Geometry

Previous months:
2025 - 2504(1) - 2506(2)

Recent submissions

Any replacements are listed farther down

[3] ai.viXra.org:2506.0064 [pdf] submitted on 2025-06-16 02:08:34

Two-Sided Symmetry and Holonic Maps: From Koestler’s Holarchy to Intuitionist Geometry and Archetypal Resonance

Authors: Stephen P. Smith
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please cite and list sceintific references)

This paper explores Arthur Koestler’s concept of Janus-faced holons within a dynamic holarchy, integrating insights from CPT symmetry, intuitionist mathematics, Michael Schneider’s generative geometry, and Karl Friston’s free energy principle. It critiques static holonic diagrams and proposes a more resonant, fractal, and bilaterally symmetrical mapping rooted in archetypal forms. Drawing from sacred geometry, musical structures, and biological patterns, the essay argues that reality unfolds through intuitive construction and pre-existing mathematical orders. Holonic development, like nature itself, reflects a deep, two-sided balance—unifying form, transformation, and perception in a cosmological vision where cognition participates in creation.
Category: Geometry

[2] ai.viXra.org:2506.0016 [pdf] submitted on 2025-06-04 22:14:30

Observer-Centric Internal Spherical Geometry

Authors: Larry Whitaker
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed sceintific references)

We present a practical mathematical framework for interior spherical geometry that en-ables complete sphere characterization and three-dimensional positioning from an observer-centric perspective. The methodology addresses fundamental limitations in traditionalspherical geometry by eliminating dependence on external reference points and establish-ing the observer as the coordinate system origin. Our approach integrates perpendicularchord measurement techniques with computational algorithms to provide accurate interiorpositioning for practical applications. The framework introduces measurement protocols forgeometric calculations, establishes cone-based coordinate systems with scalable precision,and addresses measurement uncertainty propagation. Applications include navigation systems for enclosed environments, geometric modeling of spherical structures, and scientificinstrumentation requiring interior perspective calculations.
Category: Geometry

[1] ai.viXra.org:2504.0071 [pdf] submitted on 2025-04-19 22:56:37

Study by Vector Projection of a Construction Made with a Rule and Compass to Understand Squaring the Circle

Authors: José Rodrigo Alejandro Martinez Diaz
Comments: (Improper cover page stripped by ai.viXra.org Admin)

The conditions of the problem establish the definition of a right triangle whose angle subtends the opposite cathetus with a value equal to alpha = arctan (1/ sqrt{pi}). Starting from this main condition, a series of steps are proposed to compare the precision between two idealized methods that describe the construction of a circle and a square linked to the triangle mentioned above. The first approximation is made taking into account "valid" compass and ruler constructions to obtain such geometric figures. The second construction is based on the lengths obtained by intersecting the previously mentioned geometric figures by performing the vector analysis. In both cases, the areas of the circle and square obtained are compared to find out if they are equal.
Category: Geometry

Replacements of recent Submissions

None