Difference between revisions of "Fibonacci sequence"
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
| − | + | The '''Fibonacci sequence''' is a series of numbers in which each number is the sum of the two preceding numbers. The numbers are known as '''Fibonacci numbers'''. | |
'''Example''' | '''Example''' | ||
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ... | 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ... | ||
| + | |||
| + | The Fibonacci numbers were first described by the Sanskrit linguist Pingala around the year 450 BC. They arose from the study of meters with long and short syllables. | ||
| + | |||
| + | The first Western mathematician to study this sequence was Leonardo of Pisa, commonly known as [[Fibonacci]], in the consideration of the growth of an idealized rabbit population. | ||
| + | |||
| + | [[Johannes Kepler]] discovered that the [[limit]] of the ratios between succeeding Fibonacci numbers converges to the [[golden ratio]]. Fibonacci numbers also occur in [[Pascal's triangle]] and the run-time analysis of [[Euclid's Algorithm]]. | ||
== Examples of Fibonacci Sequences == | == Examples of Fibonacci Sequences == | ||
| − | * The family trees of honey bees can be depicted using fibonacci numbers because unmated females will always hatch male young, while mated females will always hatch female young | + | * The family trees of honey bees can be depicted using fibonacci numbers because unmated females will always hatch male young, while mated females will always hatch female young |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
Revision as of 23:40, March 19, 2007
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers. The numbers are known as Fibonacci numbers.
Example
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
The Fibonacci numbers were first described by the Sanskrit linguist Pingala around the year 450 BC. They arose from the study of meters with long and short syllables.
The first Western mathematician to study this sequence was Leonardo of Pisa, commonly known as Fibonacci, in the consideration of the growth of an idealized rabbit population.
Johannes Kepler discovered that the limit of the ratios between succeeding Fibonacci numbers converges to the golden ratio. Fibonacci numbers also occur in Pascal's triangle and the run-time analysis of Euclid's Algorithm.
Examples of Fibonacci Sequences
- The family trees of honey bees can be depicted using fibonacci numbers because unmated females will always hatch male young, while mated females will always hatch female young