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We, can think of many more theoretical applications of Golden Ratio, but the problem is, we cannot apply all of them to practicality.

We cannot, possibly build a house in golden ratio, the house would look good, but the problem is, it is costly, a golden ratio house is just a fantasy, that maybe a billionaire would want to build to show off, not actually live in. In a time where, many people do not have even proper shelter to live in, even if they do, when 60% of the world do not have toilets, this application is NOT FEASIBLE.

Research is still going on, to find the shape for a flying saucer or a more efficient airplane. Some say Golden Ratio is the solution, while some, don't know, so it's application is UNCERTAIN.

Guarding someone or creating a Human Spiral to protect someone is logical, Human Circles are no better than this, as in human circle, the one in the center cannot get out. It also works in war strategies, so it is FEASIBLE.

A conch is in golden ratio, it is a natural loudspeaker which makes noise of high intensity, solely because of its shape. So analogy would suggest that, a whistle or loudspeaker or a headlight or a flashlight should work best, if the shape is in Golden Ratio (Since, if sound behaves so because of reflection, light should too).There is no issue of money, as both today's, and our idea costs the same. So these applications are FEASIBLE.

In today's digital world, we cannot just reset the whole fundamentals on how circuits or devices work. If something is wrong today, which goes to the roots of a subject, we cannot change it, it applies to each and every subject or topic that exist today. If the ancients creators, made a mistake or a wrong decision, we cannot change it today. Because what we are today, is because of millions of people working on something for billions of days, we cannot just undo that, change something, and redo what we have done, because it would probably take a millennium to do what we can do, in a year today. "Engineering mistakes cannot be undone". Eg - We all know if computers were in decimal code, rather than the binary code, the 1s 0s, they would be faster, but the problem is, we cannot undo that, it requires complex circuitry to obtain decimal logic than simple binary logic, hence we may or may not have reached today, if the founding father thought to do things in decimal, similarly, Golden Spiralled components are possible, but may not be possible today. So NOT FEASIBLE.

Yes roads can be be built however we want, so it is FEASIBLE.

Search operations can be carried out this way, than searching individual patches to cover a region, so it is also FEASIBLE.

Conclusion: Out of the Feasible applications, everything can be implemented, as many of these, are changing the things we are doing today, by just a little bit. It's success depends on implementation.

But, thinking of the Best Idea, the golden spiralled - 'Golden Whistle' or 'Golden Flash light' would be a highly successful product. This would definitely, be successful, economical and ideal.

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Yes, I am the only one working on this padlet.

Others in my group are working on their, individually separate Padlets, on different topics.

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Good work. But are you the only one working on the padlet.

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Golden Ratio is undoubtedly a Nature's Number. Every living thing grows according to it, which implies it is a stable form, that can be used in technology and architecture, mimicking nature, as we know nature is the best Architect/Engineer/Scientist. Right from plants to Galaxies everything grows in Golden Ratio.

Houses can be built in the shape of Golden Spiral, giving security yet accessibility in the center, saving space, completing whole house in a single room. Just like a shell acts as home to a Mollusc.

Spacecraft / Flying Saucers can be built, in this shape which may give better stability and efficiency.

While protecting a VIP, a person's guards can stand in a golden spiral ensuring security at the center, as there are many walls, though it is a single continuous wall. Dense walls, where center is closer to exterior and non dense walls, where center is far from exterior, provide security. As there is a single way out/in covered by walls, it may serve as an escape route too.

The above method can be used in war techniques too.

In construction of Whistle blowers, or Loudspeakers, this may be used, because of its unusual geometric properties, it may yield sound of best intensity/quality. (As Conch is also in Golden Ratio)

Similarly if sound can act this way, even light should act the same. It can be used to construct, headlights of automobiles / in flashlights(torches) / in light bulbs etc. Though many LED bulbs come in curved shape, if it is a golden spiral, quality or efficiency may increase still more.

