Difference between revisions of "Pythagorean triple"
| Line 1: | Line 1: | ||
A '''Pythagorean Triple''' is a triple of [[positive integer]]s, <math>(a, b, c)</math> such that <math>a^2 + b^2 = c^2</math>. Pythagorean Triples arise in [[geometry]], as the side-lengths of [[right triangle]]s. | A '''Pythagorean Triple''' is a triple of [[positive integer]]s, <math>(a, b, c)</math> such that <math>a^2 + b^2 = c^2</math>. Pythagorean Triples arise in [[geometry]], as the side-lengths of [[right triangle]]s. | ||
| − | ==Common Pythagorean Triples== | + | == Common Pythagorean Triples == |
These are some common Pythagorean Triples: | These are some common Pythagorean Triples: | ||
| Line 36: | Line 36: | ||
(65, 72, 97) | (65, 72, 97) | ||
| − | ==Primitive Pythagorean Triples== | + | == Primitive Pythagorean Triples == |
A Pythagorean Triple is primitive if it has no common factors. How many of the above can you spot as primitive? | A Pythagorean Triple is primitive if it has no common factors. How many of the above can you spot as primitive? | ||
| − | ==See Also== | + | == See Also == |
* [[Pythagorean Theorem]] | * [[Pythagorean Theorem]] | ||
* [[Diophantine equation]] | * [[Diophantine equation]] | ||
Revision as of 12:52, 28 February 2007
A Pythagorean Triple is a triple of positive integers, 
such that 
. Pythagorean Triples arise in geometry, as the side-lengths of right triangles.
Common Pythagorean Triples
These are some common Pythagorean Triples:
(3, 4, 5)
(20, 21, 29)
(11, 60, 61)
(13, 84, 85)
(5, 12, 13)
(12, 35, 37)
(16, 63, 65)
(36, 77, 85)
(8, 15, 17)
(9, 40, 41)
(33, 56, 65)
(39, 80, 89)
(7, 24, 25)
(28, 45, 53)
(48, 55, 73)
(65, 72, 97)
Primitive Pythagorean Triples
A Pythagorean Triple is primitive if it has no common factors. How many of the above can you spot as primitive?
