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On { N+1 Symmetric Lines } in a { N-Dimension Vector Space }

by Frank C. Fung ( 1st published in March, 2016. )

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Summary and Key Findings :

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Key Finding One :

Table of Content

Key Finding Two :

Table of Content

Table Of Content
Part I --- Introduction
Section IIntroduction
Part II --- Setting up the Symmetric Lines
Section II{ 3 Symmetric Lines } in a { 2-Dimension Plane }
Section III{ 4 Symmetric Lines } in a { 3-Dimension Space }
Section IV{ 5 Symmetric Lines } in a { 4-Dimension Space }
Section V{ 6 Symmetric Lines } in a { 5-Dimension Space }
Section VISymmetric Lines in { Higher-Dimensioned Spaces }
Part III --- Hiarchy across Spaces with different Number of Dimensions
Section VII{ Symmetric Lines in 4-D } vs. { Symmetric Lines in 3-D }
Section VIIIThe Hiarchy of the { N+1 Symmetric Lines } System
Part IV --- Absolute Symmetry vs. Relative Structural Symmetry
Section IXDefining 2 Types of Line-Symmetry
Part V --- Symmetry Expansion via the Retangle
Section XExplaining Line-Symmetry Expansion via the Rectangle
Section XILine-Symmetry Expansion via the Rectangle for 3-D
Section XIILine-Symmetry Expansion via the Rectangle for Higher Dimensions
Part VI --- 28 Symmetric Lines in a { 7-Dimension Vector Space }
Section XIIIThe { 28 Symmetric Lines } in a { 7-Dimension Space }
Section XIVStructural Flexibility for the { 28 Symmetric Lines in 7-D }
Part VII --- Line-Symmetry via the Quasi-Cube
Section XVThe Quasi-Cube in a { 4-Dimension Vector Space }
Section XVILine-Symmetry via the Quasi-Cube for Higher Dimensions
Part VIII --- Summarizing and Concluding Remarks
Section XVIISummarizing on Line-Symmetry
Section XVIIIConcluding Remarks

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Original dated 2016-3-22