On a Quick Expansion Method for Pythagorus Triples

by Frank C. Fung ( 1st published in December, 2021. )

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Section IV - The Usual Procedure for Expanding Pythagorus Triples

Summary for the Section :

• In this Section , we shall go thru :
  • the usual procedure for expanding Pythatgorus Triples .

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Combining 2 Pythagorus Triples :

• Let us bring in 2 Pythagorus Triples :
  • for the 1st Pythagorus Triple [ W1 / H1 / L1 ] , we have :
    • 

  • for the 2nd Pythagorus Triple [ W2 / H2 / L2 ] , we have :
    • 

• Let us now take a quick look at the product of the { square of [ L1 ] } and the { square of [ L2 ] } ,
  • given by :
    • 

  We can then add-and-subtract the term [ W1 x W2 x H1 x H2 ] on the right-hand-side of the above equation

  • to bring us this new equation :
    • 
      

  Consequently we have :

  • 

• And based on the above , we can now set up a new Pythagorus Triple [ W3 / H3 / L3 ] , with :
  • 

  • 

  • 

    governed by the relation :

  • 

• And we take special note here that :
  • [ L3 ] is always divisible by [ L1 ] and [ L2 ] .

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What's Next :

• Let us now go to Part III of the paper :
  • on how we happened to stumble upon the Quick Expansion Procedure for Pythagorus Triples .

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go to the next Section : Section V - Outline and Purpose for Part III

go to the last Section : Section III - Fermat's { Sum of 2 Squares } Revisited

return to the Pythagorus Triples Homepage

Original dated 2021-12-27