Can any1 give me the explanation of 'divine porpotion'?

Question

1.618 (Phi. It is not Pi=3.142)

Answer 1

if you have a rectangle with length x and
breadth 1 unit say
you then cut a 1 unit square out of this
rectangle,you are left with a smaller
rectangle with the same length/breath
ratio as the larger rectangle,namely,

x/1=1/(x-1)
x(x-1)=1
x^2-x-1=0

using the quadratic formula,

x= {1+or- sqrt(5)}/2

this value {1+sqrt5}/2 is known as the
'golden ratio' or the'divine proportion'

it's greek name is 'PHI'

also,in the fibonacci series,the ratio of
the (n+1)th term to the nth term limits to
PHI (approx 1.618033989)

PHI has some remarkable properties

i hope that this helps

Answer 2

There are lot's of different ways tyo make it show up. Here is one:

Consider the Fibbonacci sequence.

1,1,2,3,5,8,13,21,34,55,89,... off to infinity.

You create this series by defining the first two terms to be one, and the rest to be the sum of the two previous terms.

If you look at the ratios between consecutive terms, you notice a trend.

the ratio between 1 and 2 is 2, the next is 1.5, the next is 1.6666666..., the next is 1.6, the next...

these ratios approach phi as you examine terms further down the series.

The reason it is called the divine proportion was, I think, first determined by the greek mathematicians. If you have two line segments, where the length of one, let's call it L, is phi bigger than the length of the other, let's call it M, than the sum of both line segments, L + M, will be phi times the length of L.

L + M = L*1.618 = M*(1.618)^2

1.618 is, of course an approximation. Phi is an irrational number.

Answer 3

It's not rational for one thing, and is the positive solution of the equation,
x^2 - x -1 = 0

hence φ = (1 + V5) / 2
where V stands for the square root radical.
It also has the amazing properties that,
1 / φ = 1 - φ
φ^2 = 1+ φ
by definition φ satisfies the algebraic identity,
φ = (a+b) / a = a/b

hence, phi can easily be shown to be irrational.

The wikipedia article will give you more, I've merely made an inadequate outline of the mathematical properties of φ.

http://en.wikipedia.org/wiki/Golden_ratio

Answer 4

The golden ratio, usually denoted \varphi, expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. The golden ratio is the following algebraic irrational number with its numerical approximation:

φ = {1 + sqrt(5)} / 2 = 1.618033988.

The figure of a golden section on the right illustrates the defining geometric relationship. Expressed algebraically:

{a+b}/{a} = {a}/{b} = \varphi\,.

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.

Other names frequently used for or closely related to the golden ratio are golden section (Latin: sectio aurea), golden mean, golden number, and the Greek letter phi (φ). Other terms encountered include extreme and mean ratio, medial section, divine proportion (Italian: proporzione divina), divine section (Latin: sectio divina), golden proportion, golden cut,and mean of Phidias.

Answer 5

Golden ratio (1.618) occurs both in mathematics and nature. It is also found in dimension of human body. It is also closely related to Fibonacci series numbers especially digit 5, while relating to human body.

Answer 6

This is straight from "da vinci code" and my physics teacher.
phi is derived from the sequence of numbers 1,1,2,3,5,8,13...
Notice that the sum of the previous two in the sequence (Fibonacci sp?) is the the following number. The sequence of numbers, when you divide adjacent terms , the quotient approaches phi.

e.g. 2/1=2
3/2= 1.5
5/3=1.667
13/8=1.625

The ratio appears in nature often.

I don't remember any more but here are some examples I know from the book.

The distance from the tip of your head to the floor divided by the distance from your belly button to the floor.

The distance from your shoulder to your finger tip divided by the distance from your elbow to your finger tips.

Hip to floor divided by knee to floor.

The number of females divided by males in a honey bee community.


Hope this helps...

Answer 7

the basis of everything human. for example the ratio of the length from your forehead to your chin and the length from the tip of your nose to your chin, gives you 1:1.618

similarly if you measure other various lengths on your body, chances are you'll end up with the same ratio too.

it's the divine number that even artists used to refer to when creating their masterpieces: painting, sculpting etc...we're talkin about ppl like michaelangelo, da vinci etc.