DOI: https://doi.org/10.36347/sjpms.2026.v13i05.001

Pages: 218-227

In a previous independent study published in the International Journal of Pure and Mathematical Sciences, an exact and rigorous solution to the classical Greek problem of Doubling the Cube was presented, achieved using only a straightedge and compass [30]. Building upon the logical framework established in that work, the recent study investigated a related and previously unexplored problem: Halving A Cube. This proposed solution is grounded in classical geometry and elements of algebraic geometry. The methodology employs geometric constructions to position a given cube with volume a^3, and side a, inside a cube with volume na^3 in a concentric configuration. From this arrangement, the side length x of the resulting cube is derived analytically using algebraic methods. This length is then interpreted geometrically, allowing for its exact construction using a straightedge and compass. The relationship between this article and problems of doubling and halving a cube is a INDUCTIVE GENERALISATION, highlighting their structural symmetry and methodological parallels.