2006-08-24 08:55:48 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The golden ratio is phi = (1+square root(5))/2. See more details at http://en.wikipedia.org/wiki/Golden_ratio
2006-08-24 08:59:46 · answer #1 · answered by maegical 4 · 0⤊ 0⤋
Original geometric definition:
given a line segment AB, there is a unique point C on this segment such that the ratios
CB : AC = AC : AB = 1 : phi
(short) : (long) = (long) : (whole)
It follows that
AC^2 = AB CB = AB (AB - AC)
AC^2 + AB AC - AB^2 = 0
1 + phi - phi^2 = 0
phi = [1 + sqrt(5)] / 2 approx 1.618034
Remarkable facts:
1/phi = phi - 1
phi^2 = phi + 1
phi^3 = 2phi + 1
phi^4 = 3phi + 2
phi^5 = 5phi + 3
and the coefficients follow a Fibonacci sequence.
2006-08-24 16:11:53 · answer #2 · answered by dutch_prof 4 · 0⤊ 0⤋
It is the division of a segment into tow parts so that the measures agree with the rule: the measure of the big part divided by the segment measure and the measure of the small part divided by the measure of the big one are the same.
A................M......B AM/AB = MB/AM
Very important discovery... Phi = (1+sqrt(5))/2 and the name is given to honor the Greek architect Phidias
There are several occurance of this number in the world.
Read the book: The Golden Proportion
2006-08-24 16:07:44 · answer #3 · answered by vahucel 6 · 1⤊ 0⤋
If you look at the sequence 1,1,2,3,5,8,13, ... where the next term is gotten by adding the two previous terms, then the ratio of consecutive terms approaches the golden ratio as you go farther and farther along. This sequence is called the Fibonacci sequence, it appears commonly in nature. Consecutive terms in the Fibonacci sequence are often used as the dimensions of painting and photo prints because they are supposed to be the most appealing size for a rectangle ... whatever that means.
2006-08-24 23:23:06 · answer #4 · answered by TA Timmy 2 · 0⤊ 0⤋
It's a ratio that things in nature exhibit. You can find in in your body, in plants and other animals and in other mathematical things such as Pascal's triangle. Things look asthetically pleasing when they exhibit the golden ratio.
It can be derived through the Fibonnacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.
The ratio of two consecutive numbers in the series approaches 1.618...
2006-08-24 15:59:30 · answer #5 · answered by Jess 2 · 1⤊ 0⤋
It has many fascinating characteristics.
For example, in a Fibunacci sequence (where each number is the sum of the previous 2), once you get out a good ways, the ratio of one number to the next, is phi. Or approximately 1.618.
Or, 1/1.618 = .618
Or. 1.618 squared = 2.618
Its also seen in architecture, nature, etc.
2006-08-24 16:03:51 · answer #6 · answered by Harlan 2 · 1⤊ 0⤋
It's not Phi. It's roughly the 3. something, your belly button height divided by your body height.
2006-08-24 15:59:27 · answer #7 · answered by ? 5 · 0⤊ 1⤋