Pythagorean Triples
Three whole numbers a, b, c which satisfy the equation of the Pythagorean Theorem (a2 + b2 = c2) are called Pythagorean triples. A few of the smallest ones are shown in the table below. Each Pythagorean Triple corresponds with a right triangle whose side lengths are in whole-number ratios.
Pythagorean Triples |
|
3, 4, 5 |
32 + 42 = 52 9 + 16 = 25 |
6, 8, 10 |
62 + 82 = 102 36 + 64 = 100 |
5, 12, 13 |
52 + 122 = 132 25 + 144 = 169 |
8, 15, 17 |
82 + 152 = 172 64 + 225 = 289 |
Note that once you have one Pythagorean triple, you can get many more: just multiply all 3 numbers by a constant. For instance, from 3, 4, 5, we get the family of triples:
3, 4, 5
6, 8, 10
9, 12, 15
12, 16, 20
15, 20, 25
etc.
