Silverio's Fibonacci Numbers

The red and the blue lines show sets of spirals.

Fibonacci numbers are a sequence where the first two terms are both 1. Fibonnaci numbers came from Arabia. We use this numbers in math. Fibonacci numbers are also found in nature. They are found in apples too. The Golden Ratio is much harder. Ancient Greeks thought a most appealing rectangle was one with the proportion of width/length=length/length+width.

Fibonacci

http://www.mcs.surrey.ac.uk/personal/r.knott/fibonacci/fibnat.html#bees

http://www.mcs.surrey.ac.uk/personal/r.knott/fibonacci/fibnat.html#bees

http://www.mcs.surrey.ac.uk/personal/r.knott/fibonacci/fibnat.html#seeds

http://www.mcs.surrey.ac.uk/personal/r.knott/fibonacci/fibnat.html#leaf
Fibonacci numbers are sequence that start with a number of term and it creates the value of term. You can use the formula F(n).For example: 1+1=2, 2+1=3, 3+2=5..etc. To solve a rectangle you use width/lenght equal to lenght/lenght+width and then you use proportion which is cross multiplying and then use the quadratic formula.Approximate the 3decimal is called Golden ratio.

fibonacci numbers

after two starting numbers , the preceding numbers are the sum of the two last numbers
ex-0,1,1,2,3,5,8,13,21,34,55.......etc. These value of terms/ sequences are and can be found in nature.
it is found in the trees, rabbit population,and seashells. or in this case a flower with its many fibonacci sequence.
To divide divide the fib #'s you need to use a calculator for the big #'s.So for the sea shells it is the curves of the shell.
For the rabbits population it start with 1+1=2+1=3+2=5+3=8........etc

fibonacci, by muting

Fibonacci numbers are a sequence where the first two terms are both 1. for example the n is the number of the term and the F(n) is the value of the term. the number of the term are1,2,3,4,5...........but the value of the term is different, like 1, 1, 1+1=2, 2+1=3, 3+2=5, 5+3=8.........this one is a little easy, but then the golden ratio is little harder, approximate the answer to 3 decimal places, this number is call the golden ratio. you can solve the rectangle of the proportion of width/length=length/length+width by using cross multiply, the using quadratic formula.

This is the picture of a tree stem, as you know, it's kind of the Fibonacci that you can find in the nature. each length and the width of the stem is different than the other tree stem and they also have the different proportion. as you know, the line of the stem have some different . some are up and some are down and you sometime can figure out the stem by using Fibonacci

Vicky`s Fibonacci

Fibonacci numbers are a sequence where the number 1 is the first two terms. N is the number of the term and F(n) is the value of that term. The most appealing rectangle to the ancient Greeks was the one with the proportion of width/length equal to length/ length+width. You solve for x by cross multiplying, and using the quadratic formula. Approximate the answer to 3 decimal places and that number is called the Golden Ratio.

Janet's Fibonacci Numbers

Fibonacci numbers are the sequence where the first two terms are both one. In a fibonacci equation, n is the number of term, and F(n) is the value of term. To find the Golden ratio, you need to use proportion and the quadratic formula. Proportion is two ratios that are equal to each other. You also need to cross multiply to find the golden ratio. It is very easy to use fibonacci numbers, but the golden ratio is harder. The pinecone above is an example of fibonacci that is part of nature. It shows the fibonacci spirals very clearly. There are two different sets in this pinecone. All of the spirals connect to the top part of the pinecone, which is the stalk where it connects to the tree.
The seedhead above is another example of fibonacci that can be found in nature. The seedhead is called a coneflower seedhead. The seedhead has many colors on it. You can see the spirals that are coming out of the middle of the seedhead. The spiral starts in the middle and you can see it coming out. if you are looking at the seedhead from far away, you can see 55 spirals, But if you look at it in a closer view, you will see 34 spirals.
The starfish above is another example of a fibonacci that can be found in nature. Do you know why starfish is an example of fibonacci? Because a starfish has five arms and five is the 5th fibonacci number.If you draw a pentagon and put diagonals in it, you will get a star, and a star is the same a a starfish. The sides of the pentagon are one unit in length, the ratio between the diagonals and the sides is the golden ratio. The five-point symmetry with Golden proportions is found in starfish.
http://www.mcs.surrey.ac.uk/personal/r.knott/fibonacci/fibnat.html#pinecones
http://www.mcs.surrey.ac.uk/personal/r.knott/fibonacci/fibnat.html#seeds
http://jwilson.coe.uga.edu/EMAT6680/parveen/fib_nature.htm

Jenea's Fruity Paragraph About Fibonacci Numbers

In this paragraph, I'll be talking about how Fibonacci Numbers relate in nature and reality. There are very many similarities between Fibonacci numbers and different types of living plants, fruits and animals. Mathematicians are very inspired by the Fibonacci quadratic formulas, especially the Golden Ratio.


This is a real life picture example of a fruity fruit called a pineapple. As you can see the pineapple has proportions.The number of turns in the spiral (from leaf to leaf) and the number of leaves that exist in the pattern in all cases express a Fibonacci fraction and therefore a Fibonacci ratio. The same pattern repeats over and over as the plant grows up. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space. So nature isn't trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the spirals are imperfect. The plant is responding to physical constraints, not to a mathematical rule.


