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

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

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Section VI - Outline and Purpose for Part III

Summary for the Section :

• In this Section , we shall state out what we intend to accomplish in this Part III of the paper .

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Statement of Purpose for Part III :

• In the author's previous paper in 2005 :
  • An Approach to the Triangle

  we first introduce the procedure for constructing a { triangle } or { 3-Points Shape }

  • via the use of :
    • a { Referece Structure } which is a { equilateral triangle inscribed within a circle of radius [ R ] } ,

      and

    • a seed-point [ Point H ] lying within the { Circle of Radius [ R ] } ;

    as per this set of 3 diagrams below .

  

  

  We shall give further details of the construction procedure in the next Section - Section VII to come .

• The main purpose in Part III here is to identify the 3 key controlling variables , namely :
  • [ R ] being the radius of the Circle ,

  • [ Rho ] and [ Theta ] which defines the position of the seed-point [ Point H ] ;

    so that :

    • the Triangle or the { 3-Points Shape } may be fully defined and established .

  And based on these 3 controlling variables [ R ] / [ Rho ] / [ Theta ] :

  • we shall also establish the 2 corresponding mirror-imaged Equilateral Triangles ;
    • thereby confirming their existance .

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Skipping over Part III entirely :

• Part III here is considered long and tedious .

  For those readers unfamiliar with the Constuction Procedure for a Triangle / { 3-Points Shape }

  • first presented in the author's paper in 2005 , i.e. :
    • An Approach to the Triangle

  we do recommend skipping over Part III entirely in favor of Part IV

  • where we shall demonstrate how to arrive at the 2 mirror-imaged Equilateral Triangles
    • for any given random { Triangle A-B-C } .

• Nonetheless , Part III is an important part of the paper because :
  • it sets up the framework for future variability-stability analysis on a { 3-equal-mass system } .

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go to the next Section : Section VII - Constructing { Triangle A-B-C }

go to the last Section : Section V - A First Look at Mirror-Imaged Triangles

return to the Pair of Mirror-Imaged Equilateral Triangles Homepage

Original dated 2021-9-07