Pythagorean triplets: has my work been done before?












0














I've been writing a paper about generating Pythagorean triplets using functions I have not found online or in the books I've read. I believe my functions are new. They generate triplets to order and they allow me to find matching sides, perimeters, areas, and even tiles and pyramids composed of dissimilar triplets. I would like to know if I'm wasting time or if there are credits I should give.
The first function is: $$A=(2n-1)^2+2(2n-1)k:n,kinmathbb{N}$$ where $n$ is a $set$ of triplets and $k$ is the ordinal $member$ of $Set_n$. All of the other functions are $derived$ from this one. Has anybody seen this function before?



Here is a sample from which I developed the functions for A,B,C. We can see that these triplets can be viewed as members of distinct sets. (The GCD of every triplet of a given set is the square of the same odd number as are the differences between values of B and C. Also, the increment between values of $A$ are the same in each set.) This is why $A(n,k)$ is what it is. The question remains: has anyone seen this function elsewhere or has anyone ever found set groupings of this sort?



$Set_n$ $hspace{12mm}$triplet1$hspace{10mm}$triplet2$hspace{10mm}$triplet3$hspace{10mm}$triplet4



Set_1$hspace{10mm}$3,4,5$hspace{15mm}$5,12,13$hspace{10mm}$7,24,25$hspace{10mm}$9,40,41



Set_2$hspace{10mm}$15,8,17.$hspace{10mm}$21,20,29$hspace{7mm}$27,36,45$hspace{8mm}$33,56,65



Set_3$hspace{10mm}$35,12,37$hspace{9mm}$45,28,53$hspace{7mm}$55,48,73$hspace{8mm}$65,72,97



Set_4$hspace{10mm}$63,16,65$hspace{8mm}$77,36,85$hspace{6mm}$91,60,109$hspace{6mm}$105,88,137






reference-request pythagorean-triples







share|cite|improve this question




















  • 2




    I don't think that the functions are new, because we know exactly how Pythagorean triples are generated. But perhaps I am wrong, then you would find out by googling (searching) yourself - try it.
    – Dietrich Burde
    Jan 1 at 19:09






  • 5




    Why don't you upload your work on the ArXiv? Then other people can check your work and there is a verifiable way to show that it is your work.
    – Sandeep Silwal
    Jan 1 at 19:11






  • 2




    arxiv.org is a website used by professional mathematicians, physicists, and computer scientists to upload their papers before they submit to a journal. It is a way to announce to the community their work and is a very good research tool. For example: arxiv.org/abs/1509.05363 is an example paper by Terence Tao
    – Sandeep Silwal
    Jan 1 at 19:20






  • 1




    In future, please do not use the reference-request tag on its own. It should be accompanied by at least one tag describing the topic at hand.
    – Shaun
    Jan 1 at 19:52








  • 1




    You give an equation for $A$ in terms of naturals $n,k$ which can be computed. In the next line you say $n$ is a set of triplets. I think you have really grouped the triplets into sets, $n$ is an index to pick out a set, and $k$ is the index within the set. This is reminiscent of Cantor's pairing function.
    – Ross Millikan
    Jan 1 at 20:32
















0














I've been writing a paper about generating Pythagorean triplets using functions I have not found online or in the books I've read. I believe my functions are new. They generate triplets to order and they allow me to find matching sides, perimeters, areas, and even tiles and pyramids composed of dissimilar triplets. I would like to know if I'm wasting time or if there are credits I should give.
The first function is: $$A=(2n-1)^2+2(2n-1)k:n,kinmathbb{N}$$ where $n$ is a $set$ of triplets and $k$ is the ordinal $member$ of $Set_n$. All of the other functions are $derived$ from this one. Has anybody seen this function before?



Here is a sample from which I developed the functions for A,B,C. We can see that these triplets can be viewed as members of distinct sets. (The GCD of every triplet of a given set is the square of the same odd number as are the differences between values of B and C. Also, the increment between values of $A$ are the same in each set.) This is why $A(n,k)$ is what it is. The question remains: has anyone seen this function elsewhere or has anyone ever found set groupings of this sort?



$Set_n$ $hspace{12mm}$triplet1$hspace{10mm}$triplet2$hspace{10mm}$triplet3$hspace{10mm}$triplet4



Set_1$hspace{10mm}$3,4,5$hspace{15mm}$5,12,13$hspace{10mm}$7,24,25$hspace{10mm}$9,40,41



Set_2$hspace{10mm}$15,8,17.$hspace{10mm}$21,20,29$hspace{7mm}$27,36,45$hspace{8mm}$33,56,65



Set_3$hspace{10mm}$35,12,37$hspace{9mm}$45,28,53$hspace{7mm}$55,48,73$hspace{8mm}$65,72,97