Today, Circuits are constructed in a cubic manner, where layers of electronic components are kept on each other, to obtain a 3D arrangement. Variations in speed / slow speed of components, is due to non accessibility (difficulty in accessibility of a particular component at that instant) where a component is deep inside a layer. It is a challenge for the world, to find the shortest, efficient route between components, in fact the work of many engineers of today, is to find the best place for a particular component, taking into consideration factors such as timing delay, energy loss, threshold current etc, using modern circuit analysis software like NI Circuit Design Suite. We may try replacing the layered arrangement by a golden spiralled method, which may be more efficient, as there is a single way, however inside the component is. Moreover, as some components are required for almost every process, while some are not, most frequently used, can be put in the periphery, and less used in the center. While today a particular frequently used component, is placed many times in many places, just for efficiency. Thus our new design introduces hierarchy, eliminating the need of unnecessary extra components. This is just an idea though I am not qualified enough to theoretically or practically test it, though I can test it logically in my mind.

Roads can be built in a Golden Spiral, around a hill where peak is at the spiral's center.

Search investigation, of a suspected plane crash etc, can be started at the most suspected place as the spiral's center, gradually moving away and around. This covers more area in a given time. This is better than a regular spiral as in a regular spiral distance between consecutive circular shapes are constant, this is useless while searching far from suspected spot. Rate of increase of useful, new area covered, without leaving any unsearched area, is more in a golden spiral. Thus it is better than other random ways of searching.

Same can be followed in any other Search operations like Earthquake calamities, whose effects are more near center, but need thorough examination around and across the region.

It can be followed in any situation which involves a region and a center.

Yes, the ratio can be applied to many other fields to increase the aesthetic beauty of something, which is already being done.

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Unité d’Habitation - A modern housing design principle developed by Le Corbusier (style of design).

Modulor - It is an anthropometric scale of proportion, Ratio of object height to height of a one-arm-raised-man.

Phyllotaxis - Spiralling of plant leaves. (Arrangement of leaves on a plant stem).

Parthenon - Former temple on Athenian Acropolis, dedicated to Greek God Athena.

Dodecahedron - A 3-D object with 12 identical flat faces (12 faced polyhedron).

Pentagon - 5 sided closed figure (5 sided polygon).

The Vetruvian Man - A famous Leonardo-Da-Vinci painting of a symmetrical man, with 4 legs and 4 hands (this is the pin-up image of the YouTube video posted above.

Nautilus - A snail-like organism.

Apothem - A line from the centre of a regular polygon at right angles to any of its sides.

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Goal :
To find out our perceptions towards attractiveness and to investigate whether there is really, such a relationship between golden ratio and beauty.To also find, if people are aware of Golden Ratio. To find out if our surroundings/belongings affect our perception.

Questions :

1) Gender?

2) Age?

3) Do you know what Golden Ratio is? if yes, how? if no, do you like to?

4) Do you think, the things which you usually get attracted to, are in Golden Ratio? , if yes/no, why?

5) Do you think you will always get attracted, to an object in Golden Ratio?

6) Can you tell, why you get attracted to certain things, though they may not be in Golden Ratio?

7) Do you think Golden Ratio, is the sole reason behind its beauty/attractiveness ? if not, what else can be a factor?

8) If you have a pet, which do you prefer/like, your pet or some other pet which you have never seen but, is in golden ratio?

9) Do you think every famous/popular art/architecture/actors are in Golden Ratio?

10) What to you feel about Golden Ratio (as a topic, credibility, authenticity)?

11) If you are about to get married, whom do you like to marry, a person whom you have loved or a person whose face is in golden ratio, deemed as an ideal partner by many suitors?

12) What is your perception about beauty? Is it perfectly defined or varies from person to person and situation to situation?

13) If you were given an opportunity to meet someone / be friends with someone, given that A has similar facial characteristics, as your mother / any family member and B has a face in Golden Ratio, whom do you prefer ?

14) Which of the following options do you think gives the best gauge of someone’s attractiveness? arrange in descending order.

a. BMI b. Height c. Golden Ratio d. Charisma e. Personality f. Familiarity

15) What kind of faces do you think that will appeal to you? arrange in descending order.

a. round b. oval c. heart d. square e. trapezium

16) Which painting do you want to have in your room? The Mona Lisa/ The Last Supper/Starry Night or a painting which your friend/family member made for you ?

Answer the above question now, by assuming those paintings were not famous (or the paintings are just for you to see, not to show off) or assume as if these paintings, were not yet discovered as great yet, you only know they are some old paintings, made by some unknown person, now choose to keep these anonymous old paintings or a painting your friend made just for you, with love?

