The Muslim Times’ Chief Editor’s comment: We have not verified the accuracy of the claims made in this post. As it has gathered some interest among the readers we have kept it here. We do have the best collection of articles for religion and science, broadly speaking.
The Holy Qur’an reveals that God has raised heavens and has set up a measure for them.
“And the heaven He has raised high and set up a measure”( Al Qur’an 55:8)
The Golden Ratio is one such measure which is extensively applied in nature. It is represented with Greek letter phi in the mathematical calculations and its value is always 1.6180339887…..
Two quantities are said to be in the golden ratio when the ratio of the sum of the quantities to the larger quantity is equal the ratio of the larger quantity to the smaller one. Diagrammatically it can be represented as follows: (DiagramONE)
Diagram ONE
The scientists, artists, aestheticians, architects, mathematicians, financial analysts agree that application of this ratio creates perfection, proportion, beauty and balance to their works.
The Holy Qur’an also reveals that Mecca is the first house founded for the mankind.
“Surely, the first House founded for mankind is that at Becca, abounding in blessings and guidance for all peoples. (Al Qur’an 3:97)
God placed this house at the Golden Mean of our earth and following video is presented just to compliment it.
NASA on Secrets of KAABA Sharif
The other names used for the Golden Ratio are the Golden Mean, extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias.
Categories: Arab World, Asia, Islam, Religion & Science, Religion and Science, Video, World, You Tube
It appears that while a/b seems to be close to 1.618, b/c as shown cannot 1.618 as b/c <1, perhaps it is c/a and not b/c in the still above the video. The other thing that I do not like about this article is that its video carries a political message; someone is trying to collect donations for Romney!
This article reminds me of the following “discussion”.
http://sci.tech-archive.net/Archive/sci.math/2007-03/msg06044.html
In my opinion, Mecca’s importance lies in the message that emanated from Mecca. While I do not dispute the possibility of a divine design that the latitudinal circle and the longitudinal arc are split at Mecca in a ratio close to the golden ratio; if it is the case, I usually take such “discoveries” with a pinch of salt. Here is my reason why. The coveted golden ratio is an irrational number, so it may be close to but, cannot be the ratio of two lengths measured in the conventional fashion. Let me explain for those who may be able to follow the argument.
(a+ b)/a = a/b can be re-written as 1+(b/a)= a/b. If we set x = a/b then b/a =1/x. Substituting we get 1 + (1/x) = x. Which on simplifying becomes the quadratic equation x^2 -x-1 =0. This equation has two solutions. The positive solution can be written as (1 + sqrt(5))/2 and is called the golden ratio. (Here sqrt(5) stands for “the square root of 5”) This number is what they call an irrational number and it cannot be expressed as a fraction and so cannot be exactly represented by a decimal fraction. In real life we can only rely on its approximations. One approximation is 1.618 another is 1.618033989. If we keep on increasing the number of decimal places we will keep on getting better and better approximations but never the exact number. So just getting a/b =1.618 and crying voila a and b are in golden ratio does not mean much. Such statements are circumstantial at best and no serious conclusion can be drawn from them.
However there are geometrical constructions that would help you construct a golden rectangle, i.e., a rectangle with one side b, the other a such that a/b = golden ratio (theoretically exactly) and this ratio has been very popular with geometers since Euclid defined it, based on Pythagoras’ Theorem. Since then some folks associated some mystic properties with the golden ratio. With the popularity of some paintings on rectangular pieces whose sides were in golden ratio it became sort of customary for painters to paint on canvass or board that was a golden rectangle. A painting in those sizes was considered pleasant to look at.
Give a geometer a compass, a straight edge and an idea he/she will come up with all sorts of variations. So a golden triangle came to be and so did golden spirals. Someone spotted some nautilus which seemed to be in the shape of a golden spiral. Then some folks spotted seeds in some flowers arranged in golden spirals. That is what seems to have made the golden ratio popular among some scientists.
There are other reasons why the golden ratio is so golden, i.e. so much talked about. One of those reasons is the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, …, here the first two terms are 0 and 1 and after that every term is the sum of the previous two. So if F(0) = 0, F(1) =1, F(2) = F(1) +F(0) = 1, F(3) = F(2)+ F(1) = 2 etc. In fact any number, from F(2) onwards, in the infinite sequence can be found using the formula: F(n) = F(n-1) +F(n-2). The numbers in the Fibonacci sequence are called Fibonacci numbers.
Now what is interesting, is the fact that as n, in the above recursive formula, gets larger and larger the ratio F(n)/F(n-1) comes closer and closer to the golden ratio and Mathematicians have shown that the limiting value of F(n)/F(n-1) is (1 + sqrt(5))/2 the golden ratio! This information got people looking for Fibonacci numbers. It turns out that the petals of a lot of flowers are in Fibonacci numbers. (But no one will point out a four petal flower and there are plenty of them!)
However you may be able to see a divine hand at a very odd place, in the story of the beginning of the Fibonacci numbers. Leonardo Fibonacci traveled to North Africa as a boy and came back as a thirty year old Mathematician. At age 32 he published a book by the title Liber Abaci (Book of Calculation). In this book he talked about the advantages of using Hindu-Arabic number system, discussing the nine digits of the Hindus: 1, 2, 3, 4, 5, 6, 7, 8, 9 and about the place value. Being the son of a trader he kept his attention to the commercial usage, but he discussed some Mathematical topics that were of interest to Arab Mathematicians of the time.
Of importance to this write up is a problem that he “posed” and solved in Liber Abaci. The problem goes as follows: How Many Pairs of Rabbits Are Created by One Pair in One Year
A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also. (See the link below)
This is roughly what he offered as a solution:
At the start there was 1 pair
In the first month the pair bore and there were, —–2 pairs
In the second the only mature pair bore so there were, —– 3 pairs
In the third the two mature pairs bore and made a total of—- 5 pairs
In the fourth the mature pairs from the second month bore in addition to the 5 pairs –8
The pattern came to be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.
Of course when the pattern is given showing that after the second month the number in every month would be the sum of numbers in the previous two months the later Mathematicians ran with the sequence and gave it the shape that I mentioned earlier, calling the sequence the Fibonacci sequence. But of course it did not start with Fibonacci. He just regurgitated what he had learned from the Arabs. There are claims that some Hindu scholars knew the first few terms of the sequence and that the rabbit problem was known in some “Mediterranean” countries (i.e. Muslim countries.) Some analysis of Liber Abaci can be found here:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html
Now why have I spent all this time? It seems that it is the story of growth as a result of cell division. The mathematical formulas are blind and they would get to the ten thousandth term assuming all the rabbits were living. In nature, depending on the code in the DNA some cells would stay inert and some would multiply for a period of time and then go inert and stay and some would multiply and die off and get rejected by the system. So, there is a somewhat remote possibility that there is some link with Fibonacci numbers or, in the extreme situation with golden ratio. But this connection will be empirical until we know how the growth pattern of a certain part of an organism is governed by the DNA.
Now before I close this longish post, a word about the effect of the Fibonacci book. It introduced the Hindu Arabic Numerals to the West and in a short while they got rid of the shackle of the Roman Numerals and sort of started the Renaissance. His book also led as a source to knowledge the Muslim Mathematical works, and the Greek Mathematical works which were mostly available in Arabic. This started a rush to translate those works. So there was very little original Mathematics produced for at least two hundred years. I recall reading from a history book that during that period there were competition between Mathematician on who knew Mathematics of Arab origin better.