Hello,
Probably most of
you have heard of The Golden Ratio or Fibonacci Sequence while studying.
However, I do not know if you've heard how often this structure (which usually
know that a purely mathematical relationship) perfectly describe our close and
distant 'environment' from the areas of disciplines such as biology, genetics,
astronomy to music and architecture and even financial analysis or betting.
If you start to
measure different objects, for example, in your home you can see how often you
will find also the golden proportions, usually is what it seems to meet most of
these esthetic, nice, proportionate.
- I have few sources of starting something pleasant to look:
- http://io9.gizmodo.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature
- http://www.inspirationgreen.com/fibonacci-sequence-in-nature
- Through the scientific approach:
- http://phys.org/news/2005-08-fibonacci-series-microstructures.html
- Finally I would like present film:
- https://www.youtube.com/watch?v=L6Se-J5HBsQ
I also have a
few questions:
1. Is in the
course of their education often hear how this relationship occurs in nature?
2. Does the
interplay of many disciplines surprised you?
3. How do you
think whether it is natural optimization, or search according to
"force"?
4. Maybe you know more interesting examples, applications, and can see other applications?
Correction
I think
that most of you have heard about
The Golden Ratio or Fibonacci Sequence,
haven’t you? However, I do not know if you heard that this
structure can be found in nature very often? This relationship perfectly describes the world. If you look at the articles
and the film, you'll see examples:
My
questions:
1. Have you
heard of these dependencies before
2. Were you
surprised?
4. How do
you think, is it natural optimization?
4. You give
the other interesting examples?
1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteIf you ask me, I never heard about this while in school. Well, I had a teacher plowing on the golden ratio in painting, but I really hated her subject, so I forgot as soon as possible.
2. Does the interplay of many disciplines surprised you?
No, not really. It's just a mathematics anyway. That's the way the world is built, we're familiar with nature, so it is just natural that something resembling nature looks good to us.
3. How do you think whether it is natural optimization, or search according to "force"?
What do I think? I believe God creates the world this way. That's it. I really don't know why.
4. Maybe you know more interesting examples, applications, and can see other applications?
I don't think I know. I can only say, that I used Fibonacci sequence in programming (to increase the delay between retries to connect to an unresponsive network resources) and the golden ration in my own kitchen furniture design. The latter is quite different that you can buy in any shop (usually the standard size), but to me it looks great (no doubt, I am the one who designed it in the first place).
1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteTo be honest, not so often, or even very rarely. The main reason is that during education we’re provided with the most common ways or methods of finding solutions.
Fibonacci sequence is not one of these, with all due respect to Fibonacci. During education course it’s treated rather as a curiosity, kind of a sneak-peak/interlude between other bit less amazingly surprising numbers and methods.
2. Does the interplay of many disciplines surprised you?
No, not at all.
3. How do you think whether it is natural optimization, or search according to "force"?
I’d vote for natural optimisation in this case. Somehow Fibonacci sequence wherever applied ‘enforces’ proportionality. Hence a perception of something ‘natural’.
4. Maybe you know more interesting examples, applications, and can see other applications?
First application i’ve heard of, was in trading. Some belief (I’m not one of them) that fractals are useful with predicting the future trends (or finding similar patterns) for price movements.
Thank you for your response . In my opinion, this compatibility is also one of the evidence that mathematics is a good language to describe the world. If we talk about the shapes and movements - even complicated , we can be described mathematically .
ReplyDeleteVery interesting are also achieving biomathematics - that really great show consistency of science.
Correction
DeleteThank you for your response, This compatibility is one of the manifestation that mathematics is a good language to describe the world. Even, we can describe using mathematics objects. Even, we can describe using mathematics difficult to describe objects. Biomathematics shows excellent consistency of science.
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ReplyDelete1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteGood question,
I never think about this and I never hear about this too:)
But I have a couple of books in my home which a lot of examples nature which exist in education. But in my opinion a lot of things in eduction have a relationship.
2. Does the interplay of many disciplines surprised you?
No, not at all.
3. How do you think whether it is natural optimization, or search according to "force"?
In my opinion natural optimization in this because for me it is more natural :)
4. Maybe you know more interesting examples, applications, and can see other applications?
I don't have more interesting examples ad applications
1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteI've read about golden ration long time ago. Fascinating topic, 15 examples from nature proves it :) Nature is based on mathematic or mathematic is based on nature?
