Ten years after high school and a lot of counseling and medication later he bought a book on high school math and worked through it, and took some college preparation standardized tests. He was the the only balding guy with a big beard in the room, and he scored in the top 5%.
(Score: 1, Interesting) by Anonymous Coward on Thursday July 09 2020, @08:59AM
The vaccine for this effect would be to also teach kids the content of Chris Voss' book 'Never Split the Difference'.
This will give them the tools they need so they are able to defend themselves against the self-styled 'winners' who are really just luckily born rich + aggressive.
These are the same people who *think* they have developed said "skills of persuasion": anyone who resorts to force/coercion. You know, that same set who seem to find their way into being in charge. Because aggressiveness and self-ignorance-of-failure are enough to give a mistaken self-impression of being 'good' at persuasion.
A truly impressive negotiator can 'get their way' from a position of *weakness*.
But, why would one trust a 'winner' once you discover this is all they're doing? Winning from a position of strength... using strength. Any dangerous animal can do that, it doesn't even require the ability to speak, necessarily. Let the Wookie win.
Why do we all still bother listening to such people, and even letting them take charge of us? Because we're programmed to.
Humans are social animals. We are predisposed to 'be good' and minimise conflict. (so says all the science).
Even our ultimate beliefs are controlled more by peer pressure than you would at first imagine. But it is true: Surround yourself in people who believe your bullshit, and you'll believe it too. It's automatic. Want to change some believe about yourself? Convince your friends and families that it is true -- even by faking it -- and you'll come to believe it too. Such as is the power of 'confidence'.
It's just social positive-feedback, and it's also why the problem people can learn to be really good at just not hearing or seeing anything that might prove them otherwise.
We are also not in fact 'fundamentally evil' - the process about how one can become personally mistaken about this is also well-known. Recently scientist have been forced to conclude that many religions saying otherwise are in fact mistaken, following a common and very early mechanism due to individual intelligence conflicting with tradition.
The greatest of evils might come from those with the best of intentions... who also happen to be aggressive, and 'heroically willing' to do what others will not.
It seems that due to structural racism they're probably also old, white, and somewhat demented men who were born to rich parents.
One of the lessons of Voss' work is this: Whenever someone seems to be making crazy decisions -- someone (either you, or them) is missing some critical information.
If one's mind is starting to go, such that basic facts aren't held too tightly, then it's probably one self - but one also wouldn't know - for exactly the same reason.
If you see someone else acting crazy -- either they know something that you don't, or you know something they don't.
People can also become addicted to ritual (with which each practise comes with a burst of anxiety-reliving biochemicals). Those people have 'OCD', and they know they're 'crazy'. It's the ones that don't know they're crazy, that you have to watch out for.
Given that we are social beings who believe in things that 'everyone knows' this also means we all behave to limit the damage that would be caused by the hypothetical 'bad actor' -- or give into the temptation to do others bad for our own benefit because it would be expected that 'someone else will anyway'. So most of that bad behaviour probably just happens because its what we expect to happen.
Based on an inaccurate understanding of exactly what we are.
(Score: 3, Informative) by HiThere on Tuesday July 07 2020, @12:30AM (3 children)
IIRC the -b should not be included within the parenthesis.
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @02:17AM
-b(etter?)
(Score: 2) by Immerman on Tuesday July 07 2020, @01:48PM (1 child)
It definitely should be: in the traditional "math form" writing the -b is in the numerator while 2a is the denominator. Take the -b out of the parenthesis and it will no longer be in the numerator.
(Score: 2) by HiThere on Tuesday July 07 2020, @08:12PM
My mistake. It's been a long time since I used the formula, and I guess I mis-remembered it. (I.e., I did remember it, but the memory was wrong.)
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @05:06PM
If you follow the link, this isn't about replacing the formula, but teaching students how to derive the formula from first principles in a way that negates the need to memorize it.
That is, if you know WHY it is what it is, you don't actually need to know what it is, as you can quickly derive it again.
The idea is to teach factorization, and then meld that with bit of algebra to derive the equation. it is quite elegant, much more so than how this was presented to me:
1) you can solve by factoring the equation
2) factoring is hard, so here is an equation to get the factors for you
I eventually connected the two myself and realized that you could at least prove the values were correct by plugging them in, but I never figured out how to derive it myself.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @04:36PM (2 children)
So he is really clever and has come up with a new method, yet cannot use google to find out what this is called
"Completing the square"
Been using it for decades and was taught as well
(Score: 2) by vux984 on Monday July 06 2020, @08:08PM
Yes, after I read this article, that's *exactly* what it sounded like to me too. Is he actually doing something different from:
https://www.mathsisfun.com/algebra/completing-square.html [mathsisfun.com]
(Score: 2) by FatPhil on Monday July 06 2020, @11:13PM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 1, Informative) by Anonymous Coward on Monday July 06 2020, @04:49PM
Some people do find it easier to re-derive the more complex formulae than memorize them. For those, the simplified derivation can be helpful.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @05:08PM
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.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @05:41PM (3 children)
Ever try to figure one out in your head without a scientific calculator? Trippy shit.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @05:56PM
There are various recipes for solving diffieQs. For those types with known recipes, it's just a straight forward cookbook stuff.
