From 3rd no. every no=2*previous no. +pre-previous number.

In case of pythagorean triplets where 2 numbers are consecutive, the 3rd number T3has pattern. T3(1) = (1²+4)/1 =5,T3(2)=(5²+4)/1=29, T3(3)=(29²+4)/5=169, T3(4) = (169²+4)/29 =985, so on with start up no. 5. Put 5 or 1 in start no., 4 in incre ,put the no.of iteration and click near c to get T(3).TRY with different start no. and incre as start no. -1 to find patterns.

*The radius of incircle of a pythagorean triangle is always a whole number.

*Gaussian Triplets-- If A, B, C are three Gaussian numbers such that A²+B²=C², then A, B and C are called Gaussian triplets. Gaussian numbers are complex no. of the form a±bi where a, b are real numbers and i is a complex number. Exa--(1+4i)² + (8-4i)² = (7-4i)²

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.