It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this! Using The Golden Ratio to Calculate Fibonacci Numbers. And even more surprising is that we can calculate any Fibonacci Number using the Golden Ratio: x n = φ n − (1−φ) n √5

Fibonacci Numbers. There is a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it). When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio:

Illustrated definition of Fibonacci Sequence: The sequence of numbers: 0,1,1,2,3,5,8,13,21,... Each number equals the sum of the two numbers before it. ...

The Fibonacci Sequence is found by adding the two numbers before it together. The 2 is found by adding the two numbers before it (1+1) The 21 is found by adding the two numbers before it (8+13)

Fibonacci Sequence. There is a special relationship between the Golden Ratio and the Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... (The next number is found by adding up the two numbers before it.) And here is a surprise: when we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden ...

Fibonacci Sequence; Triangular Sequence; And there are also: Prime Numbers; Factorial Numbers; And many more! Visit the On-Line Encyclopedia of Integer Sequences to be amazed. If there is a special sequence you would like covered here let me know.

But mathematics is so powerful we can find more than one Rule that works for any sequence. Example: the sequence {3, 5, 7, 9, ...} We have just shown a Rule for {3, 5, 7, 9, ...} is: 2n+1

Fibonacci Sequence. Try this: make a pattern by going up and then along, then add up the values (as illustrated) ... you will get the Fibonacci Sequence. (The Fibonacci Sequence starts "0, 1" and then continues by adding the two previous numbers, for example 3+5=8, then 5+8=13, etc)

Fibonacci Sequence. The Fibonacci Sequence is the series of numbers: 0 1 1 2 3 5 8 13 21 34 ... The next number is found by adding up the two numbers before it: /numbers/fibonacci-sequence.html. Nature The Golden Ratio and Fibonacci Numbers. Plants can grow new cells in spirals such as the pattern of seeds in this beautiful sunflower.

This is a famous fractal in mathematics, named after Benoit B. Mandelbrot. It is based on a complex number equation (z n+1 = z n 2 + c) which is repeated until it: diverges to infinity, where a color is chosen based on how fast it diverges