An Approach to the Four Body Problem

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

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Section VI - Brief Summary on the Tetrahedron

Brief Summary on the Tetrahedron :

• Let us bring back this { Tetrahedron } and its { parallelogram Squashed-Box } for the summary :

  

• Let us now concentrate on the 3 pairs of { non-touching lines } on the 6-sided { Tetrahedron } :

  

• We see here that each pair of { non-touching lines } are , in fact , the diagonals of a { parallelogram } , as shown below :

  

  Several observations and comments here :

  • The 2 ( diagonals } of the { parallelogram } always form a { quasi-cross } ,

  • When the { parallelogram } becomes a { rectangle } , the lengths of the 2 { diagonals } are equal ,

  • When the { parallelogram } becomes a { square } , the lengths are equal and the 2 { diagonals } intersect at [ right-angles ] .

  Therefore ,

  • The angles [ Theta ] , [ Psi ] and [ Gamma ] are controlling on the { realtive lengths } of { non-touching / opposite sides } .

• And any cross-reference at this point to { Triple-Cross Symmetry } is purely conjectural in nature , and way too-early too .

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go to the next section : Section VII - Setting up for Angular Momentum Issues

go to the last section : Section V - The { Flattened Tetrahedron }

return to The Four Body Problem HomePage

original dated 2007-12-16