The Cube Unlike All Others



This book contains thirty-three full-color illustrations. The title piece presents a beautifully simple proof that there is a central cube, constitutionally unique among all cubes, the absolute dead center cube.  An illustration accompanies the proof.  It is additionally proven that the hypercubic volume of this cube is uniquely constituted as a natural number.  The mathematics of the unique cube and hypercube are then related to physical measures of magnitude and balance, and to the real trinary logic articulated in an earlier work, Foundation: Matter the Body Itself.  The trinary logic is, in turn, shown to have a foundational relationship to the arithmetic and geometric series,  to the series  of perfect numbers, and to the Banach-Tarski paradox.  Original geometric constructions based on the properties of the division in extreme and mean ratio are illustrated and  further related to the logarithmic spiral and to the physical constants.  Five appendices deal with Fibonacci’s rabbit tree, the rationality of the so-called irrationals, an understanding of mathematics without a notion of nothing,  the New Jerusalem cube, and ceation ex nihilo, the latter related to the structure of the Trinity.









I    The Absolute Dead Center Cube

1      Theorem and Proof                                                                                                   

2      Measure Beyond Beyond Reach                                                                              

3      The Magnitude of Being                                                                                     


II   The Cube and Real Trinary Logic  

1        Logically Outfitted Cube(s)                                                                            

2        Maxwell’s Constant and the Trinary Logic Triple-Cube                                                                                                                          

III  Real Trinary Logic Geometric Series 

1        Real Trinary Logic Geometric Series Matrix of the Numeric Geometric Series & the Series of Perfect Numbers


2     Banach-Tarski Paradox & Real Trinary Logic


IV  The Golden Section 

1        The Golden Bowl Structure: The Platonic Line, Fibonacci, and Feigenbaum

    2    The Golden Bowls & the Logarithmic Spiral


    3    The Physical Constants: Functions of the ‘Golden Bowl’ Arrangements

      on the Φ-Level of Existence Itself                                                                  



V   Appendices 

1        6BRabbit Tree & the Logic of Life’s Beginning                                    

2        7BThe Beautiful Rationality of Π, √2, & Φ                                                      

3        8BThinking Mathematics Sans Nothing


4        9BUnique Metric and the Apocalyptic New Jerusalem

5        Thinking Creation Ex Nihilo    




D.G. Leahy is the author of Beyond Sovereignty: A New Global Ethics and Morality; Faith and Philosophy: The Historical Impact; Foundation: Matter the Body Itself; and Novitas Mundi: Perception of the History of Being.  He is formerly Research Consultant to the Skin Sciences Institute, Children's Hospital Research Foundation, University of Cincinnati.  He was tenured in Classics and has taught Religious Studies at New York University and is former Distinguished Visiting Professor of Philosophy at Loyola University Maryland.

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