Fibonacci Numbers

Pronunciation: /ˌfib.oʊˈnɑ.tʃi ˈnʌm.bərz/ Explain

Fibonacci numbers Number Calculation 0 Defined as 0 1 Defined as 1 1 0 + 1 = 1 2 1 + 1 = 2 3 1 + 2 = 3 5 2 + 3 = 5 8 3 + 5 = 8 13 5 + 8 = 13 21 8 + 13 = 21 34 13 + 21 = 34 55 21 + 34 = 55 ... Table 1: Fibonacci numbers

Fibonacci numbers are a sequence of numbers starting with 0, 1. After the first two numbers, each number in the sequence is calculated by adding the two previous numbers. See table 1. Fibonacci numbers were first described in (asiatic) Indian mathematics. However, they are named after Leonardo de Pisa [c. 1170 – c. 1250] who introduced them to the western world in his book Liber Abaci (Book of Calculation). Leonardo de Pisa is also know as Fibonacci (son of Bonacci). The Fibonacci numbers have some interesting properties. Figure 1 shows a sequence of squares. The length of the side each square is one of the Fibonacci numbers. These squares form a rectangle that grows with each Fibonacci number.

Figure 1: Fibonacci Squares

References

1. McAdams, David E.. All Math Words Dictionary, fibonacci numbers. 2nd Classroom edition 20150108-4799968. pg 79. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Fibonacci numbers. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 7/11/2018. http://www.merriam-webster.com/dictionary/fibonacci numbers. Buy the book
3. Laurence Sigler. Fibonacci's Liber Abaci. Springer. November 11, 2003. Last Accessed 7/11/2018. Buy the book
4. Alfred S. Posamentier and Ingmar Lehmann. The Fabulous Fibonacci Numbers. Prometheus Books. June 21, 2007. Last Accessed 7/11/2018. Buy the book
5. Nicolai N. Vorobiev and M. Martin. Fibonacci Numbers. Birkhäuser Basel. January 31, 2003. Last Accessed 7/11/2018. Buy the book

Educator Resources

• Fibonacci Sequence Activity (movie). NASA Connect. 2/4/2010. http://www.archive.org/details/NasaConnect-Mtf-FibonacciSequenceActivity/index.htm.
• Ratios and Aircraft Design (movie). NASA Connect. 2/4/2010. http://www.archive.org/details/NasaConnect-Mtf-RatiosAndAircraftDesign/index.htm.
• Transportation Growth and Patterns. NASA Connect. 2/4/2010. http://www.archive.org/details/NasaConnect-Mtf-TransportationGrowthAndPatterns/index.htm.
• Proportionality - Modeling the Future. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Proportionality-ModelingTheFuture/index.htm.

Cite this article as:

McAdams, David E. Fibonacci Numbers. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/f/fibonaccinumbers.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/4/2010: Added "References". (McAdams, David E.)
2/10/2009: Clarified 'Indian mathematics' as 'Asiatic Indian mathematics'. (McAdams, David E.)
12/29/2008: Added link to. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)