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Pythagorean triplet
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(Definition)
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A Pythagorean triplet is a set
 of three positive integers such that
That is,
 is a Pythagorean triplet if there exists a right triangle whose sides have lengths  ,  , and  , respectively. For example,
 is a Pythagorean triplet. Given one Pythagorean triplet
 , we can produce another by multiplying  ,  , and  by the same factor  . It follows that there are countably many Pythagorean triplets.
A Pythagorean triplet is primitive if its elements are coprimes. All primitive Pythagorean triplets are given by
where the seed numbers  and  are any two coprime positive integers, one odd and one even, such that  .
Note. One can form the sequence (Sloane's A100686)
taking first the seed numbers 1 and 2 which give the legs 3 and 4, taking these as new seed numbers which give the legs 7 and 24, and so on.
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"Pythagorean triplet" is owned by drini. [ full author list (4) | owner history (1) ]
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(view preamble)
Cross-references: legs, sequence, even, odd, coprimes, primitive, factor, lengths, sides, right triangle, integers, positive
There are 9 references to this entry.
This is version 8 of Pythagorean triplet, born on 2001-10-06, modified 2007-11-06.
Object id is 138, canonical name is PythagoreanTriple.
Accessed 15184 times total.
Classification:
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Pending Errata and Addenda
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