20.05.2017
The Golden Ratio is something every designer should know about. We will explain what it is and how you can use it.
There is a common mathematical relationship found in nature that can be used in design to create pleasing, natural-looking compositions. It is called the Golden Section or the Greek letter "phi". If you are an illustrator, art director or graphic designer, you should definitely use the Golden Ratio in every project.
In this article, we'll explain how to use it, as well as share some great tools for further inspiration and learning.
Closely related to the Fibonacci Sequence, which you may remember from a math class or Dan Brown's The Da Vinci Code, the Golden Ratio describes a perfectly symmetrical relationship between two proportions.
Approximately equal to a ratio of 1:1.61, the Golden Ratio can be illustrated as the Golden Rectangle: a large rectangle containing a square (in which the sides are equal to the length of the shortest side of the rectangle) and a smaller rectangle.
If you remove the square from the rectangle, there will be another, small Golden Rectangle. This process can continue indefinitely, just like the Fibonacci numbers that work in reverse. (Adding a square with sides equal to the length of the longest side of the rectangle brings you closer to the Golden Rectangle and the Golden Ratio.)
Golden Section in action
It is believed that the Golden Mean has been used for about 4000 years in art and design. However, many people agree that this principle was also used in the construction of the Egyptian Pyramids.
In more modern times this rule can be seen in music, art and design around us. By applying a similar working methodology, you can bring the same design features to your work. Let's take a look at some inspiring examples.
Greek architecture
In ancient Greek architecture, the Golden Ratio was used to determine pleasant spatial relationships between the width of the building and its height, the size of the portico, and even the position of the columns that support the structure.
The result is a perfectly proportioned structure. The neoclassical architecture movement also used these principles.
The Last Supper
Leonardo Da Vinci, like many other artists of yesteryear, often used the Golden Mean to create pleasing compositions.
In the Last Supper, the figures are located in the lower two thirds (the largest of the two parts of the Golden Section), and Jesus is perfectly sketched between the golden rectangles.
The golden ratio in nature
There are many examples of the Golden Mean in nature - you can find them around you. Flowers, sea shells, pineapples, and even honeycombs show the same ratio.
How to calculate the Golden Ratio
The calculation of the Golden Ratio is quite simple, and starts with a simple square:
01. Draw a square
It forms the length of the short side of the rectangle.
02. Divide the square
Divide the square in half using a vertical line, forming two rectangles.
03. Draw a diagonal
In one of the rectangles, draw a line from one corner to the opposite.
04. Rotate
Rotate this line so that it is horizontal to the first rectangle.
05. Create a new rectangle
Create a rectangle using the new horizontal line and the first rectangle.
How to use the Golden Ratio
Using this principle is easier than you think. There are a couple of quick tricks you can use in your mockups, or spend a little more time and fully flesh out the concept.
Fast way
If you've ever come across the "Rule of Thirds" then you'll be familiar with the idea of dividing space into equal thirds vertically and horizontally, with where lines intersect to create natural points for objects.
The photographer places the key subject on one of these intersecting lines to create a pleasing composition. This principle can also be used in your page layout and poster designs.
The rule of thirds can be applied to any shape, but if you apply it to a rectangle with proportions of roughly 1:1.6, you will end up very close to a golden rectangle, making the composition more pleasing to the eye.
Full implementation
If you want to fully implement the Golden Ratio in your design, then simply position the main content and the sidebar (in web design) at a ratio of 1:1.61.
You can round the values up or down: if the content area is 640px and the sidebar is 400px, then this markup is quite suitable for the Golden Ratio.
Of course, you can also separate the content and sidebar areas into the same relationship, and the relationship between the web page title, content area, footer, and navigation can also be designed using the same principle.
Useful Tools
Here are a few tools to help you use the Golden Ratio in design and create proportional projects.
GoldenRATIO is an application for creating website designs, interfaces and templates suitable for the Golden Ratio. Available on Mac App Store for $2.99. Includes a visual Golden Ratio calculator.
The app also has a "Favorites" feature that saves settings for repetitive tasks and a "Click-thru" mod that lets you minimize the app in Photoshop.
This Golden Ratio calculator from Pearsonified helps you create the perfect typography for your website. Enter the font size, container width in the box, and click the button Set my type! If you need to optimize the number of letters per line, you can optionally enter a CPL value.
It's simple, useful and free app available for Mac and PC. Enter any number and the app will calculate the second digit according to the golden ratio.
This application allows you to design with golden proportions, saving you a lot of time on calculations.
You can change shapes and sizes to focus on working on your project. A permanent license costs $49, but you can download a free version for a month.
Learning the Golden Section
Here are some useful Golden Ratio tutorials (English):
In this Digital Arts tutorial, Roberto Marras shows you how to use the Golden Ratio in your artwork.
Tutorial from Tuts+ on how to use golden principles in web design projects.
A tutorial from Smashing Magazine on proportions and the rule of thirds.
Every person who encounters the geometry of objects in space is well acquainted with the golden section method. It is used in art, interior design and architecture. Even in the last century, the golden ratio turned out to be so popular that now many supporters of the mystical vision of the world have given it another name - the universal harmonic rule. The features of this method are worth considering in more detail. This will help to find out why he is interested in several areas of activity at once - art, architecture, design.
The essence of the universal proportion
The principle of the golden section is just a dependence of numbers. However, many are biased towards it, attributing some mystical powers to this phenomenon. The reason lies in the unusual properties of the rule:
- Many living objects have proportions of the torso and limbs that are close to the indications of the golden section.
