The,Fibonacci,Sequence,The,Fib education The Fibonacci Sequence
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The Fibonacci sequence is one of the most well known sequences, withnumerous links with nature, and also finds its way unexpectedly into otherareas of mathematics. In this article, I explain how the Fibonacci sequence isformed, and talk about some of the many places it can found in the world aroundus.The first two terms of the Fibonacci sequence are 1,1. From then on, eachterm is the sum of the previous two terms. This makes the third term 1 + 1 = 2,and the fourth term 1 + 2 = 3, and so on. The first ten Fibonacci numbers areshown below:1, 1, 2, 3, 5, 8, 13, 21, 34, 55A classic "real life" example of Fibonacci numbers is with rabbits.It goes a bit like this: I start with a pair of young rabbits in month 1. Fortheir first month, they do not breed, as they are too young. However, for everymonth after this, they produce one new pair of young rabbits, which in turngrow up in a month and start breeding. If we call a junior pair of rabbits JJand a senior pair SS, this is what happens:Month1. JJ = 1 pair2. SS = 1 pair3. SS + JJ = 2 pairs4. SS + SS + JJ = 3 pairs5. SS + SS + SS + JJ + JJ = 5 pairs6. SS + SS + SS + SS + SS + JJ + JJ + JJ = 8 pairsThe number of pairs of rabbits gives the Fibonacci numbers! Luckily, inreality, there are certain factors that limit this growth in population. Therabbits will eventually die and stop producing new pairs, there will be limitedfood and space, etc. According to the sequence, by the end of two years, Iwould have over 46,000 pairs of rabbits, so it is a good thing thatthis is not really what happens in nature!However, the Fibonacci sequence does have some closer links with nature. Forexample, flowers tend to have a Fibonacci number of petals. This is why it's sohard to find a four leaved clover! If you ever get really bored, you can countthe number of petals on a daisy - it may not be exact, but it should be around55 or 89! Other links with nature include the arrangement of seeds insunflowers and pines in pine cones, and even the spirals of the shells of someanimals.One final interesting property of Fibonacci numbers is that they can befound in Pascal's Triangle. They are perhaps the hardest pattern to spot of allthe commonly discussed sequences that can be found in Pascal's triangle, butthey are worth searching long and hard for, because they are one of the amazingpatterns that can be found in Pascal's triangle! (If you want a hint, thendon't look for the numbers themselves, but try adding together numbers from thetriangle to make them). Normal 0 false false false EN-GB X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable{mso-style-name:"Table Normal";mso-tstyle-rowband-size:0;mso-tstyle-colband-size:0;mso-style-noshow:yes;mso-style-priority:99;mso-style-qformat:yes;mso-style-parent:"";mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-para-margin-top:0cm;mso-para-margin-right:0cm;mso-para-margin-bottom:10.0pt;mso-para-margin-left:0cm;line-height:115%;mso-pagination:widow-orphan;font-size:11.0pt;font-family:"Calibri","sans-serif";mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi;} Article Tags: Fibonacci Sequence, Fibonacci Numbers, Pascal's Triangle
The,Fibonacci,Sequence,The,Fib