if A=a and B=b that is the only integer solution (other solutions exist on the comples plane eg: A=iB, also B=iA)
theres a few more solutions if you allow
a =/= A and b =/= B you get A=B=c (and possibly other solutions?) but this is usenet and the mixed case may be a typographic error.
-- ?? 100% natural --- news://freenews.netfront.net/ - complaints: news@netfront.net ---
How good are *you* at working out the correct answers?
This set of physics problems that will challenge even the brightest students and for that matter most high school physics teachers.
When I was at school "Physics is Fun" series were newly published and reasonably priced - especially if you had prize money to spend. They are a bit dated now and have become collectors items with insane prices.
ISTR Series of four books covering most of high school physics.
Working through the Martin Gardener series of books taken from his Mathematical Games column in SciAm is likely to be more rewarding.
Or a decent undergraduate text in whichever branch of physics he is most interested in. If you make it too much like hard work then his interest in the subject can easily be killed off at this stage.
He is probably best off borrowing books from your local library until he finds one that really catches his interest.
-- Regards, Martin Brown
I forgot to exclude a=b=0 in the problem statement although we normally allowed that option as a first try
But there is another solution with a, b, A, B != 0
Because the OP is a cross posting clueless *MORON*.
-- Regards, Martin Brown
probably you should have said positive integers at the start.
anyway:
a,b,A,B
5,5 (and more variations on Pythogaras triangle hypotenuse)1,7 and probably more like that too, certainly multiples of it.
-- ?? 100% natural --- news://freenews.netfront.net/ - complaints: news@netfront.net ---
I don't agree. I often delve into areas I have no specific knowledge in and then once I run into my limitations, seek information from other sources. At that point I have questions I want answered. When I find the answers I remember them. You can call it guessing, but the point is they learned the problem first, then learned the solution, rather than just being spoon fed lessons to be regurgitated at a later date. Do you really not see the utility of this?
I don't follow what you are saying here. Did you give her the gift card or was that in class? Are you saying that is good or bad?
Oh, you are in the classroom watching it all first hand?
Educators are left nut cases, or just the ones who promote anything you don't like?
Exactly. That's the problem, you have no respect for teachers even though you don't understand their methods.
You sound like Larkin now. But this has *nothing* to do with teaching.
Again, *nothing* to do with teaching.
*Nothing* to do with teaching.
So you acknowledge that you have learned *nothing* about teaching?!
Unlike you, teachers are all educated in *teaching* and are accredited in teaching. What are your qualifications again? Oh yeah, your qualifications are all in being *taught* by *teacher*.
I think you must be many decades older than myself. You sound like a grandparent... no you sound like *all* grandparents through history.
Yes, and your level of disrespect for others continues. You don't get that your critera for others is of no interest to the rest of the world.
So you have a huge ego. That doesn't mean you ar equalified to judge teachers.
-- Rick
Not always in the US.
Have to agree with him on this, despite his political views.
But i know the results.
My daughter graduated #2 (should have been #1 including course difficulties) in high school. 750+ SAT, 4s and 5s ACT. She is the top student by US standard, but failing some beginning courses at UCLA, where she is competing with international students who are much better prepared. She might be OK after repeating some classes, but that show you the current US educational system. Their (my son and daughter) high school is supposed to be a good school relative to others, but absolutely failing to prepare students for college. SAT and ACT are not too useful indicators either.
When i ask them to study college level materials like most international students. The answer is: My school is not teaching this stuff, why should we learn that.
You can not "learn" such a problem by guessing. You "learn" a problem by understanding how a solution is developed. That kind of problem _does_not_belong_ in a 6th grade class.
The teacher gave her the gift card.
I'm unsure. I am somewhat Pavlovian >:-}
But the problem has no business in 6th grade.
Of course not. But you have no clue how tight-knit our family is.
Teachers shouldn't be "promoting" ANY philosophy, pro or con, religion or "lifestyle" or politics... that's strictly a parent's job. Teachers should stick strictly to teaching Reading/Writing/'rithmetic, as the old saw goes. If they promote ANY philosophy they should be fired.
You are apparently of that elitist class who think teachers know better than parents what is good for their child.
They don't, and the day of retribution is coming.
DOUBLE Bwahahahahaha!
I have no respect for teachers who do other than teach. I blame administrators and school boards for curriculum, and that speeding thru courses beats rote.
It simply means I can run circles around you in math :-)
You said I was a "lay person". Clearly I'm not.
You said I was a "lay person". Clearly I'm not.
I have (very successfully) taught seminars in Integrated Circuit Design for more years than you probably are old.
Teaching is a union. I offered to teach a technician-level course at Scottsdale Community College for FREE (the course had been dropped because they had no instructor). I was denied because I didn't have a "teacher's certificate". Teaching is a union that must be busted.