17) Where do you prefer to stay/visit ? your home/cousin's place or The Parthenon (assuming its not famous again)(just a collapsed structure in golden ratio) ?

18) If you are given an object, can you estimate, whether it is in Golden Ratio?

19) While performing any task, do you consciously see patterns and take decision or use your intuition?

A pictorial survey can also be made and opinions may be taken.

Target :

General (common) Public

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Journals:

1)

Relationship between Mathematics and Art - Zeynep Aygar, TED Ankara College Foundation High School, Ankara, Turkey , May 2013.

2)

How has the knowledge on the relation between math and nature had an influence and evolved architectural design throughout history? - Madison Bozinoff, The New School Parsons, New York City, May 2015.

Videos :

Khan Academy-

3)

https://www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math-spirals-fibonacci-and-being-a-plant-1-of-3

4)

https://www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math-class-spirals-fibonacci-and-being-a-plant-2-of-3

5)

https://www.khanacademy.org/math/recreational-math/vi-hart/spirals-fibonacci/v/doodling-in-math-spirals-fibonacci-and-being-a-plant-part-3-of-3

TED / TEDx -

6)

https://www.ted.com/talks/arthur_benjamin_the_magic_of_fibonacci_numbers

7)

https://www.youtube.com/watch?v=0tAZe6pP-FM

Animation:

8)

https://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html

Other Sources:

9)

https://www.youtube.com/watch?v=fmaVqkR0ZXg

10)

http://www.britannica.com/topic/golden-ratio

11)

http://www.fastcodesign.com/3044877/the-golden-ratio-designs-biggest-myth#1

12)

http://www.sciencealert.com/mathematicians-argue-that-the-golden-ratio-is-not-the-formula-for-beauty

13)

http://www.fm-lb.org/sites/default/files/Mario_Livio_-_The_Golden_Ratio.pdf

14)

https://www.maa.org/external_archive/devlin/devlin_05_07.html

15)

http://www.goldennumber.net/golden-ratio-myth/

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I had an interest in Maths, right from my childhood days. Since I had a Diploma in Painting, When I was searching for something that relates both, one of my High School Physics teacher, had suggested me to study Golden Ratio and Fractals. I had already researched this topic based on pure interest. So when I was asked to select a topic and create a padlet out of it, it was easy.

I was aware of websites like Khan Academy, Wolfram Mathematica, MIT-OCW as I was studying them, in my Class 12. I knew of TED, Britannica as they had some amazing videos and content of every topic. So it was easy for me as I knew where to search. As for the journals, I knew of 'Google Scholar' - A Google, Journal/Research Paper search engine. The padlet wallpaper was my laptop wallpaper, which I figured out was in Golden Ratio. I already had Mario Livio's book on Golden ratio (e-book) which was suggested to me by one of my teachers.

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Brief history of Golden Ratio- Britannica Encyclopaedia 

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Brief history of Golden Ratio- Britannica Encyclopaedia 

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A short description of The What, When, Who,Where? of Golden Ratio for a layman can be found here.

http://www.britannica.com/topic/golden-ratio

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Questions which arise !! - along with answers

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Questions which arise !! - along with answers

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Are all the statements, made in these documents and videos true ?

Is Golden Ratio, just a myth ?

Just because an object is in Golden Ratio, should it be beautiful ?

Just because something is beautiful, should it be in Golden Ratio ?

Is Golden Ratio just any other Number ? Is there nothing special about it ?

The above questions may, at first confuse you. But as I researched more and more, I found out that-

There are some people out there, who popularize the Golden Ratio just to sell their product.

There are software available, where you can just give an ordinary photo of a person or a building or a painting, and the system automatically morphs the photo and comes up with many golden ratios in a photo.

Golden Ratio was first described in Euclid's Elements 2300 years ago. Everything was fine until someone named Adolf Zeising came and started applying it to things blindly. And people, now also fall, to a 150 year old scam.

