This site provides a very interesting and unusual examination of continued fractions: how they are formed and notated, patterns contained therein, and some connections to the Fibonacci numbers. Construction of continued fractions for decimal fractions and square roots is also discussed. "Silver" means are investigated along with the numbers pi and e and their continued fraction patterns. The author poses numerous questions and the end of many of the sections includes material to further involve the user in exploring the patterns given. This site is part of the award-winning site Fibonacci Numbers and the Golden Section (please see separate listing and review).
Type of Material:
Lecture/presentation; can also serve as a tutorial.
Identify Major Learning Goals:
Resource material for student investigations of continued fractions. Unusual application of basic algebra. Classroom enrichment for instructors.
Target Student Population:
Math students interested in number theory; computer science students with an interest in algorithms, students interested in (programmable) calculators. Faculty members looking for classroom enrichment materials.
Prerequisite Knowledge or Skills:
The material only requires concepts from basic algebra but the student should be comfortable applying them to new applications.
Evaluation and Observation
Useful for both experienced and casual student users. Nicely written and easy to read. Very interesting collection of related concepts. Nice set of related books and articles. Includes some unsolved hypotheses for investigation.
Please see the review for Fibonacci Numbers and the Golden Section, the parent site for the Continued Fractions web page. The parent site is a rich and growing source of materials pertaining to the Fibonacci numbers and their many relationships to nature and other areas of mathematics. The Continued Fractions pages are well-written and very easy to follow, even for a beginning math student.. There is also an extensive collection or links to related materials and sources.
Potential Effectiveness as a Teaching Tool
Unique and unusual presentation of the topic and its relationship to other math occurrences. Allows the user to see some of the deeper patterns involved. Nice listing of links to related materials and sources. The "Things to Do" included at the end of many of the sections lead the reader to investigate the ideas more fully and become actively involved in the learning process. The material could be used to encourage student exploration of calculators, computer algebra software and simple programming.
Ease of Use for Both Students and Faculty
Easily readable, even for the beginning math student. The introductory section includes a particularly attractive visual approach.