International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 10, No. 1, 8 Feb. 2024
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A Rigorous Euclidean Geometric Proof of the Cube Duplication Impossibility
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Index Terms
Euclidean geometry, Cube duplication, Impossibility proof, Geometric construction, Euclid’s Elements, Algebraic methods, Visual intuition, Classical geometry
Abstract
This paper introduces a rigorous impossibility proof in Euclidean geometry, presenting a scrupulous demonstration of the unattainability of doubling the volume of a cube through any given procedure. The proof methodically follows the rigorous principles of classical geometry, offering clarity and insight into a longstanding mathematical challenge. The paper further emphasizes the historical misconceptions and varied solutions that have emerged due to the lack of a definitive Euclidean geometric proof. It highlights the enduring strengths, independence, and richness of Euclidean geometry while dispelling the notion that algebraic methods are the exclusive avenue to tackle geometric impossibilities. The results obtained throughout this proof solidify the position of Euclidean geometry as a potent and illuminating tool, reaffirming its pivotal role in the world of mathematics. This work contributes not only to the resolution of a specific mathematical challenge but also to the broader understanding of the unique virtues and capabilities of Euclidean geometry in tackling complex geometric problems.
Cite This Paper
Alex Mwololo Kimuya, "A Rigorous Euclidean Geometric Proof of the Cube Duplication Impossibility", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.10, No.1, pp. 9-18, 2024. DOI: 10.5815/ijmsc.2024.01.02
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