Fibonacci SequenceDate: 06/18/2001 at 14:30:04 From: brandi barrigher Subject: Fibonacci sequence I need help understanding what the Fibonacci sequence really is. I have visited many different Web sites, but they have the same information. Date: 06/19/2001 at 21:25:48 From: Doctor Jodi Subject: Re: Fibonacci sequence Hi Brandi, The Fibonacci sequence is a sequence of numbers. Specifically, the sequence 1, 1, 2, 3, 5, 8, 13, 21, ... How do you get the next term in the sequence? (You add the two previous terms.) The Fibonacci sequence is named for Leonardo Pisano (his nickname was Fibonacci), an Italian educated in North Africa who lived around 1200 A.D. This famous sequence arose in connection with the following problem, taken from a book Fibonacci published in 1202: A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive? You can read more about Fibonacci's life from the MacTutor History of Mathematics archive: http://www-history.mcs.st-and.ac.uk/history/ To find Fibonacci, go first to the Biographies Index and then select F from the alphabetical index. I recommend making a table depicting the first few months of the rabbits' lives. Mature rabbits (which will bear a new pair of rabbits in the next month) should be colored one color (say red), while the newborn rabbits should be colored another (say green). (There's a beautiful illustration like this in a book called the _Number Devil_ by Hans Magnus Enzensberger.) The ratios of consecutive pairs of numbers in the Fibonacci sequence (1/1, 2/1, 3/2, 5/3, 8/5, etc.) tend to the Golden Ratio. You can find more responses to questions about the Fibonacci sequence and the Golden Ratio in the high school area of the Dr. Math archives: http://mathforum.org/dr.math/drmath.high.htmll and in the links to relevant sites on the Web in the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.golden.ratio.html Thanks for writing us and feel free to write back. - Doctor Jodi, The Math Forum http://mathforum.org/dr.math/ |
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