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#1 2012-12-15 09:27:20

21122012
Member
Registered: 2012-11-16
Posts: 278

Who knows a formula of Pythagorean numbers?

Who knows a formula on which it is possible to find everything Pythagorean numbers?

For example I want to learn all three with number 12:




"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#2 2012-12-15 09:39:03

bob bundy
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Registered: 2010-06-20
Posts: 6,466

Re: Who knows a formula of Pythagorean numbers?

hi 21122012

I would write 12^2 like this:

So you could choose factors P and Q so that PQ = 144 and find a and b.

eg

hint: a-b and a+b need the same parity ( both odd or both even )

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-12-15 10:50:16

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: Who knows a formula of Pythagorean numbers?

I didn't understand a thing!

Give so. I ask a question: how many you will be able to write on the formula of three for 24?




...

how many?


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#4 2012-12-15 11:07:10

bob bundy
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Registered: 2010-06-20
Posts: 6,466

Re: Who knows a formula of Pythagorean numbers?

and

are the same.

Find all the factors of 24^2 that have the same parity (two odd factors or two even factors) and solve

Then a^2 and b^2 will be the other two ? in the Pythagorean triple.

so

then

eg.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2012-12-15 13:14:34

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: Who knows a formula of Pythagorean numbers?

For example:

- is ONE;
- is TWO;
- is THREE;
...

You understand?

HOW MANY?

Last edited by 21122012 (2012-12-15 13:15:54)


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#6 2012-12-15 13:40:05

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,641

Re: Who knows a formula of Pythagorean numbers?

There are 7 of them.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#7 2012-12-15 14:24:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,600

Re: Who knows a formula of Pythagorean numbers?

I remember seeing a proof that all Pythagorean triplets are of the form

a-b, 2*sqrt(a*b), a+b

for natural a and b.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2012-12-15 14:27:48

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: Who knows a formula of Pythagorean numbers?

You used a formula or the computer program?


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#9 2012-12-15 14:30:53

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,641

Re: Who knows a formula of Pythagorean numbers?

Computer program. But it is easy to generate 3 of them from a formula. The rest I am still working on.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#10 2012-12-15 14:31:30

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: Who knows a formula of Pythagorean numbers?

anonimnystefy wrote:

I remember seeing a proof that all Pythagorean triplets are of the form

a-b, 2*sqrt(a*b), a+b

for natural a and b.

No!

Yes?

You look here. Here important intermediate question: As the formula

mean if an indicator

of a general view will look: n? !


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#11 2012-12-15 14:39:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,641

Re: Who knows a formula of Pythagorean numbers?

Do you already have an answer to the problem?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#12 2012-12-15 14:50:39

21122012
Member
Registered: 2012-11-16
Posts: 278

Re: Who knows a formula of Pythagorean numbers?

bobbym wrote:

Do you already have an answer to the problem?

I don't want to answer at once. And that will turn out as in other topic. All will be silent or it is simple to speak: "I don't agree" but won't reason and prove disagreement. I want to arrive now more cunning. That you gradually reached before that I want to tell.

Then you won't be able to tell that you aren't right!


"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

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#13 2012-12-15 14:56:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,641

Re: Who knows a formula of Pythagorean numbers?

This thread does not belong in help me. Help me is for people who need help. Usually they need it right away. If you already have the answer and are posing a puzzle then you should post in puzzles and games or exercises.

I have moved it.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Online

#14 2012-12-16 11:46:00

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Who knows a formula of Pythagorean numbers?

(a²+b², a²-b², 2ab) with positive integers a and b with a>b are all Pythagorean triples. 
If (x,y,z) is a Pythagorean triple then so is (kx,ky,kz) for integers k>1.  And if I recall
correctly all Pythagorean triples can be obtained from these formulas.

Most folks have trouble coming up with more than 2 or 3 Pythagorean triples.  I have
taught students to come up with many more by simply:
  1) Think of a positive integer >1.
  2)  Double it.  That's the 1st of the triple.
  3)  Square the number obtained in step 1)
  4)  Add one to that square.  That's the 2nd of the triple.
  5)  Subtract one from that square.  That's the 3rd of the triple.

Of course that's just the triple above with b set equal to 1 and a>1. smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#15 2012-12-16 11:50:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,600

Re: Who knows a formula of Pythagorean numbers?

That will not get you Pythagorean triples, noelevans.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#16 2012-12-16 17:39:33

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: Who knows a formula of Pythagorean numbers?

Hi stefy,

noelevans' method seems to work fine.

Using his method, here are some examples:- 

1)    6;   2)    6*2=12;   3&4)   6²+1=  37;   5)    6²-1= 35:  12² + 35² = 37²
1)  12;   2)  12*2=24;   3&4)  12²+1=145;   5)  12²-1=143:  24²+143²=145²
1)  17;   2)  17*2=34;   3&4)  17²+1=290;   5)  17²-1=288:  34²+288²=290²
1)  25;   2)  25*2=50;   3&4)  25²+1=626;   5)  25²-1=624:  50²+624²=626²
1)  29;   2)  29*2=58;   3&4)  29²+1=842;   5)  29²-1=840:  58²+840²=842²

The bold-font result is in the order I normally write the equation.

Last edited by phrontister (2012-12-16 18:23:07)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#17 2012-12-16 21:53:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,600

Re: Who knows a formula of Pythagorean numbers?

This is exactly the reason why I shouldn't post late at night! My brain doesn't work!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#18 2012-12-17 18:17:20

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Who knows a formula of Pythagorean numbers?

Join the club!  Mine doesn't work well late at night either. smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#19 2012-12-17 19:44:36

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,466

Re: Who knows a formula of Pythagorean numbers?

hi noelevans and Stefy,

I'm the opposite.  I don't reckon to be fully awake until 10am, and my brain is positively buzzing at 11pm.

21122012 wrote:

I don't want to answer at once. And that will turn out as in other topic. All will be silent or it is simple to speak: "I don't agree" but won't reason and prove disagreement. I want to arrive now more cunning. That you gradually reached before that I want to tell.

I'm guessing that to do what you want, you have found a formula for prime numbers.  :?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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