2. Does the interplay of many disciplines surprised you?
No, it's so common in mathematics. We can explain so many things sometimes with really simple equations. We can read more about it in dozens of articles and books. As an example: http://phys.org/news/2013-09-mathematics-effective-world.html
3. How do you think whether it is natural optimization, or search according to "force"?
The force is strong. Ask Yoda about it :D So it's natural optimization decorated with mathematics.
4. Maybe you know more interesting examples, applications, and can see other applications?
Fibonacci is very common in IT. Other examples : http://www.clickhole.com/article/5-absolutely-stunning-examples-mathematics-nature-2081
ReplyDelete1. Is in the course of their education often hear how this relationship occurs in nature?
I haven't heard about correlation between Fibonacci Numbers and nature, not in school. Really I can't recall anything in my memory connected with this.
2. Does the interplay of many disciplines surprised you?
I am not surprised. I think that everything that surrounds can be explained with some mathematical formula. Those things can be also explained with physics laws but here we are talking about math.
3. How do you think whether it is natural optimization, or search according to "force"?
Hmmm really I don't know. From one side when you are reading about Golden Ratio and Fibonacci and you see examples you may think that this nature optimisation.
But sometimes I have got weird feeling that someones tries to fit his theory into something just to prove it.
4. Maybe you know more interesting examples, applications, and can see other applications?
It may be a little far-fetched, but there you go.
Fibonacci in Rock music :-)
https://www.youtube.com/watch?v=wS7CZIJVxFY
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ReplyDeleteThank you for another interesting source. I do not know why I very rarely school show that the knowledge that is in the school shall be forwarded as words describing the world?
ReplyDeleteSometimes students do not see such examples, they do not see the meaning and usefulness of science, whether it was impossible to be used for motivation ...
Correction
DeleteThank you for your interesting source.
This example shows that learning to effectively describe the world. I think that IF the student sees that learning is effective, it will increase their motivation to learn. Aren’t you?
I've heard about Golden Ratio/Fibonacci Sequence several times during my education. Its presence in the nature was usually mentioned as a curiosity or a fun fact. Definitely the first time I've heard about it I was amazed by the interplay of many disciplines (as you put it in your question). Nowadays I feel that this is an example of natural optimisation.
ReplyDeleteSo I actually had to search a bit for an interesting example of Fibonacci numbers in action. Surprisingly I found this article http://www.fibonicci.com/fibonacci/tool-lateralus/ about Fibonacci numbers usage in "Lateralus" song by Tool. I haven't heard it for a couple of years and it's really great. Thanks for bringing up this topic!
Hi Wiesław, first time I heard about these theories in PJATK. Especially I remembered examples of fibonacci numbers in flower petals or in plant branching. It seems to me that it's a natural optimization but amazing is the fact of its occurrence. I liked the Tool example cited by Christopher. Thank you for interesting topic. Regards.
ReplyDeleteThank you for your answers, I am very pleased that the topic is not a stranger to you. A few days ago I discussed it with the first year students of computer science, it turned out that in a group of about 30 people, only one person before heard of these relationships, in my opinion it is worth disseminate
ReplyDeleteCorrection
DeleteThank you for your answers, I am very pleased that the topic is not a stranger to you.
I spoke with a group of students a few days ago. One person out of thirty heard of this before...
1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteI probably hear about that during my primary or secondary education. It was so long ago that I almost completely forgot about that. I paid attention to it some time ago when I saw exhibition about Leonard Da Vinci. I remember that I was surprised by the fact that the Golden Section was used extensively by Leonardo Da Vinci. At that time, I Noted how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio.
2. Does the interplay of many disciplines surprised you?
Not really. If you take into consideration that human have two hands etc., it natural that something symmetric looks nice to them.
3. How do you think whether it is natural optimization, or search according to "force"?
In my opinion natural optimization " works better"
4. Maybe you know more interesting examples, applications, and can see other applications?
Unfortunately that is not my favourite topic so I do not know much about that.
1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteI probably hear about that during my primary or secondary education. It was so long ago that I almost completely forgot about that. I paid attention to it some time ago when I saw exhibition about Leonard Da Vinci. I remember that I was surprised by the fact that the Golden Section was used extensively by Leonardo Da Vinci. At that time, I Noted how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio.
2. Does the interplay of many disciplines surprised you?
Not really. If you take into consideration that human have two hands etc., it natural that something symmetric looks nice to them.
3. How do you think whether it is natural optimization, or search according to "force"?
In my opinion natural optimization " works better"
4. Maybe you know more interesting examples, applications, and can see other applications?
Unfortunately that is not my favourite topic so I do not know much about that.
Thank you for your answer Marcin, as in the works of Da Vinci's Gold ratio is very often encountered ...
