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On Cube–Pyramid Coincident Configurations

Author:

Turanyanin, Dragan N.

Category:

Essays

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

November 11, 2025

File:

/Essays-Mathematics and Applied Mathematics/Download/10365

Downloads:

158

Keywords:

N/A

Abstract:

This essay presents a three-dimensional analogue of the Theorem of Coincidence previously established for regular polygons. Here, a cube is centrally inscribed within a square pyramid under strict coincidence conditions. This geometrical setup possesses two equally significant cases: basic C₁ and rotated C₂. Together with the planar blueprint, this spatial counterpart forms a coherent framework suggesting that strict central coincidences constrain dimensions through exact algebraic laws. Accordingly, connection with golden ratio φ and plastic constant ρ surprisingly emerges.

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