According to this link : http://www.fastcodesign.com/3044877/the-golden-ratio-designs-biggest-myth#1

It appears that, The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple Logo are not actually in Golden Ratio. It states that -

You don't really prefer the Golden Ratio. Many designers think its not useful - Quotes- " There are so many other numbers and formulas that are more important while designing a building". A designer says " In my own work I can't ever recall using the Golden Ratio"

This link of the popular 'Science Alert' substantiates the claim:  http://www.sciencealert.com/mathematicians-argue-that-the-golden-ratio-is-not-the-formula-for-beauty
There is a whole book called The Golden Ratio: The Story of PHI, the World's Most Astonishing Number (Mario Livio - 2002) which argues that, though Golden Ratio is undeniably a Nature's Number, it only, does not signify beauty, that though many art and architectural works are done, based on Golden Ratio, they need not be beautiful, some art works are beautiful without it too.

It appears there exists two cults- one which blindly argues Golden Ratio is the root of beauty, another which blindly argues Golden Ratio does not signify beauty. "Even PhD Mathematics students go wrong, while researching this topic, by taking sides, either telling there is no golden ratio where there is, or telling there is golden ratio where there is not".

But both agree that all organisms grow according to Golden Ratio. There is no doubt in relation between Golden Ratio and Nature. But the relation between Golden Ratio and beauty is full of doubts.

It appears that the Myth will stay forever according to the link : https://www.maa.org/external_archive/devlin/devlin_05_07.html

This is because, psychologically, we perceive things which we see everyday, as beautiful and we love them - Just like we love our family and pets though they may not be that beautiful. We start to like people who are visually and emotionally similar to them. Similarly the myth can be solved - As we see movies and serials everyday, we get accustomed to the actor's faces and we start to like them, in case of nature too because we see leaves, trees, flowers everyday, we start loving nature. As nature follows Golden Ratio, if we see anyone or anything that is in Golden Ratio, we feel attracted towards it.

Hence, if we see anything attractive or beautiful, it is because, either we are accustomed to similar objects or the things are in Golden Ratio. The reverse is not implied (it is not vice-versa). Hence validating the arguments of both the sides.

This too is explained beautifully, in the link:

http://www.goldennumber.net/golden-ratio-myth/

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Golden ratio and plants(part III)

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Doodling in math: Spirals, Fibonacci, and being a plant [3 of 3]

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Golden ratio and plants(part II)

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Doodling in math: Spirals, Fibonacci, and being a plant [2 of 3]

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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"How has the knowledge on the relation between math and nature had an influence and evolved architectural design throughout history? " by Madison Bozinoff

(approximately 2600 words according to wordcounter.net )

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Naveen Hegde

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Golden Ratio is a mathematical constant, which is roughly equal to 1.61803398875; It is represented by the symbol φ (Greek letter 'Phi')

It is an astonishing fact that - 'If the length to breadth ratio, of a part of an object, is equal to this number, then that part of the object appears visually beautiful and attractive'

Studies have found that it is the 'Nature's number' , meaning to say that whenever something grows, it grows in such a shape that approaches golden ratio.

This clearly shows that, though fractions are a part of mathematics, beauty-a part of art, growth-a part of biology, they are all unified into one, by an innocent looking φ .

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Maths is Fun - Spiral interactive animation page

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Maths is Fun - Spiral interactive animation page

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Plants can grow new cells in spirals, such as the pattern of seeds in this beautiful sunflower.

The spiral happens naturally because each new cell is formed after a turn.
"New cell, then turn,
then another cell, then turn, ..."
How Far to Turn?

So, if you were a plant, how much of a turn would you have in between new cells?

If you don't turn at all, you get a straight line.

But that is a very poor design ... you want something round that will hold together with no gaps.

Why not try to find the best value for yourself?
Remember, you are trying to make a pattern with no gaps from start to end:

images/golden-ratio-packing.js

(By the way, it doesn't matter about the whole number part, like 1. or 5. because they are full revolutions that point us back in the same direction.)

What Did You Get?

If you got something that ends like 0.618 (or 0.382, which is 1 − 0.618) then "Congratulations, you are a successful member of the plant kingdom!"

That is because the Golden Ratio ( 1.61803...) is the best solution, and the Sunflower has found this out in its own natural way.

Try it ... it should look like this.

Why?

Any number that is a simple fraction (example: 0.75 is 3/4, and 0.95 is 19/20, etc) will, after a while, make a pattern of lines stacking up, which makes gaps.

But the Golden Ratio (its symbol is the Greek letter Phi, shown at left) is an expert at not being any fraction.

It is an Irrational Number (meaning we cannot write it as a simple fraction), but more than that ... it is as far as we can get from being near any fraction.

