Who knows a formula of Pythagorean numbers?

21122012 · 2012-12-15 09:27:20

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:

Bob · 2012-12-15 09:39:03

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

21122012 · 2012-12-15 10:50:16

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?

Bob · 2012-12-15 11:07:10

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

21122012 · 2012-12-15 13:14:34

For example:

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

You understand?

HOW MANY?

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

bobbym · 2012-12-15 13:40:05

There are 7 of them.

anonimnystefy · 2012-12-15 14:24:50

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.

21122012 · 2012-12-15 14:27:48

You used a formula or the computer program?

bobbym · 2012-12-15 14:30:53

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

21122012 · 2012-12-15 14:31:30

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? !

bobbym · 2012-12-15 14:39:48

Do you already have an answer to the problem?

21122012 · 2012-12-15 14:50:39

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!

bobbym · 2012-12-15 14:56:45

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.

noelevans · 2012-12-16 11:46:00

(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.

anonimnystefy · 2012-12-16 11:50:39

That will not get you Pythagorean triples, noelevans.

phrontister · 2012-12-16 17:39:33

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)

anonimnystefy · 2012-12-16 21:53:56

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

noelevans · 2012-12-17 18:17:20

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

Bob · 2012-12-17 19:44:36

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

Math Is Fun Forum

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

Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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

Re: Who knows a formula of Pythagorean numbers?

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