Exact Doubling the Cube with Straightedge and
Compass by Euclidean Geometry

Tran Dinh Son

doi:https://doi.org/10.14445/22315373/IJMTT-V69I8P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P506

Exact Doubling the Cube with Straightedge and Compass by Euclidean Geometry

Tran Dinh Son

Received	Revised	Accepted	Published
14 Jun 2023	29 Jul 2023	12 Aug 2023	29 Aug 2023

Citation :

Tran Dinh Son, "Exact Doubling the Cube with Straightedge and Compass by Euclidean Geometry," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 45-54, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P506

Abstract

This independent research shows an exact precision and accurate solution for the ancient Greek challenge – “Doubling The Cube” using a straightedge and a compass only. Mathematics tools and propositions used in this solution are all in Geometry and algebraic geometry at the 6 th Form level of today’s United Kingdom. The methodology of the solution includes geometrical methods to arrange the given cube and its double volume cube into a concentric position of which side x of the double cube can be calculated accurately by algebra then in terms of geometrical length the side is constructive. And then, use the straightedge and the compass to construct the double-volume cube.

Keywords

Cube duplicating, Double a cube, Double cube volume, Doubling the cube, Geometrical duplicating cube.

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