I can kick your ass in math or circuit design any day of the year, grandparent or not.
Wrong! I am qualified because I have a huge math, science and engineering background... because M.I.T. teaches undergrad to a level exceeding what most universities offer as graduate level courses. (And the ASU Physics level was just plain JUVENILE.)
Rickman, I have authorized your graduation to the rank of butt-buddy. Bye >:-} ...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
I should perhaps have said non-zero but it was normal not to bother.
The even powers mean that positive or negative makes no difference.
Anyone that didn't spot a=b=A=B=0 as a solution would fail immediately.
Valid concrete examples I grant you.
The final problem statement is for given a,b,c with
a^2 + b^2 = c^2
find algebraic expressions for A,B
s.t A^2 + B^2 = 2c^2
-- Regards, Martin Brown
I wasn't sure how you wanted to define the relationship between a,b and A,B, but if that is the only thing that relates them, and you just want A,B in terms of a,b, then...
A^2 + B^2 = 2(a^2 + b^2)
...and simplify, solving for A and B.
Am I misunderstanding the question again, or are you really just asking for a restatement of that equation with A and B isolated?
Maybe I forgot how to read math books, but I used to understand the questions at least, a long time ago.
-- Reply in group, but if emailing remove the last word.
It's that "new math" >:-} ...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
I learned with new math. It seems like anybody with a deep understanding would prefer it since it uses place value logically. Don't you think so?
-- Reply in group, but if emailing remove the last word.
Of course. I agree wholeheartedly! ...Jim Thompson
-- | James E.Thompson | mens | | Analog Innovations | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at
You have one equation and two unknowns. How do you propose to do that?
The algebraic solution is in the form
A = F(a,b) B = G(a,b)
Where A,B,a,b are all integers with some of them non-zero. In the general case they are all non-zero. Your task is to find the functions F(), G().
There isn't a lot of math involved. This is more of a puzzle. Only basic high school algebra is required.
-- Regards, Martin Brown
No. It is actually very old math, but it does require some innate mathematical ability to see the correct solution.
How someone approaches this problem is very informative at interview even if they cannot immediately see the right answer.
A much nastier Victorian one is construct with rule and compasses the triangle specified by two sides and the radius of the inscribed circle.
-- Regards, Martin Brown
functions?
F(a,b) = sqrt(a^2+b^2) G=F that seems way too easy
-- ?? 100% natural --- news://freenews.netfront.net/ - complaints: news@netfront.net ---
sqrt(a^2+b^2) isn't an integer except in a handful of special cases.
There is a closed form exact algebraic solution for all a,b.
-- Regards, Martin Brown
.
Hi Martin, I assume you have heard of the "back of the envelope" column written by Ed Purcell for AJP back in the 80's. Here's a web link, if not.
Good fun!
George H.
That I'm OK with.
But you can't "reason" your way to a numerical answer. You can reason that the flat piece of cardboard has no volume, and that cutting away all the cardboard yields no volume. But you have to plot it to find the maximum.
As soon as you state "integers" it becomes a guessing game. I "guess" the engineer in me frowns on guessing.
I took the exam and was admitted to Mensa (at age 30), but most of the exam questions were guessing.
Yep. I've already ordered several of the recommended books to make sure she has a solid background in Algebra.
I've "unamused" a number of teachers along the way.
"In my day" we had Algebra, Plane Geometry, Trigonometry and Solid Geometry in High School. My first exposure to Calculus was my Freshman year at M.I.T. By then it was easy for me to understand. I ended up taking 6 semesters of Calculus... all the way up to Tensors.
Modern "education" seems to think quantity is better than quality... just because you've taken a course labeled "Calculus" makes everything all marvelous.
She's up to it. The reason she's visiting us this summer is that we pay her way every year to Phoenix Valley Youth Theater Summer Camp. She's been three years now... and has managed to be the star in their final performance every time. She's quite the thespian and she's an honor student... in spite of my fuming over the teaching methods.
I'm a master of those games... I still remember how to construct a pentagon with compass and straight-edge ;-)
Certainly! Make it fun, and you don't ever have to "work". I've never worked a day in my life ;-)
It's not. Just to circuit groups. ...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
Hmm, Well in a few days will you post it. I can only get there by guessing.
So just picking Pythagorean triples (a,b,c) 3,4,5; A=1 and B=7 works (as Jasen said.) Then for 5,12,13; A=7 and B=17 works. But that?s the end of the line for simple triples that I know.
Maybe I'm missing the obvious, but I see no closed-form solution as soon as you say "integer"... you have to guess. ...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |
I love to cook with wine. Sometimes I even put it in the food.
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