Difference between revisions of "Pythagorean triple"

Revision as of 11:51, 28 February 2007

A Pythagorean Triple is a triple of positive integers, $(a, b, c)$ such that $a^2 + b^2 = c^2$ . 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?

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Difference between revisions of "Pythagorean triple"

Revision as of 11:51, 28 February 2007

Common Pythagorean Triples

Primitive Pythagorean Triples

See Also

@@ 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.
-{{stub}}
+==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?
 ==See Also==
 * [[Pythagorean Theorem]]
 * [[Diophantine equation]]