Series of Primitive Right-Angled Triangles

Martin W. Bredenkamp

doi:doi:10.11648/j.acm.20130202.15

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Series of Primitive Right-Angled Triangles

Martin W. Bredenkamp

Published in Applied and Computational Mathematics (Volume 2, Issue 2)

Published: 2 April 2013

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Abstract

From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle. This allows for the creation of a series of fractions that have as their limit an irrational number. Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed. Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well.

Published in	Applied and Computational Mathematics (Volume 2, Issue 2)
DOI	10.11648/j.acm.20130202.15
Page(s)	42-53
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Pythagorean Triple Series, Non-Pythagorean Right-Angled Triangle Limit, Rational Series With Irrational Limits

References

[1]	MW Bredenkamp, Pure and Applied Mathematics Journal, 2013, 2, 36-41.

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APA Style

Martin W. Bredenkamp. (2013). Series of Primitive Right-Angled Triangles. Applied and Computational Mathematics, 2(2), 42-53. https://doi.org/10.11648/j.acm.20130202.15

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ACS Style

Martin W. Bredenkamp. Series of Primitive Right-Angled Triangles. Appl. Comput. Math. 2013, 2(2), 42-53. doi: 10.11648/j.acm.20130202.15

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AMA Style

Martin W. Bredenkamp. Series of Primitive Right-Angled Triangles. Appl Comput Math. 2013;2(2):42-53. doi: 10.11648/j.acm.20130202.15

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@article{10.11648/j.acm.20130202.15,
  author = {Martin W. Bredenkamp},
  title = {Series of Primitive Right-Angled Triangles},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {42-53},
  doi = {10.11648/j.acm.20130202.15},
  url = {https://doi.org/10.11648/j.acm.20130202.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.15},
  abstract = {From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle.  This allows for the creation of a series of fractions that have as their limit an irrational number.  Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed.  Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well.},
 year = {2013}
}

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TY  - JOUR
T1  - Series of Primitive Right-Angled Triangles
AU  - Martin W. Bredenkamp
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.15
DO  - 10.11648/j.acm.20130202.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 42
EP  - 53
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.15
AB  - From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle.  This allows for the creation of a series of fractions that have as their limit an irrational number.  Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed.  Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well.
VL  - 2
IS  - 2
ER  -

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Author Information

Martin W. Bredenkamp

Department of Science, Asia-Pacific International University

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Plain Text BibTeX RIS

APA Style

Martin W. Bredenkamp. (2013). Series of Primitive Right-Angled Triangles. Applied and Computational Mathematics, 2(2), 42-53. https://doi.org/10.11648/j.acm.20130202.15

Copy | Download

ACS Style

Martin W. Bredenkamp. Series of Primitive Right-Angled Triangles. Appl. Comput. Math. 2013, 2(2), 42-53. doi: 10.11648/j.acm.20130202.15

Copy | Download

AMA Style

Martin W. Bredenkamp. Series of Primitive Right-Angled Triangles. Appl Comput Math. 2013;2(2):42-53. doi: 10.11648/j.acm.20130202.15

Copy | Download

@article{10.11648/j.acm.20130202.15,
  author = {Martin W. Bredenkamp},
  title = {Series of Primitive Right-Angled Triangles},
  journal = {Applied and Computational Mathematics},
  volume = {2},
  number = {2},
  pages = {42-53},
  doi = {10.11648/j.acm.20130202.15},
  url = {https://doi.org/10.11648/j.acm.20130202.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130202.15},
  abstract = {From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle.  This allows for the creation of a series of fractions that have as their limit an irrational number.  Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed.  Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Series of Primitive Right-Angled Triangles
AU  - Martin W. Bredenkamp
Y1  - 2013/04/02
PY  - 2013
N1  - https://doi.org/10.11648/j.acm.20130202.15
DO  - 10.11648/j.acm.20130202.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 42
EP  - 53
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20130202.15
AB  - From the infinite matrix of right-angled triangles, series of triangles are found that approach a right-angled triangle that has one irrational side such as the 45 triangle.  This allows for the creation of a series of fractions that have as their limit an irrational number.  Formulae for finding the next triangle in the triangle series, and thus the next fraction in the fraction series, are also developed.  Such a series can be found for the square root of every uneven number that is not a perfect square, and for those of some of the even numbers as well.
VL  - 2
IS  - 2
ER  -

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