Continued Radicals

If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.

Name thesis:degree_name

Master of Science

Discipline thesis:degree_discipline

Department of Mathematics and Computer Science

Year

2005

Author dc:creator

• Johnson, Jamie

Contributors dc:contributor

• Dr. Tom Richmond (Director), Dr. John Spraker, Dr. Daniel C. Biles

• Radical Numbers
• Mathematics
• Geometry and Topology

Repository record dc:identifier

https://digitalcommons.wku.edu/theses/240

OAI identifier oai:identifier

oai:digitalcommons.wku.edu:theses-1243