JP Journal of Algebra, Number Theory and Applications
Volume 30, Issue 1, Pages 35 - 46
(August 2013)
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ON CONSTRUCTING REAL 5th ROOTS BY MARKED RULER AND COMPASS THROUGH VERGING BETWEEN A LINE AND A CIRCLE
Elliot Benjamin
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Abstract: In this paper, we consider the construction using a marked ruler and compass of real 5th roots of real numbers constructible by marked ruler and compass, where the possibility of constructing these real 5th roots is restricted to verging between a line and a circle by means of the intersection of a limacon and a line. We demonstrate that in some particular cases, namely when the verging point is the origin and the lines are vertical, horizontal, or pass through the origin, it is not possible to construct nontrivially in this way the real 5th root of a real number constructible by marked ruler and compass. |
Keywords and phrases: marked ruler and compass construction, limacon and line construction, conchoid and circle construction, verging, signed distance, constructing directly. |
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