*In Pythagorean triplets, long side
is always odd number, the other 2 sides-one even and the other odd. If the
last digit of
2 short sides is (0,1),(0,9)--> long side is (1 or 9).
2 short sides is (3,4),(3,6),(7,4),(7,6)--> long side is (5).
2 short sides is (5,2),(5,8)--> long side is (3 or 7).
* If product of 2 short sides which are integers is divided by the long
side which is also an integer and the result is an integer, then the
perpendicular from the right angle on hypotenuse will be an integer which
does not happen. The perpendicular divides the long side in the ratio,
say a & b, then a = square of 1 shortside/ longside and b= square of other
short side/ long side; * Some of the irreducible Pythagorean triplets are
(3,4,5),(5,12,13),(8,15,17),(7,25,29),(20,21,29),(12,35,37),(9,40,41),(28,45,53),(11,60,61),(16,63,65),(33,56,65),(48,55,73),(13,84,85),(36,77,85),(39,80,89),(20,99,101),(65,72,97),(15,112,113),(60,91,109),(45,108,117),(44,117,125),(17,144,145),(24,143,145),(88,105,137),(51,140,149),(19,180,181),(52,165,173)
with total 12,30,40,56,70,84,90,126,132,144,154,
176,182,198,208,220,234,240,260, 270,286,306, 312,330 ,340,380,390
respectively in between 1-400. Those triplets in red have the same long side
but different short sides. The long side can be a diameter of a circle and
the 2 short sides are integer valued short sides meeting at a point on the
circumference subtending a right angle. All other short sides meeting at a
point on the circumference are not of integer value. * Sum of Pythagorean triplets is
always even number. |