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A SIMPLE GEOMETRIC CONSTRUCTION INVOLVING ULTRARADICALS

Part of: Real and complex geometry

Published online by Cambridge University Press:  11 October 2011

J. ROBERTSON  and
C. SNYDER
J. ROBERTSON
Affiliation:
1807 County Road, New Limerick, Maine 04761, USA (email: james.robertson@umit.maine.edu)
C. SNYDER*
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469, USA (email: snyder@math.umaine.edu)
*
✉For correspondence; e-mail: snyder@math.umaine.edu
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Abstract

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We give a new type of geometric construction that allows for the construction of families of quintic irrationalities, and is quite rich in algebraic properties. This construction may be considered as our first attempt at characterizing points constructible with compass and twice-notched ruler, a problem that seems to have been known in some form for more than two millennia.

Keywords

constructible numbermarked-ruler constructionquintic extensionultraradical

MSC classification

Secondary: 51M15: Geometric constructions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 1 , August 2011 , pp. 103 - 124
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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