Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2, representing the sides of a right-angled triangle. In this context, ‘a’ represents the length of the perpendicular side, ‘b’ signifies the length of the base, and ‘c’ corresponds to the length of the hypotenuse. The most renowned and compact triplets include (3, 4, 5), serving as a classic example illustrating this mathematical relationship.
Pythagoras, a renowned mathematician, held a deep fascination for mathematics, science, and philosophy. Born around 570 BC in Greece, his enduring legacy lies in the discovery of a fundamental geometric principle, the Pythagorean Theorem.
This theorem pertains to right-angled triangles, specifically those with 90-degree angles. In such triangles, the side opposite the right angle, known as the hypotenuse, is symbolized as ‘r.’ Adjacent to the right angle, the shorter of the two sides is designated as ‘p.’ Pythagoras’ profound insight into the relationships between these sides continues to shape the foundation of geometry and mathematical understanding to this day.
Pythagorean Triples Example
Pythagorean Triples consist of three positive integers (a, b, c) that fulfill the Pythagorean Theorem, a^2 + b^2 = c^2, representing integer solutions to this mathematical relationship.
For example, consider the Pythagorean Triple (3, 4, 5):
When we compute it:
3^2 + 4^2 = 5^2
9 + 16 = 25
As a result, we identify 3, 4, and 5 as a Pythagorean Triple. While “triplets” is also acceptable, “triples” is the preferred term.
Pythagorean Triples List from 1 to 100
| Pythagorean Triples |
|---|
| (3, 4, 5) |
| (5, 12, 13) |
| (8, 15, 17) |
| (7, 24, 25) |
| (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) |
| (65, 72, 97) |
List of Pythagorean Triples Above 100
Here is a list of Pythagorean triples with values of ‘c’ greater than 100:
| Pythagorean Triples with c > 100 |
|---|
| (20, 99, 101) |
| (60, 91, 109) |
| (15, 112, 113) |
| (44, 117, 125) |
| (88, 105, 137) |
| (17, 144, 145) |
| (24, 143, 145) |
| (51, 140, 149) |
| (85, 132, 157) |
| (119, 120, 169) |
| (52, 165, 173) |
| (19, 180, 181) |
| (57, 176, 185) |
| (104, 153, 185) |
| (95, 168, 193) |
| (28, 195, 197) |
| (84, 187, 205) |
| (133, 156, 205) |
| (21, 220, 221) |
| (140, 171, 221) |
| (60, 221, 229) |
| (105, 208, 233) |
| (120, 209, 241) |
| (32, 255, 257) |
| (23, 264, 265) |
| (96, 247, 265) |
| (69, 260, 269) |
| (115, 252, 277) |
Pythagorean Triples List PDF
Download the list of Primitive Pythagorean Triples of numbers from 1 to 3000 from below link.
http://aleph0.clarku.edu/~djoyce/numbers/pyth.pdf
https://www.math.brown.edu/johsilve/frintdir/frintch2ch3.pdf
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