ArticleOpen Access http://dx.doi.org/10.26855/jamc.2025.12.003
Every Cube Has Three Line Segments that Approximate Twice the Cube Root Infinitely
Jiucheng Zhong
Baoxing County Zhongba High School, Ya'an 625000, Sichuan, China.
*Corresponding author:Jiucheng Zhong
Published: December 16,2025
Abstract
The inability to construct roots of threefold cubes using a compass and straight-edge (conventional geometric tools) led to the exclusion of dodecahedron constructions. However, since these tools can perform basic arithmetic operations and square roots, we established a fixed ratio between given cube edges and dodecahedron edges. This enabled the creation of line segments equivalent to dodecahedron roots, resulting in the paper “Constructing Line Segments Equal to Dodecahedron Roots Using Given Cube Edges”. To address criticisms regarding the universality, precision, and apparent contradiction with classical proofs, we further explored fixed ratios between relevant line segments and dodecahedron roots within given cube constructions. My research revealed two additional line segments with fixed ratios to dodecahedron roots, which are congruent with 15-digit line segments constructed from cube edges. This innovative work represents an expansion of research into Galois theory through advanced cognitive development.
Keywords
Doubling of a cube; Compass and straightedge; Square root; Cube root; Geometric construction
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How to cite this paper
Every Cube Has Three Line Segments that Approximate Twice the Cube Root Infinitely
How to cite this paper: Jiucheng Zhong. (2025) Every Cube Has Three Line Segments that Approximate Twice the Cube Root Infinitely. Journal of Applied Mathematics and Computation, 9(4), 238-248.
DOI: http://dx.doi.org/10.26855/jamc.2025.12.003