Set_4$hspace{10mm}$63,16,65$hspace{8mm}$77,36,85$hspace{6mm}$91,60,109$hspace{6mm}$105,88,137






reference-request pythagorean-triples







share|cite|improve this question




















  • 2




    I don't think that the functions are new, because we know exactly how Pythagorean triples are generated. But perhaps I am wrong, then you would find out by googling (searching) yourself - try it.
    – Dietrich Burde
    Jan 1 at 19:09






  • 5




    Why don't you upload your work on the ArXiv? Then other people can check your work and there is a verifiable way to show that it is your work.
    – Sandeep Silwal
    Jan 1 at 19:11






  • 2




    arxiv.org is a website used by professional mathematicians, physicists, and computer scientists to upload their papers before they submit to a journal. It is a way to announce to the community their work and is a very good research tool. For example: arxiv.org/abs/1509.05363 is an example paper by Terence Tao
    – Sandeep Silwal
    Jan 1 at 19:20






  • 1




    In future, please do not use the reference-request tag on its own. It should be accompanied by at least one tag describing the topic at hand.
    – Shaun
    Jan 1 at 19:52








  • 1




    You give an equation for $A$ in terms of naturals $n,k$ which can be computed. In the next line you say $n$ is a set of triplets. I think you have really grouped the triplets into sets, $n$ is an index to pick out a set, and $k$ is the index within the set. This is reminiscent of Cantor's pairing function.
    – Ross Millikan
    Jan 1 at 20:32














0












0








0







I've been writing a paper about generating Pythagorean triplets using functions I have not found online or in the books I've read. I believe my functions are new. They generate triplets to order and they allow me to find matching sides, perimeters, areas, and even tiles and pyramids composed of dissimilar triplets. I would like to know if I'm wasting time or if there are credits I should give.
The first function is: $$A=(2n-1)^2+2(2n-1)k:n,kinmathbb{N}$$ where $n$ is a $set$ of triplets and $k$ is the ordinal $member$ of $Set_n$. All of the other functions are $derived$ from this one. Has anybody seen this function before?



Here is a sample from which I developed the functions for A,B,C. We can see that these triplets can be viewed as members of distinct sets. (The GCD of every triplet of a given set is the square of the same odd number as are the differences between values of B and C. Also, the increment between values of $A$ are the same in each set.) This is why $A(n,k)$ is what it is. The question remains: has anyone seen this function elsewhere or has anyone ever found set groupings of this sort?



$Set_n$ $hspace{12mm}$triplet1$hspace{10mm}$triplet2$hspace{10mm}$triplet3$hspace{10mm}$triplet4



Set_1$hspace{10mm}$3,4,5$hspace{15mm}$5,12,13$hspace{10mm}$7,24,25$hspace{10mm}$9,40,41



Set_2$hspace{10mm}$15,8,17.$hspace{10mm}$21,20,29$hspace{7mm}$27,36,45$hspace{8mm}$33,56,65



Set_3$hspace{10mm}$35,12,37$hspace{9mm}$45,28,53$hspace{7mm}$55,48,73$hspace{8mm}$65,72,97



Set_4$hspace{10mm}$63,16,65$hspace{8mm}$77,36,85$hspace{6mm}$91,60,109$hspace{6mm}$105,88,137






reference-request pythagorean-triples







share|cite|improve this question















I've been writing a paper about generating Pythagorean triplets using functions I have not found online or in the books I've read. I believe my functions are new. They generate triplets to order and they allow me to find matching sides, perimeters, areas, and even tiles and pyramids composed of dissimilar triplets. I would like to know if I'm wasting time or if there are credits I should give.
The first function is: $$A=(2n-1)^2+2(2n-1)k:n,kinmathbb{N}$$ where $n$ is a $set$ of triplets and $k$ is the ordinal $member$ of $Set_n$. All of the other functions are $derived$ from this one. Has anybody seen this function before?



Here is a sample from which I developed the functions for A,B,C. We can see that these triplets can be viewed as members of distinct sets. (The GCD of every triplet of a given set is the square of the same odd number as are the differences between values of B and C. Also, the increment between values of $A$ are the same in each set.) This is why $A(n,k)$ is what it is. The question remains: has anyone seen this function elsewhere or has anyone ever found set groupings of this sort?



$Set_n$ $hspace{12mm}$triplet1$hspace{10mm}$triplet2$hspace{10mm}$triplet3$hspace{10mm}$triplet4



Set_1$hspace{10mm}$3,4,5$hspace{15mm}$5,12,13$hspace{10mm}$7,24,25$hspace{10mm}$9,40,41



Set_2$hspace{10mm}$15,8,17.$hspace{10mm}$21,20,29$hspace{7mm}$27,36,45$hspace{8mm}$33,56,65



Set_3$hspace{10mm}$35,12,37$hspace{9mm}$45,28,53$hspace{7mm}$55,48,73$hspace{8mm}$65,72,97



