The Cube Duplication Solution (A Compass straightedge (Ruler) Construction)

Kimuya .M. Alex; Josephine Mutembei

doi:https://doi.org/10.14445/22315373/IJMTT-V50P549

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 50 | Number 5 | Year 2017 | Article Id. IJMTT-V50P549 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P549

The Cube Duplication Solution (A Compass straightedge (Ruler) Construction)

Kimuya .M. Alex, Josephine Mutembei

Citation :

Kimuya .M. Alex, Josephine Mutembei, "The Cube Duplication Solution (A Compass straightedge (Ruler) Construction)," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 5, pp. 307-315, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P549

Abstract

This paper objectively presents a provable construction of generating a length of magnitude; , as the geometrical solution for the ancient classical problem of doubling the volume of a cube. Cube duplication is believed to be impossible under the stated restrictions of Euclidean geometry, because the Delian constant is classified as an irrational number, which was stated to be geometrically irreducible (Pierre Laurent Wantzel, 1837) [1]. Contrary to the impossibility consideration, the solution for this ancient problem is theorem , in which an elegant approach is presented, as a refute to the cube duplication impossibility statement. Geogebra software as one of the interactive geometry software is used to illustrate the accuracy of the obtained results, at higher accuracies which cannot be perceived using the idealized platonic straightedge and compass construction.

Keywords

Doubling a cube, Delian constant, Compass, Straightedge (Ruler), Classical construction, Euclidean number, Irrational number, GeoGebra software.

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