On a Quick Expansion Method for Pythagorus Triples

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

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Section XXI - Summarizing on Part IV

Summary for the Section :

• In this Section , we shall summarize our findings so far thru Part IV .

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Summarizing on Part IV :

• Results from the last 10 Sections here in Part IV then tell us that :
  • the { Quick Expansion Procedure } we first developed in Section IX in Part III
    • does seem to work proper for the time being .

  The question then arise as to whether or not :

  • this particular { Quick Expansion Procedure } for Pythagorus Triples would remain valid thru to infinity .

• This was baffling to the Author at the first instance and consequently :
  • prompted the Author to try something different next in Part V , namely :
    • Doubling-Up on the 2 base Triangles and :
      • do the same { Quick Expansion Procedure } using 2 { 3-4-5 Pythagorus-Triple Triangles } ;
        • as opposed to using the { 3-4-5 Triangle } and the { 5-12-13 Triangle } as the 2 base Triangles here in Part IV .

• And we shall be coming back to the full development of the formula :
  • for the { Quick Expansion Procedure } first developed in Part III ,
    • in Part VI of the paper .

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What's Next :

• Let us now go to Doubling-Up Process in Part V , next .

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

go to the last Section : Section XX - Results for the [ 20-21-29 / 12-35-37 ] Pythagorus-Triple Pair

return to the Pythagorus Triples Homepage

Original dated 2021-12-27