Just being irrational is not enough

Pi ( 3.141592654...), which is also irrational.

Unfortunately it has a decimal very close to 1/7 (= 0.142857...), so it ends up with 7 arms.

e ( 2.71828...) also irrational, does not work either because its decimal is close to 5/7 (0.714285...), so it also ends up with 7 arms.

So, How Does the Golden Ratio Work?

One of the special properties of the Golden Ratio is that it can be defined in terms of itself, like this:

(In numbers: 1.61803... = 1 + 1/1.61803...)

That can be expanded into this fraction that goes on for ever (called a "continued fraction"):

So, it neatly slips in between simple fractions.

Fibonacci Numbers

There is a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it).

When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio:

So, just like we naturally get seven arms when we use 0.142857 (1/7), we tend to get Fibonacci Numbers when we use the Golden Ratio.

Try counting the spiral arms - the "left turning" spirals, and then the "right turning" spirals ... what numbers did you get?

Spiral Leaf Growth

This interesting behavior is not just found in sunflower seeds.

Leaves, branches and petals can grow in spirals, too.

Why? So that new leaves don't block the sun from older leaves, or so that the maximum amount of rain or dew gets directed down to the roots.

In fact, when a plant has spirals the rotation tends to be a fraction made with two successive (one after the other) Fibonacci Numbers, for example:

A half rotation is 1/2 (1 and 2 are Fibonacci Numbers)

3/5 is also common (both Fibonacci Numbers), and

5/8 also (you guessed it!)

all getting closer and closer to the Golden Ratio.

And that is why Fibonacci Numbers are very common in plants.
1, 2, 3, 5, 8, 13, 21, ... etc occur in an amazing number of places.

Here is a daisy with 21 petals
(but expect a few more or less, because
some may have dropped off or be just growing)

But we don't see this in all plants, as nature has many different methods of survival.

Golden Angle

So far we have been talking about "turns" (full rotations).

The equivalent of 0.61803... rotations is 222.4922... degrees, or about 222.5°.

In the other direction it is about 137.5°, called the "Golden Angle".
So, next time you are walking in the garden, look for the Golden Angle, and count petals and leaves to find Fibonacci Numbers,
and discover how clever the plants are ... !
Exercise

Why don't you go into the garden or park right now, and start counting leaves and petals, and measuring rotations to see what you find.

You can write your results on this form:

(But remember: nature has its own rules, and it does not have to follow mathematical patterns. But when it does it is awesome to see.)

* Notes About the Animation

Sunflower seeds grow from the center outwards, but on the animation I found it easier to draw the younger seeds first and add on the older ones.

The animation should continue longer to be the same as the sunflower - this would result in 55 clockwise spirals and 34 counterclockwise spirals (successive Fibonacci Numbers). I just didn't want it to take too long.

The spirals are not programmed into it - they occur naturally as a result of trying to place the seeds as close to each other as possible while keeping them at the correct rotation.

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Nature, The Golden Ratio and Fibonacci Numbers

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Plants can grow new cells in spirals, such as the pattern of seeds in this beautiful sunflower. The spiral happens naturally because each new cell is formed after a turn. "New cell, then turn, then another cell, then turn, ..." So, if you were a plant, how much of a turn would you have in between new cells?

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Golden ratio and plants (part I) - Victoria Hart known as Vi Hart

She is a widely popular 'Mathemusician'

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Doodling in math: Spirals, Fibonacci, and being a plant [1 of 3]

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Part 2: http://youtu.be/lOIP_Z_-0Hs Part 3: http://youtu.be/14-NdQwKz9w Re: Pineapple under the Sea: http://youtu.be/gBxeju8dMho

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"Relashionship Between Mathematics and Art" by Zeynep Aygar

(approximately 4500 words according to wordcounter.net)

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Mathematics Professor;  Known for Mental Maths and 'Mathemagics' ; Selected by The Princeton Review as one of The Best 300 Professors, 2012

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Arthur Benjamin: The magic of Fibonacci numbers

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Math is logical, functional and just ... awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)

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-Matthew Cross

A Fortune 100 Strategist, Author, Speaker; Founder CEO of Leadership Alliance

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Golden Ratio Fibonacci Sequence TEDxEast: Matthew Cross

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Non Authentic Youtube Video

- bricke321