Difference between revisions of "Fibonacci numbers"

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==Mathematics==
==Mathematics==
The ratio <math> \frac {F_n}{F_{n+1}} \ </math> approaches the [[golden ratio]] as <math>n</math> approaches infinity.
The ratio <math> \frac {F_n}{F_{n+1}} \ </math> approaches the [[golden ratio]] as <math>n</math> approaches infinity.
 
[[File:PascalTriangleFibanacci.png|thumb|right|360px|The Fibonacci numbers are the sums of the "shallow" diagonals (shown in red) of [[Pascal's triangle]].]]
The Fibonacci numbers occur in the sums of "shallow" diagonals in [[Pascal's triangle]].
The Fibonacci numbers occur in the sums of "shallow" diagonals in [[Pascal's triangle]].
:<math>F_n = \sum_{k=0}^{\left\lfloor\frac{n-1}{2}\right\rfloor} \binom{n-k-1}{k}</math>
:<math>F_n = \sum_{k=0}^{\left\lfloor\frac{n-1}{2}\right\rfloor} \binom{n-k-1}{k}</math>


== Resources: ==
== Resources: ==
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