Algebra

Pythagorean Triple

Pythagorean triples are integer solutions (x,y,z) of the equation

x2 + y2 = z2 ,

standing for the sides of right-angled triangles.

The program computes all coprime Pythagorean triples not bigger than a determined number.

Example:

For x, y, z between 100 and 400 we get:

( 119|120|169 )    ( 104|153|185 )    ( 133|156|205 )    ( 105|208|233 )    
( 140|171|221 )    ( 115|252|277 )    ( 120|209|241 )    ( 161|240|289 )    
( 160|231|281 )    ( 207|224|305 )    ( 175|288|337 )    ( 135|352|377 )    
( 136|273|305 )    ( 204|253|325 )    ( 225|272|353 )    ( 189|340|389 )    
( 180|299|349 )    ( 252|275|373 )    ( 152|345|377 )    ( 228|325|397 )  

An application of Pythagorean triples is the twelve-knot cord, with which a right-angled triangle of sides 3, 4 and 5 can be marked.

See also:

Wikipedia: Pythagorean triple | Pythagorean theorem | Knotted Cord
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