The Fibonacci sequence was discovered by studying population growth.
Population growth is also related to the Fibonacci series. In 1202, Leonardo Fibonacci investigated the question of how fast rabbits could breed under ideal circumstances. Here is the question that he posed:
Suppose a newborn pair of rabbits, one male and one female, is put in the wild. The rabbits mate at the age of one month. At the end of its second month, a female can produce another pair of rabbits. Suppose that the rabbits never die and that each female always produces one new pair, with one male and one female, every month from the second month on. How many pairs will there be in one year?
The answer is found in series of numbers now known as the Fibonacci series. Pair A of rabbits gives birth to pairs B, C, D and E. Each of these new pairs in turn gives birth to other pairs B1, B2, B3, C1, and C2, who in turn give birth to B11, etc. At the end of each month, the total population of rabbits will be a number in the Fibonacci series:
| Month | Rabbits from A: | from B: | from C: | D: | B1: | Total | ||||||||
| 0 | A | 1 | ||||||||||||
| 1 | A | 1 | ||||||||||||
| 2 | A | B | 2 | |||||||||||
| 3 | A | B | C | 3 | ||||||||||
| 4 | A | B | C | D | B1 | 5 | ||||||||
| 5 | A | B | C | D | E | B1 | B2 | C1 | 8 | |||||
| 6 | A | B | C | D | E | F | B1 | B2 | B3 | C1 | C2 | D1 | B11 | 13 |
| etc. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | etc. |
The Fibonacci series can be used to predict urban populations
It appears that the Fibonacci series can even be used to predict populations of major cities, as shown by the relationships of various U.S. urban areas in 1970:
| Area | Census Rank | Actual Population | Predicted Population | |
| Method 1 | Method 2 | |||
| New York, NE NJ | 1 | 16,206,841 | ||
| LA Long Beach CA | 2 | 8,351,266 | 10,016,379 | 10,016,379 |
| Chicago NW IN | 3 | 6,714,578 | 6,190,462 | 5,161,366 |
| Detroit, MI | 5 | 3,970,584 | 3,825,916 | 4,149,837 |
| Washington DC | 8 | 2,481,459 | 2,364,546 | 2,453,956 |
| Houston, TX | 13 | 1,677,863 | 1,461,370 | 1,533,626 |
| Cincinnati, OH | 21 | 1,110,514 | 903,176 | 1,036,976 |
| Dayton, OH | 34 | 685,942 | 558,194 | 686,335 |
| Richmond, VA | 55 | 416,563 | 344,983 | 423,935 |
| Las Vegas, NV | 89 | 236,681 | 213,211 | 257,450 |
| New London, CT | 144 | 139,121 | 131,772 | 146,277 |
| Great Falls, MT | 233 | 70,905 | 81,439 | 85,982 |
Method 1 takes the population of the largest city and divides it again and again by phi. Method 2 takes the population of each successive city and divides it by phi.
Source: http://www-personal.umich.edu/~sarhaus/
Multicellular organisms
In biology, once an egg is fertilized, it divides and multiplies in count until it reaches a point at which the ratio of the succeeding number of cells to the previous number of cells is phi (1.618 …).
Since God designed the DNA, the Golden Ratio used is designed by God. In the colours of the rainbow, music keys and many other designs, it is staring us in the face. Is it possible, that everything God designed is connected one to the other? Of course it is. Supernatural design in everything. This is the significant proof that God exists. No wonder it is also called the Divine Ratio.
No the basis is the natural number system which are necessary truths, nothing whatsoever to do with a supernatural designer.
That two views exists when people observe the same thing is the challenge, isn’t it. Some things in life are the result of basic mathematics and “natural” laws. Other things show characteristics that appear to be there for no reason other than to make life a possibility, to create beauty and our ability to perceive. Stephen Hawking once said, “The laws of science, as we know them at present, contain many fundamental numbers, like the size of the electric charge of the electron and the ratio of the masses of the proton and electron. … The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life.” Similarly, many aspects of the golden ratio express fundamental mathematics, while some appear where there is no clear reason other than to create and express beauty.
I an atheist, but once I found a video claims that Ka’aba( which is the destination of Muslims beliefs) is located to form Fibonacci ratio ,, I didn’t believe this claim until I measured it myself in Google earth , the result chocked me and I am now very confused. I want the truth is there a god ?
First of all, I don’t think the word destinations means what you think it means. If you mean where the Muslims believe they go after death, how could you possible get a location from Google Earth?
Second, the Fibonacci sequence, when found in plant life is, for lack of a better word, controlled by hormones put out by the plant. This hormone is a substance that repels things like leaves and flower petals causing them, as they develop, to move as far from one another as possible.This hormone causes the leaves, or petals to try their darndest to keep as much space between themselves and the other leaves or petals by taking up space or, in some cases the leaves act towards each other in the same way opposing magnets repel each other.
