An Approach to the Triangle

by Frank Charles Fung ( 1st published in December, 2005. )

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TABLE OF CONTENT
Section IIntroduction & Key Findings
Section IITriangles in general
Section IIIThe Area of the Triangle { A-O-T }
Section IVThe { Congruent-Triangles Tetrahedron }
Section VShape Classifications based on the { Fermat Point }
Section VIAn Infinite Series of { Triangles }
Section VIIThe { Nine Circles } of the Triangle
Section VIIIMapping { Triangles } onto { Triangles }
Section IXThe { Sine-Square } & { Cosine-Square } Functions
Section XConcluding Remarks
Appendix ABrief Notes on the { Fermat Point }
Appendix B{ Centroid } for { Triangle D-E-F } & { Triangle R-S-T }

This paper is published in honor of my father , the late Charles Hok-Ling Fung ( 1909 - 2002 ) , on the occasion of his 96th birthday on 2005-12-07.

Section I --- Introduction & Key Findings

In { An Approach to the Three Body Problem } back in 1996 , it was not determined as to how the 3 Degrees-Of-Freedom ( DOF's ) associated with a triangle should be broken-down into :

This paper is an effort towards a better understanding of the { Triangle } .

KEY FINDINGS :

ONE. --- The { C-T Tetrahedron }

TWO. --- An Infinite Series of { Triangles }

THREE. --- Matching { Fermat Point } onto { Fermat Point }

FOUR. --- Triangles with Integer Sides

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Original dated 2005-12-07 *** Updated 2008-11-01 / 2009-10-26