Q: How do you use the Fibonacci sequence in the real world?

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The exact first date of use is unknown, but one of the earliest uses was by Plato in the 400s BC. The connection of phi to Pascal's triangle was made when Leonardo Fibonacci created his Fibonacci sequence.

The main use for the golden ratio is its aesthetic appeal - in art and architecture. Rectangles with the golden ratio as their aspect appeal to the human mind (for some reason). So various aspects of the Parthenon in Athens, for example, have dimensions whose ratio is phi. Phi is closely related to the Fibonacci sequence: the ratio of successive terms of the sequence approaches phi and so, just like the Fibonacci sequence, phi appears in many natural situations. However, there is no particular application based on phi.

Different authors use different conventions for indexing the Fibonacci sequence (n.b., "sequence" not "series"). For example, in Cameron's Combinatorics, he defines F1=1, F2=2. The most common choice, used for example in Sloane's Online Encyclopedia of Integer Sequences (http://www.research.att.com/~njas/sequences/), is to define thezeroth Fibonacci number to be 0 and the first to be 1; thus the second is also 1. With this choice, a number of formulas become simpler and we have this particularly nice number-theoretic result: if m divides n, then the mth Fibonacci number divides the nth Fibonacci number.

The "golden ratio" is the limit of the ratio between consecutive terms of the Fibonacci series. That means that when you take two consecutive terms out of your Fibonacci series and divide them, the quotient is near the golden ratio, and the longer the piece of the Fibonacci series is that you use, the nearer the quotient is. The Fibonacci series has the property that it converges quickly, so even if you only look at the quotient of, say, the 9th and 10th terms, you're already going to be darn close. The exact value of the golden ratio is [1 + sqrt(5)]/2

Because it is so interesting.. . .. ... ..... ........ ............. .....................Fibonacci first published a use for the pattern to explain bunny population growth in his book Liber Abaci (1202).Other interesting uses for the Fibonacci Sequence:The Golden Ratio and The Golden Spiral (as seen in DaVinci's Vitruvian Man)Phyllotaxis (how leaves appear on stem)Predicting stock share pricing (Fibonacci retractment)Graphs interconnecting parallel and distributed systems (Fibonacci Cubes)The Core in Cornwall, UK (architecture)The chorus of Astronomy, a hip-hop song by Black StarThe time signatures and syllable structure of the Toolsong LateralusAncestry of male bees

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You use the sequence in making robots and programing computers.

the numbers branches, stems, petals coincide with the Fibonacci sequence.

yes!

Langdon used the Fibonacci sequence to identify the key numbers in Sauniere's message, which helped him decipher the message as a series of numerical codes. By recognizing the Fibonacci sequence in the arrangement of the codes, Langdon was able to uncover the hidden message left by Sauniere.

The 6th number of the Fibonacci sequence is 8.0 + 0 = 00 + 1 = 11 + 1 = 21 + 2 = 32 + 3 = 53 + 5 = 8Notice how it is the 6th equation meaning its the 6th Fibonacci number.Note that some people like to use 1 twice instead of 0.http://en.wikipedia.org/wiki/Fibonacci_number

Fibonacci sequence, also known as golden section sequence, is also known as "rabbit sequence" because mathematician Leonardoda Fibonacci introduced it by taking rabbit breeding as an example , refers to such a sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34,... Mathematically, Fibonacci sequence is defined recursively as follows: F (1) = 1, f (2) = 1, f (n) = f (n-1) + F (n-2) (n > = 2, n ∈ n *) The difficulty of Fibonacci sequence lies in the algorithm. If it becomes a generator, it needs to use the for loop to traverse the iteratable generator The first recursive method def fib_recur(n): assert n >= 0, "n > 0" if n

The exact first date of use is unknown, but one of the earliest uses was by Plato in the 400s BC. The connection of phi to Pascal's triangle was made when Leonardo Fibonacci created his Fibonacci sequence.

Leonardo Pisano Fibonacci, or Leonardo of Pisa, was a famous mathematician, who introduced the modern numeric system that many nations use nowadays, born and raised in Italy. Alongside introducing numbers, he developed the now famous Fibonacci Sequence, which adds together the two previous numbers in the sequence; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.

Leonardo Fibonacci was an Italian mathematician who advocated the use of Arabic numerals. He wrote a book called LiberAbaci, which demonstrated the use of the number system. Fibonacci numbers, a sequence used in the book to illustrate its message, had been known before his time, but the numbers took his name because they were connected with the book.

Fictitious (ficticius artificial, feigned, from fictus) is the use of your imagination to create something. for example making a flag using the Fibonacci Sequence.

The Fibonacci sequence uses recursion to derive answers. It is defined as: F0 = 0 F1 = 1 Fn = F(n - 1) + F(n -2) To have this sequence printed by a php script use the following: function fibonacci($n) { if($n 1) return 1; //F1 else return fibonacci($n - 1) + fibonacci($n - 2); //Fn } This recursive function will print out the Fibonacci number for the integer n. To make it print out all the numbers in a particular set add this to your script. for($i = 0; $i < 15; $i++) { echo fibonacci($i) . "<br />"; } So your final result would look like. <?php function fibonacci($n) { if($n 1) return 1; else return fibonacci($n - 1) + fibonacci($n - 2); } for($i = 0; $i < 15; $i++) { echo fibonacci($i) . "<br />"; } ?>

yes Not explicitly, but many spiral cones - pine cones, sunflower seeds - are based on the Fibonacci sequence. Plans also use the sequence in determining the rotation between successive branches (or leaves) so as to maximise exposure to sunlight.