For other types, they are "research problems."
No need for jacked-up calculator, unless you want numerical approximation.
(Score: 2) by Rupert Pupnick on Monday July 06 2020, @08:43PM (1 child)
You don't use a calculator for solving a differential equation unless you're talking about a particular solution using numerical methods.
Generally speaking, the solution to a differential equation is just another equation.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @02:18AM
Until eventually all the terms cancel except 42.
(Score: 2) by jasassin on Monday July 06 2020, @05:45PM (4 children)
If I could have lived the rest of my life without hearing the words "Quadratic equation", i would've been much happier.
For me, the quadratic equation made no sense. I remember staying up from after school till going to bed, trying to solve four problems. I even went in to get help during study hall and after school and the teacher couldn't figure it out either (God bless her heart for trying so hard). Now I have to repress all those horrible memories again.
jasassin@gmail.com GPG Key ID: 0x663EB663D1E7F223
(Score: 3, Funny) by Anonymous Coward on Monday July 06 2020, @05:58PM (1 child)
The next time you drive a car look at the speedometer. It's a Quadratic equation calculator. Now you have something to always remind you of the happy times in school.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @09:19PM
> The next time you drive a car..
Probably not for newer cars--they count pulses on a tone wheel in the transmission (geared to the final drive) and divide by the time. All very linear (and done digitally).
Previous generation of speedometers used eddy current "motors" to move the pointer,
https://www.explainthatstuff.com/how-speedometer-works.html [explainthatstuff.com] which are linear analog devices, depending on Kx for the hairspring constant.
There is a brief mention that some early speedometers used something like a centrifugal governor--and since centrifugal/centripetal force is a function of V^2 those ancient speedometers solved a quadratic, but just the most simple kind (x^-2), no linear or constant term. Don't recall seeing one of these, they might have solved the square root with a nonlinear readout scale?
(Score: 3, Informative) by JoeMerchant on Monday July 06 2020, @07:35PM (1 child)
Graphing parabolas might have helped - your solutions are the X axis intercepts - if this is all too much, just stay away, it's not a big part of daily life for most people.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @12:56PM
maybe if the ignorant were properly shamed for being ignorant, and forced to learn some math, we wouldn't be in the situation when "exponential growth" is a crucial notion that people can't understand.
(Score: 4, Insightful) by VLM on Monday July 06 2020, @05:55PM (7 children)
I was put in the pipeline for smart kids where we skipped a grade of math and took college calculus as seniors, of the 50 of us about 20 made it thru in my year, and we had to derive the quadratic eqn not just apply or memorize it, and frankly it wasn't THAT hard, it was relatively lightweight and had few surprises, whereas this alternative looks worse with the WTF virtual z factor getting tossed in.
I'm not saying its necessarily a bad idea, but it is more complicated to learn to derive than the original quadratic eqn.
I'm not sure its useful to teach zero finding as a skill in and of itself as I've never needed the zeros of a quadratic in practice whenever I've needed a zero its something hideous so wolfram alpha or mathematica or some numerical method or whatever other option. So given that zero finding of quadratics is NOT, and probably never was, a practical vocational skill, the only point in learning the q-eqn is to learn how to think, and I think the classic q-eqn fits in better with the curriculum than the new eqn. I suppose they could just move the new eqn to a better location in the overall math education process and then it would be fine, but the kids would miss out on the nifty learning experience of the q-eqn.
(Score: 2) by JoeMerchant on Monday July 06 2020, @07:39PM
To me, he's just taking the one-step classical quadratic equation and breaking it up into two - perhaps simpler to execute - steps. It's harder to derive, perhaps simpler to execute, maybe gives a little more insight into what's happening with the parabola graph than the straight single equation does.
I'd also swear I've seen this before, maybe he tweaked it a little, but the presentation with B/2 +/- U gives me a lot of deja-vu'
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(Score: 2, Interesting) by Anonymous Coward on Monday July 06 2020, @07:54PM (1 child)
I've come to the opinion that success as a student is partly determined by raw talent but partly determined by how well your teachers can communicate in a way that's meaningful to you. My dad had his bachelor's degree in math, and in one on one discussions at home he could explain clearly. I breezed through math in school. My classmates who only had the mediocre teachers and their own parents who couldn't explain the material as well struggled. I didn't have more talent, I was just lucky.
I'm not sure I can judge the educational value of this formula fairly, I learned the standard one decades ago. I would want a fresh set of eyes on the problem - not mine (someone biased towards the status quo just because it's familiar), and not the person who proposed using this one either (someone who at least appears to be biased in favor of doing something different just for its own sake).
I also agree that teaching these skills in school may not be that useful. I've heard the argument, "If you can learn advanced math, you can learn anything". But school should be about more than drilling facts into a kid's skull, it should be about teaching critical thinking and fostering a life long interest in learning. There have got to be more engaging things to learn, in and out of mathematics.
