On the Constructibility of Real 5th Roots of Rational Numbers with Marked Ruler and Compass. (5th June 2012)

• Record Type: Journal Article
• Authors: Benjamin, Elliot
• Other Names: de Graaf W. Academic Editor.; Raianu S. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2012(2012)
• Publication Date: 2012-06-05
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2012/487275
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : We demonstrate that there are infinitely many real numbers constructible by marked ruler and compass which are unique real roots of irreducible quintic polynomials over the field of rational numbers. This result can be viewed as a generalization of the historical open question of the constructibility by marked ruler and compass of real 5th roots of rational numbers. We obtain our results through marked ruler and compass constructions involving the intersection of conchoids and circles, and the application of number theoretic divisibility criteria.