# Fibonacci Numbers

Leonardo Fibonacci, sometimes called Leonardo of Pisa, was a thirteenth-century Italian mathematician. He was instrumental in bringing the Arabic numbering system to Europe to replace the use of Roman numerals. He is also remembered for a series of numbers that now bears his name. The Fibonacci sequence starts with 1, 1 and each subsequent number is the sum of the two previous numbers. The first ten numbers in the Fibonacci series are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

• ## Fibonacci Numbers and the Golden Section5 stars

My Fibonacci pick of the week belongs to Dr. Ron Knott, and is hosted by Surrey University. It is very extensive, and certainly has something for everybody. Those wanting an introduction will first find a definition of the Fibonacci sequence by clicking the underlined link "add the last two to get the next" or scrolling down to the "Fibonacci Numbers and Golden Sections in Nature" section. Must see clicks include the Easier and Harder Fibonacci Puzzles Pages, and the Mathematical Magic page which looks at patterns in the Fibonacci numbers.

• ## Math Forum: Ask Dr. Math: Golden Ratio, Fibonacci Sequence4 stars

"Please tell me about the Golden Ratio (or Golden Mean), the Golden Rectangle, and the relation between the Fibonacci Sequence and the Golden Ratio." Dr. Math answers these three frequently asked questions, and then provides links to related Fibonacci questions from the Dr. Math Archive. Wondering how to calculate the Fibonacci numbers? The first three answers in the archive list describe three different methods.

• ## Plus Magazine: Life and Numbers of Fibonacci3 stars

From the pages of Plus Magazine, this one-page article is a synopsis of Dr. Knott's larger Fibonacci site (see above) but many will find it less intimidating. It begins with a short biography, and then introduces the Fibonacci sequence and the golden section ("normally denoted by the Greek letter phi.") It shows how phi relates to the five-pointed pentagram star used in the American flag, and how the Greeks used the golden ratio in architecture.

• ## Thinkquest: Fibonacci Series5 stars

Created for the 1999 ThinkQuest competition, this Fibonacci site was built by three high school students. The site explores the concepts of the Fibonacci series, Binet's formula, the Fibonacci spiral and the Golden Ratio. The best clicks are the animations they created to explain the various formulas. Their animations and proofs can be found by following the A and P icons next to the navigation arrows at the bottom of most pages. A complete list of animations (and chapter quizzes) can be found in the site index on the home page.

• By . Originally written on Dec 20, 2006. Last Modified on Feb 22, 2010.

• #### Honorable Mentions

The following links are either new discoveries or sites that didn't make it into my newspaper column because of space constraints. Enjoy!

• ### Math World: Fibonacci Number

•  Fibonacci Trading: How to Master the Time and Price Advantage by Carolyn Boroden (Hardcover) - Usually ships in 24 hours Price: \$40.51
 Blockhead: The Life of Fibonacci by Joseph D'Agnese (Hardcover) - Usually ships in 24 hours Price: \$9.43
 Fibonacci Analysis (Bloomberg Financial) by Constance Brown (Hardcover) - Usually ships in 24 hours Price: \$16.23