On Breaking-down any Triangle into
a pair of Mirror-Imaged Equilateral Triangles

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

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Section XXXIII - Summarizing on Part V

Summary for the Section :

• In this Section , we shall summarize our findings in Part V .

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Recalling the solution procedure :

• Let us recall that in Part IV of this paper ,
  • we were successful in establishing the 2 mirror-imaged Equilateral Triangles
    • via solving the { 3rd-Order Polynomial Equation } associated with { Triangle A-B-C }

  

  

  so that :

  • [ Vector O-X1 ] = [ Vector O-T1 ] + [ Vector O-U1 ]

  • [ Vector O-X2 ] = [ Vector O-T2 ] + [ Vector O-U2 ]

  • [ Vector O-X3 ] = [ Vector O-T3 ] + [ Vector O-U3 ]

  In this part V of the paper , we were able to establish that :

  • if we were to rotate the { X-Y Axis } clockwise thru an angle [ Delta ] ,
    • and solve for the 2 Equilateral Triangles using the new set of [ X-Y Axis ] ;

    the end result is that the 2 resultant Equilateral Triangles would remain in their same positions as before ,

    • unchanged in size and unchanged in orientation .

  

  

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What's Next :

• Let us now move on to Part VI , next .

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go to the next Section : Section XXXIV - Outline and Purpose for Part VI

go to the last Section : Section XXXII - [ U1 ] / [ U2 ] / [ U3 ] - OLD vs. NEW

return to the Pair of Mirror-Imaged Equilateral Triangles Homepage

Original dated 2021-9-07