DeleteThere is a very big misunderstanding when people are talking about so called "mysteries" of Fibbonaci Numbers. There is absolutely no mysteries involved. The whole issue is usually presented backwards, as if the Nature was trying to fulfill some magical mathematical wonders. It is completely the other way around. Relations like Fibboncie Sequence are simple mathematical discoveries that fit and explain the natural behaviors. Like construction of sea shell or spider web. The same way Einstein discovered his E=mc2 equations as the rule for energy and mass and not the other way around.
ReplyDeleteI agree with you Kinga, this shows how well we can describe the world, the only thing that amazes how this description is perfect, if mówim of firmule E = mc ^ 2 it was in my opinion great discovery of our civilization, although some of its applications were bad for humanity, but every tool we can use for both precious and destructive goals.
DeleteHi and thanks for presenting the material that you have found on this interesting subject. The first time I heard about the golden ration it was in high school however it was very general and we studied it in more detail at some of the subjects during bachelor/engineer level studies. I was very amazed to find out that ancient civilizations were already using such a principle in their calculations when building their monumental buildings. One of the many examples that I also watched an interesting video not so long ago was the Parthenon on top of Acropolis in Athens.
ReplyDeleteAs seen in this picture:
http://britton.disted.camosun.bc.ca/goldslide/gold08.jpg
At this moment they are trying to renovate it so that it won't collapse since its a ruin and seen better times. However the scientists were amazed to find out how every element is different because the ancients didn't use straight lines but intentionally curved the surfaces to create an optical illusion of the pillars breathing. you can find more details in this video:
https://www.youtube.com/watch?v=sgEAn1c11tY
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DeleteThank you for your response and very interesting sources, which would recommend to others ...
DeleteRegards
I've heard or read somewhere about the golden ratio. At this time it was fascinating to me. Now I take it as something obvious. The term "natural optimization" fits better. On the other hand, the math can be applied to explain huge part of our world (at least in theory). Unfortunately, I don't remember anything beside that what you wrote in article.
ReplyDeleteThank you for your comment, well, memory is volatile - unfortunately :)
DeleteThis comment has been removed by the author.
DeleteHi Wiesław,
ReplyDeleteSo interesting topic! Answering your questions:
1. Is in the course of their education often hear how this relationship occurs in nature?
Actually I cannot remember if this subject was raised even once in my education. I remember the lesson about Fibonacci numbers and Golden Ratio, but it was completely separated from their existence in nature. But the first time when I heard about Golden Ration wasn't at school, but much earlier, and it was Donald Duck who persented it to me :) You can find it on youtube: https://www.youtube.com/watch?v=AJgkaU08VvY
I didn't understand much from the mathematics, that time, but I liked the cartoon a lot :)
2. Does the interplay of many disciplines surprised you?
Not really. All formulas presented in the topic are very natural and it seems that they are the most convenient and easy proportions for nature.
3. How do you think whether it is natural optimization, or search according to "force"?
As I don't believe in any "force" (except the one from Star Wars of course ;)), I think it is a natural optimization.
Maybe the reason that all those relationships look "magical" is the construction of our mathematics. Maybe if we have some other basis, the Golden Ratio will be more obvious :)
4. Maybe you know more interesting examples, applications, and can see other applications?
I cannot remember anything in this moment.
Thank you for your interest, I chose this subject because I see here a huge coherence and beauty, I wanted to write about it because I like this themes
DeleteThanks for the answers. The authors show the consistency of science.
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ReplyDelete1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteIn schools I had had presented a lot of patterns but without proper explanation. In my opinion this isn't right way to develop creative young talents.
2. Does the interplay of many disciplines surprised you?
No, should I be surprised? :-)
3. How do you think whether it is natural optimization, or search according to "force"?
I must agree with Paweł that the simple explanation of this answer is God create world in such way. It is mentioned in video attached for this article.
4. Maybe you know more interesting examples, applications, and can see other applications?
I was not expected to dig in this field so unfortunately I haven’t have any information in this interesting area.
1. Is in the course of their education often hear how this relationship occurs in nature?
ReplyDeleteI did not hear about relationships between nature and Fibonacci Numbers.
2. Does the interplay of many disciplines surprised you?
Not, it don’t surprised me.
I think that everything what have something symmetric has look more nice.
3. How do you think whether it is natural optimization, or search according to "force"?
I would like to say that natural optimization is better that everything else.
4. Maybe you know more interesting examples, applications, and can see other applications?
Unfortunately I am not good in that specyfic topic. Maybe in the future my knowledge will be more develop in that topic.