Q: What value do you learn from the nature to obey Fibonacci sequence?

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Each number in the Fibonacci sequence is the sum of the two previous numbers. The first two numbers are 1. If you add them together, you get 2. Then add 2 to one to get 3. 3+2=5, and so on, until you get the 8th value. It is important to remember that the first two ones are part of the sequence.1, 1, 2, 3, 5, 8, 13, 21

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

As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.

F658

A sequence cannot be defined by one number. At least, not a sequence of any value.

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0, 1, 1, 2, 3, 5, 8 so the 7th term is 8

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 />"; } ?>

Each number in the Fibonacci sequence is the sum of the two previous numbers. The first two numbers are 1. If you add them together, you get 2. Then add 2 to one to get 3. 3+2=5, and so on, until you get the 8th value. It is important to remember that the first two ones are part of the sequence.1, 1, 2, 3, 5, 8, 13, 21

This is a combination of 2 mathematical things -- the Golden ratio and the Fibonacci sequence. The Golden ratio is (a+b)/a = a/b or ((1 + sqrt(5))/2 = 1.618...). A rectangle with sides of length a and b (with a>b) can have a square of size b removed from one end and leave a rectangle with the same ratio of sides as the original, but smaller of course. The simplest Fibonacci sequence is (0,1,1,2,3,5,8,13,21,...) start with 0 and 1, add them together to get 1. The last 2 entries are now (1,1), add them to get 2. The last 2 entries are (1,2), add them to get 3. Etc. The 2 are related in that dividing an entry in the Fibonacci sequence by the one before it gets closer to the numeric value of the Golden ratio the higher the entry number is

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

As you expand the Fibonacci series, each new value in proportion to the previous approaches the Golden Ratio.

F658

Here is a good answer for recursion Fibonacci series. #include <stdio.h> #include <conio.h> long Fibonacci(long n); int main() { long r, n,i; printf("Enter the value of n: "); scanf("%ld",&n); for(i=0;i<=n;i++) { printf(" Fibonacci(%ld)= %ld\n", i,Fibonacci(i)); } getch(); return 0; } long Fibonacci(long n) { if(n==0 n==1) return n; else { return (Fibonacci(n-1)+Fibonacci(n-2)); } } for n=5; Output: Fibonacci(0)=0 Fibonacci(1)=1 Fibonacci(2)=1 Fibonacci(3)=2 Fibonacci(4)=3 Fibonacci(5)=5

It creates a decreasing sequence.

Unlike some other types of numbers like prime numbers, calculating large Fibonacci numbers can be done quite easily with even a standard household computer. The process involves only repeated addition (rather than the intense division processes involved with large prime numbers). Beyond that, large Fibonacci numbers do not serve as much purpose as other large numbers (like primes). Because of this, these large numbers are generally left for quick calculation by machine if ever necessary. An example of a computer program that could calculate the nth Fibonacci number (n greater than 1 and counting the first 1 in the sequence as the second term) is given below in pseudo-code: Function Fibonacci(n) a = 0 b = 1 k = 2 While n > k ( a + b = c a = b b = c k = k + 1 ) Print b A very large Fibonacci number is the 250th in the sequence which has a value of: 12776523572924732586037033894655031898659556447352249. The 1000th term in the sequence is: 4346655768693745643568852767504062580256466051737178040248172908953655 5417949051890403879840079255169295922593080322634775209689623239873322 471161642996440906533187938298969649928516003704476137795166849228875. Much, much larger values (even beyond the 10,000,000th term) can be calculated quite quickly with a simple, well-written program. See related links for a site which can quickly calculate large Fibonacci numbers (using the form Fibonacci n).

A sequence cannot be defined by one number. At least, not a sequence of any value.

The following is a schematic program. Details will depend on the language.n1 = 1output n1n2 = 1output n2.start loopn3 = n1 + n2output n3got enough numbers?if yes go to end elsen1