“Fibonacci Numbers and the Golden Section”
Fibonacci Numbers and the Golden Section
May 11, 2001
- This excellent site contains a large and interesting selection of material on Fibonacci Numbers and their myriad related concepts. It includes web and text references to the rich literature of Fibonacci numbers. It also features a variety of images, graphics and animations. Many of the topics include student investigations for NCTM standard type explorations. The content includes standard motivational examples and applications in nature, but also mathematical explanations and puzzle pages. The site has already won several awards.
- Type of Material:
- Mainly reference material but includes some interactive animations and some material for student projects.
- Technical Requirements:
- Most of the materials simply require a browser. Links are provided to download plug-ins such as Quicktime for animations. Certain areas also include the ability to work with other software if available, such as Maple or Geometer's Sketchpad.
- Identify Major Learning Goals:
- Resource material for student papers/research on general math and applications - particularly in nature. Classroom enrichment for instructors and students. A good motivational tool.
- Target Student Population:
- 1) General arts students with little mathematical knowledge who want to investigate the surprising appearances of the Fibonacci numbers. 2) Math students wishing to learn more of the underlying mathematics. 3) There are occasional reference comments for mathematicians.
- Prerequisite Knowledge or Skills:
- None for the applications in nature material. Some algebra for the mathematical explanations.
- This site features a large amount of material, initially broken into Fibonacci Numbers, Golden Section and Golden String. There are 14 sub-pages such as Fibonacci Numbers and Nature, Golden Section and Nature, Mathematics of Fibonacci Numbers, Golden Section in Art, Architecture and Music. The Fibonacci Numbers and Nature page then features eleven specific examples plus web links and references. There is an intriguing page of mathematical formulas related to the Fibonacci numbers. There are two pages of puzzles, sorted as "easy" which have a readily apparent connection with the Fibonacci numbers, and "hard" where the connection and reason are not obvious. There is an opportunity to contribute related puzzles. The Mathematics of Fibonacci Numbers page includes formulas, proofs and calculator exercises for the student. There is a history of Leonardo of Pisa, alias Fibonacci. Two of the more unusual features include links to the Mandelbrot set and a Quicktime audio track of the Golden Sequence.
This is an excellent entry point for students to first investigate Fibonacci numbers and their rich collection of applications. The site includes motivational examples to attract attention and many suggestions for further work and sources of information.
- The two initial pages on Fibonacci Numbers and Nature should be very effective at attracting and holding student attention with eye-catching and interesting natural examples. The first starts with the traditional rabbit problem, familiar to many students, and leads in to many variants involving other animals and plants. The material is written in a friendly easy-to-read style and includes many visuals, some of which are animated.
The site has already received twelve educational web-site awards. This is a topic that is effective for introductory student projects.
- There are some links to commercial sites such as book vendors - but they are not intrusive.
- The main page of this large multi-page site starts with an attractive animated interpretation of the standard Fibonacci number definition. It then includes a quick summary to orient new users and a "what's new" list for return users that features additions by date. There are appropriate links to download sites for any required plug-ins. There are links to internet available references and also many standard references. Reference books are linked to an online purchase site. Navigation is fairly straightforward for such a large site and pages download quickly despite many images.
- Creative Commons: