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By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s. In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation with seed values The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci (a contraction of filius Bonaccio, "son of Bonaccio".) Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics. From Wikipedia under the
GNU Free Documentation License  jesystems.com 679px x 624px | 59.00kB [source page] The Golden Mean and Fibonacci Numbers  stockinvestingideas.com 350px x 387px | 11.90kB [source page] If the trend is rising the retracement lines will descend from 100 to 0 If the trendline is falling the retracement lines will ascend from 0 to 100 Fibonacci Extensions Levels used in Fibonacci retracement to forecast areas of support or resistance Extensions consist of all levels drawn beyond the standard From Yahoo Image Search: "Fibonacci Numbers"  homeschoolblogger.com unknown Mon, 10 Aug 2009 21:14:00 GM I remember reading about . Fibonacci numbers. . (I may not have spelled that right.) Anyway, how they do it is 1+2=3, 2+3=5, 3+5=8... so your . numbers. climb rather quickly because you are always adding the second . number. of the previous ...  lernc.blogspot.com Pankaj A.H. Sun, 16 Aug 2009 15:21:00 GM #include int main() { int i; int . fibonacci. = 1; int prevfib = 0; int tmp; for(i = 1; i <= 10; i = i + 1) { printf("%d %d\n", i, . fibonacci. ); tmp = . fibonacci. ; . fibonacci. = . fibonacci. + prevfib; prevfib = tmp; ...  blog.investraction.com Deepak Shenoy Sun, 02 Aug 2009 09:54:00 GM Note that the first "support" was somewhere between two fibo levels - which is ignored because it didn't follow the . fibonacci number. strategy. Going this way you can find ANY . fibonacci number. that matches something because at some point ... From Google Blog Search: "Fibonacci Numbers"  news.google.com DailyForex The Fibonacci sequence was developed by Leonardo Fibonacci . He is famous for working out the Fibonacci sequence of numbers . The sequence is obtained by ... news.google.com Forex Hound The $913 level corresponded with the 61.8% Fibonacci retracement of the move from $865 to $990. Additionally, Barclays Capital believes that gold could see ... and more » news.google.com Gold Investing News Incidentally, this is the 38.2 per cent Fibonacci retracement, and is roughly where August gold stopped twice in the last week. Above this, $960 will be the ... and more » From Google News Search: "Fibonacci Numbers" What is the relationship between the Fibonacci numbers and the Golden Ratio? Q. a) Fibonacci numbers are the same as golden ratios. b)The sum of the members of the Fibonacci series approaches the Golden Ratio as a limit. or c) The ratio of the members of the Fibonacci series approaches the Golden Ratio as a limit. Also, What is the Golden Proportion? a) If the ratio between the sum of two quantities and the larger one is the same as the ratio between the sum of the two quantities and the smaller one, we have a golden proportion. b) If the ratio between the sum of two quantities and the smaller one is the same as the ratio between the smaller one and the larger, we have a golden proportion. c) If the ratio between the sum of two quantities and the larger one is the same as the ratio between the larger one and the… [cont.] Asked by heyhhc - Wed May 6 16:03:22 2009 - - 1 Answers - 0 Comments Prove that that exists a perfect square and perfect cube in the infinite series of Fibonacci numbers? Q. {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 91 ...} How can I go about to prove that there exists or there doesn't exist a perfect square and perfect cube in the series. If there exists these numbers, how can i possibly find the smallest one? obviously, exclude 1 :) Asked by Man - Sun Nov 25 12:03:45 2007 - - 5 Answers - 0 Comments A. First, there is a mistake in your question. 91 should be 89. Next, start hunting! You already have a cube, F_6 = 8. Also 55+ 89 = 144 = 12 . Here's what's known about these questions: 1,1 and F_12 = 144 are the only squares in the Fibonacci sequence. This was proved by J.H.E Cohn in 1964. 1,1 and F_6 = 8 are the only cubes. This was proved by Yours Truly in 1967. It was part of my doctoral dissertation. You can find a simplified proof of this in my paper On Nth Powers in the Lucas and Fibonacci Series, Fibonacci Quarterly,16.5 (1978) 451 Very recently, it was proved that there are no higher powers in this sequence except 1 and 1. This proof is exceedingly complicated and relies on estimations for linear forms in the logarithms of 3… [cont.] Answered by steiner1745 - Sun Nov 25 12:24:23 2007 What are Fibonacci numbers used for?
Q. I was just thinking about it. They seem to have absolutely no purpose. Does anyone know? Asked by hihihi - Sun Feb 24 16:40:15 2008 - - 5 Answers - 1 Comments A. i love that sequence... There are a few things in which the sequence can be found... but as far as practical use, its not entirely mathematically relevant... mostly because we have yet to find a way of creating a single mathematical formula that describes the sequence (we can only say what the sequence is... there's no formula for A [Sub N]) However, the sequence has a few interesting appearances in the world... First off you have to understand the Golden Spiral. If you map out squares, whose sides are in ration to the fibonacci sequence, and then connect the nodules of the squares, you create a spiral... here's an image: This spiral can be seen everywhere in nature... from ocean waves, to pine cones, to the human body, to the way… [cont.] Answered by Jake Scot - Sun Feb 24 16:58:39 2008 From Yahoo Answer Search: "Fibonacci Numbers"
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Fibonacci Numbers, Phi and the Golden Ratio
Fibonacci Numbers
Fibonacci resources