Set_4$hspace{10mm}$63,16,65$hspace{8mm}$77,36,85$hspace{6mm}$91,60,109$hspace{6mm}$105,88,137






reference-request pythagorean-triples




reference-request pythagorean-triples






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago

























asked Jan 1 at 19:06









poetasis

328117




328117








  • 2




    I don't think that the functions are new, because we know exactly how Pythagorean triples are generated. But perhaps I am wrong, then you would find out by googling (searching) yourself - try it.
    – Dietrich Burde
    Jan 1 at 19:09






  • 5




    Why don't you upload your work on the ArXiv? Then other people can check your work and there is a verifiable way to show that it is your work.
    – Sandeep Silwal
    Jan 1 at 19:11






  • 2




    arxiv.org is a website used by professional mathematicians, physicists, and computer scientists to upload their papers before they submit to a journal. It is a way to announce to the community their work and is a very good research tool. For example: arxiv.org/abs/1509.05363 is an example paper by Terence Tao
    – Sandeep Silwal
    Jan 1 at 19:20






  • 1




    In future, please do not use the reference-request tag on its own. It should be accompanied by at least one tag describing the topic at hand.
    – Shaun
    Jan 1 at 19:52








  • 1




    You give an equation for $A$ in terms of naturals $n,k$ which can be computed. In the next line you say $n$ is a set of triplets. I think you have really grouped the triplets into sets, $n$ is an index to pick out a set, and $k$ is the index within the set. This is reminiscent of Cantor's pairing function.
    – Ross Millikan
    Jan 1 at 20:32














  • 2




    I don't think that the functions are new, because we know exactly how Pythagorean triples are generated. But perhaps I am wrong, then you would find out by googling (searching) yourself - try it.
    – Dietrich Burde
    Jan 1 at 19:09






  • 5




    Why don't you upload your work on the ArXiv? Then other people can check your work and there is a verifiable way to show that it is your work.
    – Sandeep Silwal
    Jan 1 at 19:11






  • 2




    arxiv.org is a website used by professional mathematicians, physicists, and computer scientists to upload their papers before they submit to a journal. It is a way to announce to the community their work and is a very good research tool. For example: arxiv.org/abs/1509.05363 is an example paper by Terence Tao
    – Sandeep Silwal
    Jan 1 at 19:20






  • 1




    In future, please do not use the reference-request tag on its own. It should be accompanied by at least one tag describing the topic at hand.
    – Shaun
    Jan 1 at 19:52








  • 1




    You give an equation for $A$ in terms of naturals $n,k$ which can be computed. In the next line you say $n$ is a set of triplets. I think you have really grouped the triplets into sets, $n$ is an index to pick out a set, and $k$ is the index within the set. This is reminiscent of Cantor's pairing function.
    – Ross Millikan
    Jan 1 at 20:32








2




2




I don't think that the functions are new, because we know exactly how Pythagorean triples are generated. But perhaps I am wrong, then you would find out by googling (searching) yourself - try it.
– Dietrich Burde
Jan 1 at 19:09




I don't think that the functions are new, because we know exactly how Pythagorean triples are generated. But perhaps I am wrong, then you would find out by googling (searching) yourself - try it.
– Dietrich Burde
Jan 1 at 19:09




5




5




Why don't you upload your work on the ArXiv? Then other people can check your work and there is a verifiable way to show that it is your work.
– Sandeep Silwal
Jan 1 at 19:11




Why don't you upload your work on the ArXiv? Then other people can check your work and there is a verifiable way to show that it is your work.
– Sandeep Silwal
Jan 1 at 19:11




2




2




arxiv.org is a website used by professional mathematicians, physicists, and computer scientists to upload their papers before they submit to a journal. It is a way to announce to the community their work and is a very good research tool. For example: arxiv.org/abs/1509.05363 is an example paper by Terence Tao
– Sandeep Silwal
Jan 1 at 19:20




arxiv.org is a website used by professional mathematicians, physicists, and computer scientists to upload their papers before they submit to a journal. It is a way to announce to the community their work and is a very good research tool. For example: arxiv.org/abs/1509.05363 is an example paper by Terence Tao
– Sandeep Silwal
Jan 1 at 19:20




1




1




In future, please do not use the reference-request tag on its own. It should be accompanied by at least one tag describing the topic at hand.
– Shaun
Jan 1 at 19:52






In future, please do not use the reference-request tag on its own. It should be accompanied by at least one tag describing the topic at hand.
– Shaun
Jan 1 at 19:52






1




1




You give an equation for $A$ in terms of naturals $n,k$ which can be computed. In the next line you say $n$ is a set of triplets. I think you have really grouped the triplets into sets, $n$ is an index to pick out a set, and $k$ is the index within the set. This is reminiscent of Cantor's pairing function.
– Ross Millikan
Jan 1 at 20:32




You give an equation for $A$ in terms of naturals $n,k$ which can be computed. In the next line you say $n$ is a set of triplets. I think you have really grouped the triplets into sets, $n$ is an index to pick out a set, and $k$ is the index within the set. This is reminiscent of Cantor's pairing function.
– Ross Millikan
Jan 1 at 20:32










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