Fibonacci


 * Fibonacci is in many flowers, since the number of petals on many plants are a Fibbonacci number like lilies that have 3 petals, buttercups have 5, and marigolds with 8.- Sunil **
 * Fibonacci Sequence-Alex Pham**
 * Leonardo Fibonacci discovered the sequence- Sunil **

The Fibbonacci Numbers in the human skeleton-1+1+=2+1=3+2=5+3=8- ZM In the Fibbonacci ratio above, you add 1 to the first number, then two to the sum, then three and so on.

Musical scales are based on Fibonacci numbers
> A scale is composed of 8 notes, of which the > 5 th and 3 rd notes create the basic foundation of all chords, and are based on whole tone which is > 2 steps from the root tone, that is the > 1 st note of the scale. || In a scale, the dominant note is the 5th note of the major scale, which is also the 8th note of all 13 notes that comprise the octave. This provides an added instance of Fibonacci numbers in key musical relationships. Interestingly, 8/13 is .61538, which approximates phi. What's more, the typical three chord song in the key of A is made up of A, its Fibonacci & phi partner E, and D, to which A bears the same relationship as E does to A. This is analogous to the "A is to B as B is to C" basis for the golden section, or in this case "D is to A as A is to E." ||
 * [[image:http://goldennumber.net/images/piano.gif width="124" height="100" caption="Piano keyboard - even music is based on the Fibonacci series"]] || The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as: > There are 13 notes in the span of any note through its octave.
 * Note too how the piano keyboard scale of C to C above of 13 keys has 8 white keys and 5 black keys, split into groups of 3 and 2 . While some might "note" that there are only 12 "notes" in the scale, if you don't have a root and octave, a start and an end, you have no means of calculating the gradations in between, so this 13th note as the octave is essential to computing the frequencies of the other notes. The word "octave" comes from the Latin word for 8, referring to the eight whole tones of the complete musical scale, which in the key of C are C-D-E-F-G-A-B-C.

The sequence, in which **each number is the sum of the two preceding numbers** is known as the **Fibonacci series:** 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181... To get from one number to the next you must add the two previous numbers to fuind the next one. The Fiboncacci sequence can go one forever withought stopping. - Doug

Jen Nam
-Andrew Himes *These three pictures all show how the Fibonacci sequence occurs in real life.- Justin White The fibonacci sequence is the reverse of the golden ratio- CJ

The Fibonacci Sequence is found in a golden rectangle, the sequence is taking two numbers starting at 1 and 1, adding them, then adding the sum and the previous last number highest number. -Andrew Himes

Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 55, 89, 144, 233, 377,. . . Fibonacci, while studying how many rabbits would be born from an original pair of rabbits, assumed that every month each pair would produce another pair and that rabbits would begin to breed when they are two months old. After the process got started, the total number of pairs of rabbits at the end of each month would be as follows: 1, 2, 3, 5, 8, 13, 21, 55, 89, 144, 233. Each successive number is the sum of the two preceding numbers. Divide any of the Fibonacci numbers by the next higher number [and] the sequence of ratios will converge to 0.618. Dividing a number by its previous number will converge to 1.618. The Greeks knew this proportion and called it the ‘Golden Mean’. -CJ This is an example of fibonacci because the previous two sections of the instrument combined equals the next part-CJ

The Fibonacci sequence is a set of numbers which if you take one number, then add the two numbers previous; it will equal the original number. Example; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025. This sequence could be applied to real – life situations in the following ways; the amount of buds growing on a tree or the petals growing on the iris flower. - Matt H

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 * This is an example of a recursive sequence which means **each term of the sequence is defined as a function of the preceding terms, obeying the simple rule that to calculate the next term one simply sums the preceding two and a formula hat you can use to find the next number is======

** -Sunil **


This is the Pascal's triangle where if you start at the Number 1 on the left side and go diagonal and add the numbers together you will end up with a number in the Fibonacci Sequence that is in the right sequence. -Sunil