DOI: https://doi.org/10.36347/sjpms.2026.v13i04.004

Pages: 184-196

The problem of tripling a cube consists in constructing, by means of an unmarked straightedge and compass within the framework of Euclidean geometry, a cube whose volume is exactly three times that of a given cube. While the classical Greek problems squaring the circle, trisecting an angle, and doubling the cube have been extensively studied, the analogous problem of tripling a cube has not appeared in the traditional canon [8]. In this paper, we formulate and investigate the problem of tripling a cube for an arbitrary given cube, as a natural extension of prior work on the exact doubling of the cube ("Exact Doubling the Cube with Straightedge and Compass by Euclidean Geometry, by Tran Dinh Son in the Scholars Journal of Physics, Mathematics and Statistics | Volume-12-Issue-02, in 2025, Sch J Phys Math Stat | 24-32, DOI : https://doi.org/10.36347/sjpms.2025.v12i02.001”.). We present a construction-based approach that yields an exact solution using only classical Euclidean tools, without recourse to transcendental quantities such as π. The method is grounded in elementary geometric principles, though its full development requires a nontrivial sequence of constructions. The results establish a novel straightedge-and-compass construction for achieving a cube of triple volume and introduce a systematic framework referred to as the Tripling a Cube method that enables precise and reproducible solutions. This work contributes a new perspective to classical geometric construction problems and extends the scope of constructability within Euclidean geometry.