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URN: urn:nbn:de:0030-drops-1286
URL: http://drops.dagstuhl.de/opus/volltexte/2005/128/
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Johnson, Jamie ; Richmond, Tom

Continued Radicals

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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.

BibTeX - Entry

@InProceedings{johnson_et_al:DSP:2005:128,
  author =	{Jamie Johnson and Tom Richmond},
  title =	{Continued Radicals},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  year =	{2005},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  number =	{04351},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2005/128},
  annote =	{Keywords: Continued radical}
}

Keywords: Continued radical
Seminar: 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
Issue Date: 2005
Date of publication: 22.04.2005


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