Advisor(s) - Committee Chair
Dr. Tom Richmond (Director), Dr. John Spraker, Dr. Daniel C. Biles
Department of Mathematics and Computer Science
Master of Science
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.
Geometry and Topology | Mathematics
Johnson, Jamie, "Continued Radicals" (2005). Masters Theses & Specialist Projects. Paper 240.