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 creation ex nihilo, the latter related to the structure of the Trinity.