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The Dottie Number

by Samuel R. Kaplan (University of North Carolina at Asheville)

This article originally appeared in:
Mathematics Magazine
February, 2007

Subject classification(s): Single Variable Calculus | Calculus
Applicable Course(s): 4.19 Complex Variables | 3.1 Mainstream Calculus I

The unique root of \(cos(x)=x\), the Dottie number, is a simple non-trivial example of a universal attracting fixed point. The author gives pedagogical examples for several courses ranging from Calculus I to Complex Analysis.

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