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THE FIBONACCI NUMBERS

\Fibonaccinumbers"is usedto describe theseriesof numbersgener-atedby thepattern1;1;2;3;5;8;13;21;34;55;89;144 :::,whereeach number in thesequenceis given by thesumof theprevioustwo given byu1= 1,u2= 1 andtherecursive formulaun=un 1+un 2; n > fromthefamous\rabbitproblem"of 1228,theFibonaccinumberswereoriginallyus edto represent thenumber of pairsof rabbitsbornof onepairin a assumethata pairof rabbitsis introducedinto acertainplacein the rstmonth of rabbitswillproduceonepairof o springeverymonth,andeverypairof rabbitswillbeginto reproduceexactlytwo dies,andeverypairof ,in the rstmonth,we have onlythe rstpairof ,in thesecondmonth,we againhave onlyourinitialpairof ,by thethirdmonth,thepairwillgive birthto anotherpairof rabbits,andtherewillnowbe two ,we ndthatin monthfourwe willhave 3 pairs,then5 pairsin month ve, then8,13,21,34.

quite apparent that this sequence directly corresponds with the Fibonacci sequence introduced above, and indeed, this is the rst problem ever associated with the now-famous numbers. Now that we have seen one application of the Fibonacci numbers and established a basic de nition, we will go on to examine some of the simple properties regarding

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