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, ...(each number is the sum of the previous two).
The ratio of successive pairs is so-called golden section (GS)- 1.618033989 . . . . .
whose reciprocal is 0.618033989 . . . . . so that we have 1/GS = 1 + GS.
The Fibonacci sequence, generated by the rule f1 = f2 = 1 , fn+1 = fn + fn-1,
is well known in many different areas of mathematics and science.
Pascal's Triangle and Fibonacci Numbers
The triangle was studied by B. Pascal, although it had been described centuries earlier by Chinese mathematician Yanghui (about 500 years earlier, in fact) and the Persian astronomer-poet Omar Khayyám.
Pascal's Triangle is described by the following formula:
The "shallow diagonals" of Pascal's triangle
sum to Fibonacci numbers.
It is quite amazing that the Fibonacci number patterns occur so frequently in nature ( flowers, shells, plants, leaves, to name a few) that this phenomenon appears to be one of the principal "laws of nature". Fibonacci sequences appear in biological settings, in two consecutive Fibonacci numbers, such as branching in trees, arrangement of leaves on a stem, the fruitlets of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone. In addition, numerous claims of Fibonacci numbers or golden sections in nature are found in popular sources, e.g. relating to the breeding of rabbits, the spirals of shells, and the curve of waves The Fibonacci numbers are also found in the family tree of honeybees.
In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller.
Expressed algebraically:
The golden ratio is often denoted by the Greek letter phi (Φ or φ).
The figure of a golden section illustrates the geometric relationship that defines this constant. The golden ratio is an irrational mathematical constant,approximately 1.6180339887.
Golden Rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1: j (one-to-phi),that is, 1 : or approximately 1:1.618.
A golden rectangle can be constructed with only straightedge
and compass by this technique:
Construct a simple square
Draw a line from the midpoint of one side of the square to an opposite corner
Use that line as the radius to draw an arc that defines the height of the rectangle
mud nak tnye..nomor ni kalo bahagikan sesama dorang..akan dpt nombor yg sama kan??
pe application yg real world ye??
kelapamuda Post at 3-4-2010 11:00
bila di bahagi dengan nombor sesama mereka , nilai akan di perolehi akan bermula dgn nila 1.6xxx, sehingga semakin besar nombor yg digunakan, perubahan dgn nilai terdahulu semakin kecil~~
fibonacci - susunan pada bunga , the petals tu, kan ? semua entity organic mostly, ada mengikut pola fibonacci
interesting actually , sophie neveu ( da vinci ) talked about thsi with Prof Langdon, hmm...subhanallah life 's beautiful actually...kan?
god blends both arts and hard core science in such perfect harmony...superbly enchanting
explain la malang~~ share2 info
chewan Post at 7-4-2010 13:11
banyak..contohnya ketinggian kita,nisbah antara dari kepala ke pusat dan pusat ke kaki,kalau kaki,jarak dari paha ke lutut dgn lutut ke tapak kaki, kalau tgn,pun sama
bila di bahagi dengan nombor sesama mereka , nilai akan di perolehi akan bermula dgn nila 1.6xxx, sehingga semakin besar nombor yg digunakan, perubahan dgn nilai terdahulu semakin kecil~~ {:1_152: ...
chewan Post at 4-4-2010 00:55
agaknya..kalo wat application for modeling the building sewuence or anything arrangement like...
ley apply fibo tak??
sbbkan sifatnya cantik and terataur..maybe ley bg benefits through profit and strategic location..
banyak..contohnya ketinggian kita,nisbah antara dari kepala ke pusat dan pusat ke kaki,kalau kaki,jarak dari paha ke lutut dgn lutut ke tapak kaki, kalau tgn,pun sama
lin0me Post at 7-4-2010 15:39
motip avvy baru gambo eli??
aah...panjang and kelarasan anggota badan kita...sume nisbah nomot fibo nih...
esp..ukuran muka...
Post time 2-4-2010 05:53 PM
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