Series of Primitive Right-Angled Triangles
Applied and Computational Mathematics
Volume 2, Issue 2, April 2013, Pages: 42-53
Received: Mar. 11, 2013;
Published: Apr. 2, 2013
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Martin W. Bredenkamp, Department of Science, Asia-Pacific International University; PO Box 4, MuakLek, Saraburi Province, 18180, Thailand
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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.
Pythagorean Triple Series, Non-Pythagorean Right-Angled Triangle Limit, Rational Series With Irrational Limits
To cite this article
Martin W. Bredenkamp,
Series of Primitive Right-Angled Triangles, Applied and Computational Mathematics.
Vol. 2, No. 2,
2013, pp. 42-53.
MW Bredenkamp, Pure and Applied Mathematics Journal, 2013, 2, 36-41.