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Series of Primitive Right-Angled Triangles

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.
Cite This Article
  • 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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    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
  • Department of Science, Asia-Pacific International University

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