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On Periodic Sequences for Algebraic Numbers

โœ Scribed by Thomas Garrity

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
145 KB
Volume
88
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

For each positive integer n 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 x 3 +kx 2 +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.

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