Pythagorean Triangle with Hypotenuse -4(Area/Perimeter)is 3 Times a Square Integer
M.A. Gopalan1, S. Vidhyalakshmi2, N. Thiruniraiselvi3
1Dr. M.A. Gopalan, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India.
2Dr. S. Vidhyalakshmi, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India.
3N. Thiruniraiselvi, Research Scholar, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India.
Manuscript received on April 28, 2015. | Revised Manuscript received on May 02, 2015. | Manuscript published on May 15, 2015. | PP: 1-5 | Volume-3 Issue-6, May 2015. | Retrieval Number: F0851053615/2015©BEIESP
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Abstract: We present infinity many Pythagorean triangles, where, in each, the hypotenuse -4(Area/Perimeter) is a square multiple of 3. A few numerical examples are presented. Also, a few interesting relations among the sides of the Pythagorean triangles are given. Further, by considering suitable linear combination among the generators of the Pythagorean triangles, Diophantine 3-tuples and special dio-3 tuples with suitable property are obtained.
Keywords: Area/perimeter, Pythagorean triangle, square integer.