Pythagorean Triangle with (One leg of right triangle p2-q2)-2 Area/Perimeter = α3 - β3

Authors

  • S. Sriram  Assistant Professor, P. G & Research Department of Mathematics, National College, Tiruchirappalli, Tamilnadu, India
  • P. Veeramallan  Post Graduate Assistant in Mathematics,GHSS, Perumangalam, Villupuram, Tamilnadu, India

Keywords:

Pythagorean Triangle, Ratio (Area/Perimeter) As Difference Of Two Cubic Integers.

Abstract

Pattern of Pythagorean Triangle for each of which, the ratio (One leg of right triangle p2-q2)-2 Area/Perimetermay be expressed as the difference to two cubes as integers. A few interesting relations are also given.

References

  1. Dicksen, L.E., History of the theory of numbers, Vol. II, Chelsea Publishing Company, New York (1952).
  2. Smith, D.E., History of Mathematics, Vol. I and II, Dover Publications, New York (1953).
  3. Boyer, Carl, B. and Merzbach, U.T.A.C., A History of Mathematics, John Wiley and Sons (1989).
  4. Akituro, Nishi, A method of obtaining Pythagorean Triples, Amer. Math. Monthly, Vol. 94, No. 9, 869-871 (1987).
  5. Albert H. Beiler, "Recreations in the Theory of Numbers", Dover Publications, New York, 1963.
  6. B. Malik, "Basic Number Theory", Vikas Publishing House Pvt. Limited, New Delhi. 1998.
  7. J. Mordell, "Diophatine Equations", Academic Press, New York, 1969.
  8. G. Telang, "Number Theory", Tata McGraw-Hill Publishing Company, New Delhi, 1996.
  9. Thomas Koshy, "Elementary number Theory with Applications", Academic Press, 2005.
  10. Nagell, "Introduction to Number Theory", plencem, New York, 1969.
  11. Gopalan, M.A., Note on Integral Solutions of X2 +Y2 = Z2, ActaCienciaIndica, Vol. XXVII M, No. 4, 493 (2001)
  12. A. Gopalan and S. Leelavathi "Pythagorean Triangle with 2(Area / Perimeter) as a Cubic Integer", Bulletin of Pure and Applied Sciences, Vol. 27, No. E(2),2007, pp. 197-200.
  13. A. Gopalan and G. Janaki "Pythagorean Triangle with Area / Perimeter as a special polygonal number", Bulletin of Pure and Applied Sciences,Vol.27, No.E(2),2007, pp.393-402.
  14. A. Gopalan and S. Devibala, Pythagorean Triangle: A Treassure House, Proceeding of the KMA National Seminar on Algebra, Number Theory and Applications to Coding and Cryptanalysis, Little Flower College, Guruvayur, September 16-18, 2004
  15. A. Gopalan and S. Devibala, "Pythagorean Triangle with Triangular number as a leg", Impact J.Sci.Tech.vol.2(4),2008,pp.195-199..
  16. A. Gopalan and S. G.Janaki, "Pythagorean Triangle with Nasty number as a leg",Journal of Applied Mathematical Analysis and Appliations",vol.4(1-2),2008,pp.13-17.
  17. A. Gopalan and S. G.Janaki,"Pythagorean Triangle with Perimeter as a pentagonal number", AntarcticaJ.Math.,vol.5(2),2008,pp.15-18.
  18. A. Gopalan and G. Gnanam "Pythagorean Triangles and special polygonal numbers",International Journal of Mathematical Sciences vol.9(1-2),,2010,pp.211-215.
  19. A. Gopalan and G. G. Sangeetha, "Pythagorean Triangles with Perimeter as Triangular number",Global Journal of Applied Mathematics and Mathematical Sciences,vol.3(1-2), 2010,pp.93-97.
  20. A. Gopalan and B. Sivakami, "Pythagorean Triangle with Hypotenuse minus2(Area /Perimeter) as a Square Integer", Archimedes J.Math.,vol.2(2),2012, pp. 153-166.
  21. A. Gopalan and V. Geetha, "Pythagorean Triangle with Area / Perimeter as a special polygonal number", International Refereed Journal of Engineering and Science, vol.2(7),2013, pp.28-34.
  22. A. Gopalan and ManjuSomanath and K. Geetha, "Pythagorean Triangle with Area / Perimeter as a special polygonal number", IOSR-JM,vol.7(3),2013, pp. 52-62.
  23. A. Gopalan and ManjuSomanath and V. Sangeetha, "Pythagorean Triangles and pentagonal number", Cayley J.Math,vol.2(2),2013, pp.151-156.
  24. A. Gopalan and ManjuSomanath and V. Sangeetha, "Pythagorean Triangles and speial pyramidal numbers", IOSR-JM,vol.7(4),2013, pp. 21-22.
  25. Thirunavukkarasu and S. Sriram, "Pythagorean Triangle with Area / Perimeter as quartic integer", International Journal of Engineering and Innovative Technology (IJEIT),vol.3(7),2014, pp.100-102.
  26. M A. Gopalan and R. Anbuselvi, A Special Pythagorean Triangle, ActaCienciaIndica XXXI M, No. 1, p. 053, 2005.
  27. A. Gopalan and S. Devibala, On a Pythagorean Problem, ActaCienciaIndica, XXX II M, No. 4, p. 1451, 2006.
  28. Sriram, "Pythagorean Triangle with (one Leg of Right Triangle p^2-q^2 )- 2(area/perimeter)=αβ", International Journal of Engineering and Innovative Technology, IJEIT, vol. 6, Issue. 2, august2016.
  29. A. Gopalan and S. Leelavathi "Pythagorean Triangle with Area / Perimeter as a Square Integer", International Journal of Mathematics, Computer Sciences and Information Technology Vol. 1, No. 2, July-December 2008, pp. 199-204.
  30. A. Gopalan and J. Kaliga Rani, A Special Pythagorean Triangle, ActaCienciaIndica, XXX II M, No. 4, p. 1451, 2006.

International Journal of Scientific Research in Science, Engineering and Technology

Downloads

Published

2016-12-30

Issue

Volume 2, Issue 6, November-December-2016

Section

Research Articles

License

Copyright (c) IJSRSET

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
S. Sriram, P. Veeramallan "Pythagorean Triangle with (One leg of right triangle p2-q2)-2 Area/Perimeter = α3 - β3" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 2, Issue 6, pp.12-14, November-December-2016.