(Score: 2) by VLM on Tuesday July 07 2020, @02:56PM
Its worth pointing out that my wife could handle math so she did STEM degree so I eventually met her at a STEM employer and eventually married etc. Meanwhile my SiL couldn't handle math, so she went for a K12 educator degree instead of STEM, and she's been teaching math to the next generation of STEM students for more than a quarter century. So the sister who knows math designs and implements the call center queuing statistical analysis formulas in your PBX firmware, but doesn't teach anyone math, whereas the sister who couldn't learn math is teaching math. Hmm.
Given the extreme income disparity between something like a BSEd vs BSCS or BSEE, I would think anyone who can pass calculus is almost certainly not teaching kids math, which in the long term would seem to be a problem for the next generation of calculus learners.
I'm not sure if its good or bad news that the district curriculum is so detailed and specific that she's practically reading prepared materials to the kids or showing approved multimedia all day rather than actually teaching in the traditional sense of 1 on 1 learning. In a similar sense I don't know anything about playing Rugby, but given an authoritarian micromanaged enough school district curriculum I could "teach" rugby by word for word reading of the school district issued mandatory rugby textbook, and accidentally some kids might learn rugby from "me" in the sense that they heard me create a live audiobook presentation of the textbook they probably wouldn't read on their own without me crack'n the whip on them.
(Score: 0) by Ethanol-fueled on Tuesday July 07 2020, @02:02AM (2 children)
Working with zero crossing (and hell, any threshold crossing) is everywhere in electronics. Sure, you can MATLAB it all away, but it helps to have a more intuitive understanding of the underlying math mechanisms.
But that's why that level of education is shit in America. The worst travesty of lower-level American education is that basic vectors are taught separately from complex numbers and when complex numbers are first taught there are no real-world applications taught with them. So students before the internet had their "what the fuck is this used for"-isms for complex numbers just like you had with root-finding in general.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @02:23AM
If only they would start with the axioms of set theory and get straight onto tensor calculus then we could derive the math test and solve it before it was even written. Bastards.
(Score: 2) by VLM on Tuesday July 07 2020, @02:43PM
Yeah but it never ends up as a quadratic eqn, or never seems to. Sure would be convenient, but...
Its always stuff like IC=beta(Vcc-Vbe)/RB or Is*exp[(VBE/VT)-1] or worse. Just plop it into SPICE or similar simulator and solve/simulate for zero voltage or whatever.
(Score: 2) by Nuke on Tuesday July 07 2020, @04:27PM
Agreed. IDK what age of kids you are referring to, but we derived it in second year at UK grammar school which means most of us would have been 12 years old. Seemed perfectly logical to me. I never forgot the formula, and we used it in hundreds of school excercises. I'm old enough that it was before calculators, and we were not allowed to use Napier's Bones - I mean slide rules - either.
(Score: 0) by Anonymous Coward on Monday July 06 2020, @06:22PM (2 children)
That's as quadratic as it gets.
All your fancy "math" is like doing arithmetic in Java
(Score: 2) by gawdonblue on Tuesday July 07 2020, @09:33AM (1 child)
Isn't it just Add and Divide?
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @06:45PM
I don't know.
Yeah, I can see where multiplication is just adding multiples, but of the other two, which is more fundamental? Division or subtraction?
(Score: 1, Flamebait) by darkfeline on Monday July 06 2020, @08:44PM (4 children)
It looks like it's basically just this video [1] (the video cites Loh as the inspiration)
[1]: https://www.youtube.com/watch?v=MHXO86wKeDY [youtube.com]
I mean, it's a clever way of framing the problem, but it's just a partially solved quadratic equation, the idea being that the partially solved form is easier to grok than the final equation. It certainly doesn't deserve such a clickbait title.
Also, maths is not a word. Maths is not the plural form of math. Mathematics is not the plural form of mathematic. Mathematic is not a word. Mathematics is a noncountable noun. Saying maths makes you sound uneducated the same way using the wrong their or your does. Yes, I'm implying that the British are uneducated in this regard.
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(Score: 1, Funny) by Anonymous Coward on Monday July 06 2020, @09:14PM
Anyone who's ever listened to BBC radio knows Brits suck at language.
(Score: 2) by ledow on Monday July 06 2020, @11:41PM
Maths is just fine, thanks.
You can argue with my degree in it from a university that's existed for 184 years or, if you prefer, friend's degrees from (variously) universities that existed before the US was discovered or the 11th Century, your choice. They all refer to it as mathematics.
It doesn't need to be pluralised to have an 's' but Google say:
Origin:
late 16th century: plural of obsolete mathematic ‘mathematics’, from Old French mathematique, from Latin (ars) mathematica ‘mathematical (art)’, from Greek mathēmatikē (tekhnē), from the base of manthanein ‘learn’.
It's not used as a plural *now* but there are other words like that.
(Score: 2) by Immerman on Tuesday July 07 2020, @02:08PM (1 child)
"Math" is not a word either - the word is mathematics, and there are two common ways to shorten it "math" and "maths". And "maths" is the preferred form in English, the native language of England. I believe "math" is preferred only in the the bastardized American version of the language.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @09:09PM
Math is actually the older of the two contractions.
http://www.word-detective.com/2011/05/math-vs-maths/ [word-detective.com]