explain::DIVINE PROPORTION (i.e)GOLDEN SECTION?

Question

its relation 2 fibonnaci series in detail

Answer 1

Check out

http://www.vashti.net/mceinc/golden.htm
http://goldennumber.net/fibonser.htm
http://local.wasp.uwa.edu.au/~pbourke/other/phi/
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html

The ancient Greeks thought that the 'Golden Mean' represented the most perfect ratio (of height t width, etc.) that could be used in art, architecture, etc.


Doug

Answer 2

the Fibonacci series was formulated by beginning with two numbers

0 1 and then using each pair to form the following number each time

so

0 1 1 2 3 5 8 13

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3

etc

when you take each number and divide it by the following number and compare it with the other way about

say 8/13 and compare with 13/8

you will find the number behind that golden ratio

the higher it goes the closer to the golden number you will obtain that way

i wont spoil it by doing all the calculations for you - a calculator will be invaluable to you for your own research on this matter

Answer 3

Another property, which is sort of mentioned above is that the golden ratio is a number such that squaring the golden ration is the same as adding one to it which gives rise to the quadratic equation
x^2=x+1 but remember, here the number x won't be unique because this equation has two distinct real roots.

Answer 4

Also referred to as the Golden Mean. It's approx1.61....

It is the quadratic solution to the equation X^2 -x -1 = 0;

It equals ( sqrt(5) -1 ) / 2 which equals 0.6180339...

If it's inverted then it's 1.6180339... M-(1/M) = 1

When the fibonacci series is iterated (1,1,2,3,5,8,13...) The term
f(n) / f(n-1) approaches the golden mean as n appraoches infinity.

Answer 5

I looked at the first poster's sites. The one that comes closest to what I think you're after is the third one.

You seem to want to know precisely why the ratios of Fn+1:Fn=>phi as n=>infty. The answer has to do with how the infinite continued fraction solution to the "golden quadratic" is approximated by cutting off the iteration at one point or another.

Try it out--it's fun.

Answer 6

the divine proportion is the proportion of the (n+1) number of the fibbinocci sequence divided by N number as N goes to infinity.
for example 13/8 is closer to the divine proportion than 5/3 which is closer than 3/2
There is a way to prove it but i dont remeber it any more, but it is probbaly on wikipedia.

Answer 7

Read Da Vinci Code