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1、FibonacciNumbers,theGoldensectionandtheGoldenStringFibonacciNumbersandtheGoldenSectionThisistheHomepagefortheFibonaccinumbers,theGoldensectionandtheGoldenstring.TheFibonaccinumbersare0,1,1,2,3,5,8,13,...(addthelasttwotogetthenext)Thegoldensectionnumbersare±0·618033
2、9887...and±1·6180339887...Thegoldenstringis1011010110110101101...asequenceof0sand1swhichiscloselyrelatedtotheFibonaccinumbersandthegoldensection.Thereisalargeamountofinformationatthissite(morethan200pagesifitwasprinted),soifallyouwantisaquickintroductionthenthefirs
3、tlinktakesyoutoanintroductorypageontheFibonaccinumbersandwheretheyappearinNature.TherestofthispageisabriefintroductiontoallthewebpagesatthissiteonFibonacciNumberstheGoldenSectionandtheGoldenStringtogetherwiththeirmanyapplications.What'sNew?7June2001Arecentback-uper
4、rormeansthatI'vejustlostallemailssenttomeduringMarchandApril.Pleasecanyoure-sendyouremailifyou'vehadnoreply-sorry!FibonacciNumbersandGoldensectionsinNatureFibonacciNumbersandNatureFibonacciandtheoriginalproblemaboutrabbitswheretheseriesfirstappears,thefamilytreesof
5、cowsandbees,thegoldenratioandtheFibonacciseries,theFibonacciSpiralandseashellshapes,branchingplants,flowerpetalandseeds,leavesandpetalarrangements,onpineapplesandinapples,pineconesandleafarrangements.AllinvolvetheFibonaccinumbers-andhere'showandwhy.TheGoldensection
6、inNatureContinuingthethemeofthefirstpagebutwithspecificreferencetowhythegoldenhttp://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html(1of8)[12/06/200117:11:49]FibonacciNumbers,theGoldensectionandtheGoldenStringsectionappearsinnature.NowwithaGeometer'sSketch
7、paddynamicdemonstration.ThePuzzlingWorldofFibonacciNumbersApairofpageswithplentyofplayfulproblemstoperplextheprofessionalandthepart-timepuzzler!TheEasierFibonacciPuzzlespagehastheFibonaccinumbersinbrickwallpatterns,Fibonaccibeelines,seatingpeopleinarowandtheFibonac
8、cinumbersagain,givingchangeandagamewithmatchsticksandevenwithelectricalresistanceandlotsmorepuzzlesallinvolvetheFibonaccinumbers!TheHarderFibonac