When leaves separate in the spiral configuration that you see in the Fibonacci Spiral, they are optimizing their chances of absorbing sun light for energy. For example, if the leaves of a plant were stacked one directly atop another the lower leaves wouldn’t get as much sun because the higher ones would be shading them. Now, not every plant, flower, etc. grows to the exact ratio created by the Fibonacci numbers. Some follow other number sequences such as the Lucas sequence, which is similar in the way it works, but results in a different ratio (not the Golden or so called Divine Ratio),
So if one is to believe that some divine being created the Fibonacci sequence to make all these things come out “perfect”, which they are not or they would all be the same (there’s no such thing as being more perfect), which they are not and some are even down right faulty, then you would also have to believe that this divine being is imperfect. Therefore, no divine, infallible being created nature.
But then your logic to conclude that there is no God is dependent upon believing that all things must come out “perfect.” Perfect does not imply identical. Every face is different. Every snowflake is different. Variation is part of the beauty that creates “perfection.” In addition, there are always trade-offs in any feat of design and engineering. Your smart phone could be equipped with a battery that lasts a month, but it would then weigh far too much. There’s no need to assume that EVERY aspect of EVERYthing should be perfect. So we can’t use this logic to then conclude that there’s no God behind the incredible sophistication of this biological hardware and software that we call life.
By God, someone finally realizes. Thank you.
I am a ninth grade student trying to learn about the Fibonacci sequence, not be preached to. Thank you and good night. Amen.
I am a 5th grader trying to learn about what the heck the author of the Da Vinci code meant and i agree with this dude
I am a seventh grade student trying to answer “how many pairs of rabbits exist after one year?”. Thank you very much because I still don’t have the answer.
The answer depends on your assumptions. Does the first pair breed immediately, or do they have to wait a month to mature? The traditional approach is to assume that you have 1 newborn pair of rabbits that will mature and produce offspring at the end of 1 month, and that each newborn pair will do the same. If you start with two rabbits on January 1, the growth then looks like this:
Date Pairs Rabbits
1/1 1 2
2/1 1 2
3/1 2 4
4/1 3 6
5/1 5 10
6/1 8 16
7/1 13 26
8/1 21 42
9/1 34 68
10/1 55 110
11/1 89 178
12/1 144 288
1/1 233 466
Here’s an article that shows it more visually:
https://www.mathscareers.org.uk/the-mathematics-of-rabbit-island/
自圆其说 (Justified)
It was aliens with missiles and stuff.
Everything got created by a big bang and is going to finish by the big crush theory.
We live in a multiverse and can switch if we have the correct direction and the correct speed to reach wormhole. How can somebody make pyramid with every stone weighing almost 50 tonnes, and even if they can lift how can they take it up ? I don’t think a super just came out of nowhere and helped them and went back. It was the aliens. The pyramids have precision and bare hands can’t do that. If god was so mighty, why was there a world war ? I don’t think somebody would be enjoying a war with caramel popcorn and a cold drink lying down a couch.
Hello. I have prepared simplified diagram to demonstrate dependencies between world population and Fibonacci numbers. https://obrazki.elektroda.pl/7858429700_1538941465.png
Try to remember that when the age of enlightenment first started and many of the earlier important minds to mathematics, physics and other applied sciences first lived, that a belief in science and the scientific method didn’t preclude belief in a higher power.
Just like ‘one man’s trash is another’s treasure,’ one person’s proof in the almighty is another person’s proof in the randomness of the cosmos (or something like that).
I’d like to add my piece to this obscure, nine year long comment thread. I think the belief in an orchestrated universe doesn’t require a belief in an orthodox religious doctrine. the fact that the golden ratio is applicable in plant growth, population growth, storm systems, market prediction, the formation of galaxies, and the composition of beautiful paintings (just to name a few) is almost too mind-blowing to comprehend. there is no man in the sky, there is no Heaven and Hell, but I’d be absolutely flabbergasted if we found out that everything is random and that the universe exists completely by chance with no grand design or purpose.
Good thoughts, but how do they logically lead to the conclusion that “there is no man in the sky” or God. If you’re flabbergasted by your observation of diverse appearances of the golden ratio, consider some of the information I’ve compiled in this video: https://www.youtube.com/watch?v=AcGw21Wbcgk
Thanks for sharing, very interesting video. I think maybe I wasn’t clear enough in my statement but I’m saying that I DO believe there is a god and/or a grand design. I don’t think that god looks anything like the god described in religious doctrine but nevertheless i believe we have a creator. Also against science as a belief system. Almost every modern and contemporary philosopher foretold the death of god and the championing of science as a belief system rather then just a method/process and we are seeing the fallout of gods death now.
Gary, have you come across this website. I’ve started reading it and it’s interesting as it suggests alternatives to the breeding rabbits model.
The Fibonacci Numbers and Nature
https://r-knott.surrey.ac.uk/Fibonacci/fibnat.html#section1
Yes I have. Ron Knott’s site is a classic that has been around for over 20 years.