This is a real life picture example of a flower, it forms a Fibonacci Sprial.


The Following Links I Used:


[ Still Under Construction ]

Jon's Fibonacci Numbers

The appears in many proportion of famous Greek temples.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#art
The plans for the college are based on the fibonacci numbers and several geometric diagrams.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#art
The cows are a adapted way of Fibonacci's rabbit but making the problem more realistic in the way we observed them.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#dudeneyscows

The fibonacci numbers are a sequence where the firswt two terms are both 1. Subsequent terms are generated by finding the sum of the 2 previous terms. The sequence is 1, 1, 2, 3, 5, ... N is the number of term and F(n) is the value of that term. Proportion is two ratios that are equal to each other. The quadratic formula is the formula to determine the root of a quadratic equation from its coefficient. To figure out the equal of the proportion you need to cross multiply to figure out the answer. The golden ratio is used to find the proportion of height to width when laying out test or illustrations.

Fibonacci numbers by Susan

The one that has the black background is with lines that show what does it has to do with Fibonacci numbers and that and that it is a swan neck that is curved. So then, the black graphing one explains why the swan's curved neck is somehow using Fibonacci numbers or the Arabic-Hindu number system by Leonardo of Pisa. I got the swan picture from this website: http://www.flickr.com/photos/kaddy/85792192/. Also for the black graphing one i got it from here: http://iluvkids.myweb.uga.edu/Goldenspiral.html

The next picture is the lightening and this picture is from this link: http://iluvkids.myweb.uga.edu/nature.html. Fibonacci also says that the number system that he introduced to Europe will also explain nature in numbers. Or the secret of nature.

After the lightening is the DNA. I got this picture here: http://goldennumber.net/images/dna-b.gif. how is DNA related to Fibonacci numbers? Well the DNA's pattern are kind of repeating and so its similar to the Fibonacci numbers pattern and also, it can be replaced as numbers with the molecules of the DNA. So if you want to know what is the Fibonacci numbers are is the next paragraph.

Fibonacci numbers is a unending sequence of numbers that is the sum of 2 numbers before it. Here is a example: If F(1) = 1 and F(2) = 1 it equals to 1+1=2 and after that you take the solution that would be 2 and the number before it that would be 1 and that equals a problem that is 2+1=3 and so on and the solutions that is beore also equals to the F(n) = value of a term. So n would be any term or number that would be subtituted to F(n). All of this is by a italian mathematician whose name is Leonardo of Pisa that lived approximately from 1170s to 1250s. He was nicknamed as Finoacci and that he was also the person that introduced the Hindu- Arabic number system to Europe by his book called "Liber abaci". To find things like finding perimeter of a house like today and other things we use today are things that are from Arabic-Hindu number system. To solve things and also that the golden ratio is also created by him. If you want to find the golden ratio you have to know the Fibonacci numbers. To get a golden ratio, First we have to find the proportion then cross muiltply it then use another formula that is called the quadratic formula to find the golden ratio.

Jenny's Fibonacci

Are you interested to know what is fibonacci about? Fibonacci numbers are a sequence where the first terms are both 1. It is also used for many things such as mathematics also you could also found around the nature. Fibonacci camed from Arabic Number from a book called Liber Arabic. However, there is another way to figure out ancient greek by using proportion. While you are doing proportion, we needs to do cross multiply. When you do the fibonacci, you needs to divide the fibonacci then you needs to used the quadratic formula to figure out the sequences. When we tries to find out the sequences you needs to used F(n) is the output and the N is the input which helps to found out the next value of terms.

Here is the picture of a finger, music, and modern architecture.

FINGERS:
In the fingers, you needs to measure the length of the bones in your finger like slightly bending your fingers. Also you cant finger out the ratio of the longest bone in a finger to the middle bone is PHI. It is actually about the golden section ratios of bone lengths in the human hand. "The lengths of fingers from their rotation points in almost 200 hands and again fails to find to find phi (the actual ratios found were 1:1 or 1:1.3)."

MUSIC: Piano:The basic structures of a regualr instruments display of Fibonacci numbers and the Golden section. The most widely used instrument in music, the piano, displays the use of Fibonacci numbers. For instance, there are 13 notes that separate each octave of 8 notes in a scale. The foundation of a scale is based around the 3rd and the 5th tones. Both pitches are whole tones, which are 2 steps from the 1st note of the scale, also called the root.

Ear Effection: The Fibonacci sequence can also display the preference of the human ear to music. The following is some Fibonacci music. It consists of the first eight Fibonacci numbers. For each new number that is performed, the note length is decreased rotationally by 1/2 or 1/3. After four steps of the sequence are completed the tune starts over at the root, one octave up, while the other one continues, so there is an overlapping effect.

Music: The keys of a piano also portray the Fibonacci numbers. Within the scale consisting of 13 keys, 8 of them are white, 5 are black, which are split into groups of 3 and 2.

ARCHITECTURE: This picture is a Core which has an inspiration from the tree, incorporating a central trunk and canopy roof that shades the ground and harvests the sun. The design is based on the Fibonacci code, Nature's fundamental growth blueprint, in which opposing spirals follow the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34...where every number is the sum of the previous two.

This is a place where I got all the pictures from:
Finger: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#rabeecow
Music: http://techcenter.davidson.k12.nc.us/Group2/music.htm
Modern Architecture: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#art

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