MATRICES THAT DEFINE SERIES OF PYTHAGOREAN TRIPLES THAT HAVE A TRIANGLE WITH ONE IRRATIONAL SIDE AS LIMIT

Martin William Bredenkamp

Abstract


Making use of the universal set of Pythagorean triples, series of triples are defined where triple n + 1 is obtained by multiplying triple n with a specific 3 × 3 matrix. In terms of Pythagorean triangles, the shape of the limiting triangle in these series is a triangle with one of its sides having an irrational ratio with respect to the other sides. These specific matrices may be directly associated with the square roots of uneven positive integers (that are not perfect squares), and also some of the even positive integers since the limit of the powers of these matrices, applied to any 3 × 1 matrix of real numbers leads to a specific right-angled triangle that contains that square root as one of its sides.

Full Text:

PDF


DOI: http://dx.doi.org/10.19044/esj.2014.v10n10p%25p


European Scientific Journal (ESJ)

 

ISSN: 1857 - 7881 (Print)
ISSN: 1857 - 7431 (Online)

 

Contact: contact@eujournal.org

To make sure that you can receive messages from us, please add the 'eujournal.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.




Publisher: European Scientific Institute, ESI.
ESI cooperates with Universities and Academic Centres on 5 continents.