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Continued Radicals

Authors: Jamie Johnson and Tom Richmond

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)

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.

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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)

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@InProceedings{johnson_et_al:DagSemProc.04351.10,
  author =	{Johnson, Jamie and Richmond, Tom},
  title =	{{Continued Radicals}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.10},
  URN =		{urn:nbn:de:0030-drops-1286},
  doi =		{10.4230/DagSemProc.04351.10},
  annote =	{Keywords: Continued radical}
}

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Continued Radicals

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