What does it mean by the pythagorean triplet
Answers
Pythagorean Triplet :
A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:
a^2 + b^2 = c^2
Example: The smallest Pythagorean Triple is 3, 4 and 5.
Let's check it:
3^2 + 4^2 = 5^2
Calculating this becomes:
9 + 16 = 25
Yes, it is a Pythagorean Triple!
NOTE : When a triangle's sides are a Pythagorean Triple it is a right angled triangle.
pythagoras squares a^2 + b^2 = c^2
The Pythagorean Triple of 3, 4 and 5 makes a Right angled triangle .
Here are two more Pythagorean Triples:
1. 5, 12, 13 2. 9, 40, 41
5,12,13 Triangle 9,40,41 Triangle
52 + 122 = 132 92 + 402 = 412
25 + 144 = 169 (try it yourself)
And each triangle has a right angle!
Here is a list of the first few Pythagorean Triples (not including "scaled up" versions mentioned below):
(3,4,5) (5,12,13) (7,24,25).
(8,15,17). (9,40,41) (11,60,61)
(12,35,37) (13,84,85). (15,112,113)
(16,63,65) (17,144,145) (19,180,181)
(20,21,29) (20,99,101). (21,220,221)
(23,264,265). (24,143,145) (25,312,313)
(27,364,365) (28,45,53). (28,195,197)
(29,420,421). (31,480,481) (32,255,257)
(33,56,65) ( 33,544,545) (35,612,613)
(36,77,85). (36,323,325) (37,684,685) ...
infinitely many more.