Difference between revisions 3684408 and 3684409 on mswiki

{{pelbagai isu|{{cleanup|reason=memerlukan penterjemahan segera kerana sudah ditinggalkan sejak tahun 2008|date=Ogos 2014}}{{Terjemah|en|fabonacci number|date=Ogos 2014}}}}
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[[Image:FibonacciBlocks.svg|thumb|180px|right|Suatu ubinan dengan segi empat yang tepinya adalah nombor Fibonaci berturut-turut pada panjangnya]]
(contracted; show full):<math>\displaystyle  5^2 + 12^2 = 13^2 \,.</math>
Example 2: let the Fibonacci numbers be 8, 13, 21 and 34. Then:
:<math>\displaystyle  a = 8 \times 34 = 272</math>
:<math>\displaystyle  b = 2 \times 13 \times 21 = 546</math>
:<math>\displaystyle  c = 13^2 + 21^2 = 610 \,</math>
:<math>\displaystyle  272^2 + 546^2 = 610^2 \,.</math>

==Magnitud
e of nombor Fibonacci numbers==
Since ==
Memandangkan<math>F_n</math> is [[adalah [[berasyimptotic]] tokepada <math>\varphi^n/\sqrt5</math>, the number of digits in the base ''b'' representation ofbilangan digit dalam asas perwakilan ''b'' <math>F_n\,</math> is adalah berasyimptotic to kepada <math>n\,\log_b\varphi</math>.

In bDalam asase 10, for every integer greater thanuntuk setiap integer yang lebih besar daripada 1 there are 4 or 5 Fibonacci numbers with that number of digits, in most casdapat 4 atau 5 nombor Fibonacci dengan bilangan digit itu, dalam kebanyakan kes 5.

==Applications==

The Fibonacci numbers are important in the run-time analysis of [[Euclidean algorithm|Euclid's algorithm]] to determine the [[greatest common divisor]] of two integers: the worst case input for this algorithm is a pair of consecutive Fibonacci numbers.

[[Yuri Matiyasevich]] was able to show that the Fibonacci numbers can be defined by a [[Diophantine equation]], which led to [[Matiyasevich's theorem|his original solution]] of [[Hilbert's tenth problem]].

(contracted; show full)
*[http://web.archive.org/web/20070715032716/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=630&bodyId=1002 Fibonacci Numbers] at [http://web.archive.org/web/20060212072618/http://mathdl.maa.org/convergence/1/ Convergence]
* [http://www.tools4noobs.com/online_tools/fibonacci/ Online Fibonacci calculator]

[[Kategori:Fibonacci numbers|*]]
[[Kategori:Articles containing proofs]]

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