Continued Radicals

Johnson, Jamie; Richmond, Tom

doi:10.4230/DagSemProc.04351.10

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Continued Radicals

Authors Jamie Johnson, Tom Richmond

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 4351
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2005-04-22

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DOI: 10.4230/DagSemProc.04351.10
URN: urn:nbn:de:0030-drops-1286

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Continued radical

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Abstract

A nested radical with terms $a_1, a_2, \ldots , a_N$ is an expression  of form $\sqrt{a_N + \cdots + \sqrt{a_2 + \sqrt{a_1}}}$.  The limit 
as $N$ approaches infinity of such an expression, if it exists, 
is called a continued radical.  We consider the set of real
numbers $S(M)$ representable as a continued radical whose terms $a_1, a_2, \ldots$ are all from a finite set $M$ of nonnegative real numbers.  We give conditions on the set $M$ for $S(M)$ to be (a) an interval, and (b) homeomorphic to the Cantor set.

Cite As Get BibTex

Jamie Johnson and Tom Richmond. Continued Radicals. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005) https://doi.org/10.4230/DagSemProc.04351.10

Author Details

Jamie Johnson

Tom Richmond

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