An Approach to the Four Body Problem

by Frank C. Fung - 1st published in December, 2007.

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Section V - The { Flattened Tetrahedron }

The { Flattened Tetrahedron } :

• The { Flattened Tetrahdreon } may simply be constructed , using a { parallelogram squashed-box } :
  • with all 8 corners residing on the same { planer surface } .

  

• And we take note here that , whenever the { parallelogram squashed-box } is totally flattened ,
  • the sum of [ Theta ] , [ Psi ] and [ Gamma ] always add up to [ 360 degrees ] .

  And hence , it doesn't seem possible that [ Theta ] , [ Psi ] and [ Gamma ] can add up to more than [ 360 degrees ] .

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A Quick-Look at a Special Case :

• We note here that we have actually constructed the above { Flattened Tetrahedron } using :
  • [ Theta ] = [ Psi ] = [ Gamma ] = [ 120 degrees ] .

  

• We simply note here that :
  • [ Point K ] is the { Fermat Point } of { Triangle A-B-C } , and
  • [ Point D ] is the { Fermat Point } of { Triangle G-H-J } .

  Rather interesting , and for the interested reader's further thoughts .

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go to the next section : Section VI - Brief Summary on the Tetrahedron

go to the last section : Section IV - Constructing the { General Tetrahedron }

return to The Four Body Problem HomePage

original dated 2007-12-16