About Lesson
Pythagorean Triplets
A Pythagorean triplet consists of three positive integers (a, b, c) that satisfy the equation:
a² + b² = c²
Examples of Pythagorean Triplets
-
(3, 4, 5) → 3² + 4² = 9 + 16 = 25 = 5²
-
(5, 12, 13) → 5² + 12² = 25 + 144 = 169 = 13²
-
(8, 15, 17) → 8² + 15² = 64 + 225 = 289 = 17²
Generating Pythagorean Triplets
A simple formula to generate triplets:
-
If n is a natural number:
-
(2n, n² – 1, n² + 1) forms a Pythagorean triplet.
-
For example, if n = 2:
-
(2 × 2, 2² – 1, 2² + 1) = (4, 3, 5)
If n = 3:
-
(2 × 3, 3² – 1, 3² + 1) = (6, 8, 10)
This pattern helps in finding infinite Pythagorean triplets.