Newton's Method and the Wada Property: A Graphical Approach

Authors: Frame, Michael; Neger, Nial

Source: The College Mathematics Journal, Volume 38, Number 3, May 2007 , pp. 192-204(13)

Publisher: Mathematical Association of America

Buy & download fulltext article:

Price: $20.00 plus tax (Refund Policy)

Abstract:

Imagine trying to paint a picture with three colors - say red, blue, and yellow - with a blue region between any red and yellow regions, a red region between any blue and yellow regions, and a yellow region between any red and blue regions, down to infinitely fine details. Regions arranged in this way satisfy what is called the Wada property. At first thought, it may not be so clear that any regions at all satisfy the Wada property. Borrowing a simple geometrical construction from a first course on dynamical systems, we show that the Wada property arises naturally in Newton?s method as introduced in first-semester calculus.

Document Type: Research article

Publication date: 2007-05-01

More about this publication?

The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. CMJ publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.
Information for Authors
Submit a Paper
Subscribe to this Title
Membership Information
Information for Advertisers
Terms & Conditions
MAA Bookstore
Loci
Math Horizons
ingentaconnect is not responsible for the content or availability of external websites