Journal of the Australian Mathematical Society

Research Article

A SIMPLE GEOMETRIC CONSTRUCTION INVOLVING ULTRARADICALS

J. ROBERTSONa1 and C. SNYDERa2 c1

a1 1807 County Road, New Limerick, Maine 04761, USA (email: james.robertson@umit.maine.edu)

a2 Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469, USA (email: snyder@math.umaine.edu)

Abstract

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.

(Received August 25 2010)

(Accepted May 15 2011)

(Online publication October 11 2011)

2010 Mathematics subject classification

  • primary 51M15

Keywords and phrases

  • constructible number;
  • marked-ruler construction;
  • quintic extension;
  • ultraradical

Correspondence:

c1 For correspondence; e-mail: snyder@math.umaine.edu

Footnotes

Communicated by M. G. Cowling