1999/06/02 by Thomas Garrity, Garrity, Thomas
Mathematics · #11J70 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J70
paper · pdf · doi:10.48550/arxiv.math/9906016
22 pages. An error in section five of the original paper has been corrected, resulting in some slight alterations in the statements in the theorems in section six
arxiv created 1999/08/13 · arxiv updated 2009/11/30
For each positive integer n greater than or equal to 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n=2 case is equivalent to the standard continued fraction algorithm. For n=3, it reduces to a new iteration of the triangle. Cubic irrationals that are roots of x3 + k x2 + x - 1 are shown to be precisely those numbers with purely periodic expansions of period length one. For general positive integers n, it reduces to a new iteration of an n dimensional simplex.