- Dependencies 1.62 or 0.63 determine the size ratios only for living beings. Objects related to inanimate nature very rarely correspond to the meaning of the harmonic rule.
- The golden proportions of the body structure of living beings are an essential condition for the survival of many biological species.
The golden ratio can be found in the structure of the bodies of various animals, tree trunks and shrub roots. Supporters of the universality of this principle are trying to prove that its meaning is vital for representatives of the living world.
You can explain the golden section method using the image of a chicken egg. The ratio of the segments from the points of the shell, equally distant from the center of gravity, is equal to the golden ratio. The most important indicator for the survival of birds is the shape of the egg, and not the strength of the shell.
Important! The golden ratio is calculated based on the measurements of many living objects.
Origin of the golden ratio
Mathematicians already knew about the universal rule Ancient Greece. It was used by Pythagoras and Euclid. In the famous architectural masterpiece - the pyramid of Cheops, the ratio of the dimensions of the main part and the length of the sides, as well as the bas-reliefs and decorative details, correspond to the harmonic rule.
The golden section method was adopted not only by architects, but also by artists. The mystery of harmonic proportion was considered one of the greatest mysteries.
The first to document the universal geometric proportion was the Franciscan monk Luca Pacioli. His ability in mathematics was excellent. The golden section gained wide recognition after the publication of Zeising's results on the golden section. He studied the proportions of the human body, ancient sculptures, plants.
How was the golden ratio calculated?
To understand what the golden ratio is, an explanation based on the lengths of the segments will help. For example, inside a large one there are several small ones. Then the lengths of the small segments are related to the total length of the large segment as 0.62. Such a definition helps to figure out how many parts a certain line can be divided into so that it complies with the harmonic rule. Another advantage of using this method is that you can find out what the ratio of the largest segment to the length of the entire object should be. This ratio is 1.62.
Such data can be represented as the proportions of measured objects. At first they were sought out, selecting empirically. However, now the exact ratios are known, so it will not be difficult to build an object in accordance with them. The golden ratio is found in the following ways:
- Construct a right triangle. Split one of its sides, and then draw perpendiculars with secant arcs. When carrying out calculations, it is necessary to build a perpendicular from one end of the segment, equal to ½ of its length. Then a right triangle is completed. If you mark a point on the hypotenuse, which will show the length of the perpendicular segment, then a radius equal to the rest of the line will cut the base into two halves. The resulting lines will be related to each other according to the golden ratio.
- Universal geometric values get in another way - by building a pentagram of Durer. She is a star that is placed in a circle. It contains 4 segments, the lengths of which correspond to the rule of the golden section.
- In architecture, the harmonic proportion is used in a modified form. To do this, a right-angled triangle should be divided along the hypotenuse.
Important! Compared to the classical concept of the golden ratio method, the architect's version has a ratio of 44:56.
If in the traditional interpretation of the harmonic rule for graphics, it was calculated as 37:63, then 44:56 was more often used for architectural structures. This is due to the need to build high-rise buildings.
The secret of the golden ratio
If in the case of living objects the golden ratio, which manifests itself in the proportions of the body of people and animals, can be explained by the need to adapt to the environment, then the use of the rule of optimal proportions in the 12th century to build houses was new.
The Parthenon, preserved from the time of Ancient Greece, was erected using the golden section method. Many castles of the nobles of the Middle Ages were created with parameters corresponding to the harmonic rule.
The golden ratio in architecture
The many buildings of antiquity that have survived to this day serve as confirmation that architects from the Middle Ages were familiar with the harmonic rule. The desire to maintain a harmonious proportion in the construction of churches, significant public buildings, residences of royal persons is very clearly visible.
For example, Notre Dame Cathedral was built in such a way that many of its sections correspond to the golden section rule. You can find many works of architecture of the 18th century that were built in accordance with this rule. The rule was also applied by many Russian architects. Among them was M. Kazakov, who created projects for estates and residential buildings. He designed the Senate building and the Golitsyn hospital.
Naturally, houses with such a ratio of parts were erected even before the discovery of the golden section rule. For example, such buildings include the Church of the Intercession on the Nerl. The beauty of the building becomes even more mysterious, given that the building of the Intercession Church was erected in the 18th century. However modern look building acquired after restoration.
In writings about the golden ratio, it is mentioned that in architecture the perception of objects depends on who is observing. The proportions formed using the golden section give the most relaxed ratio of the parts of the structure relative to each other.
A striking representative of a number of buildings that comply with the universal rule is the Parthenon, an architectural monument erected in the fifth century BC. e. The Parthenon is arranged with eight columns on the smaller facades and seventeen on the larger ones. The temple was built of noble marble. Due to this, the use of coloring is limited. The height of the building refers to its length 0.618. If you divide the Parthenon according to the proportions of the golden section, you will get certain ledges of the facade.
All these structures have one thing in common - the harmony of the combination of forms and the excellent quality of construction. This is due to the use of the harmonic rule.
The importance of the golden ratio for a person
The architecture of ancient buildings and medieval houses is quite interesting for modern designers. This is due to such reasons:
- Thanks to the original design of houses, you can prevent annoying clichés. Each such building is an architectural masterpiece.
- Mass application of the rule to decorate sculptures and statues.
- Thanks to the observance of harmonic proportions, the eye is drawn to more important details.
Important! When creating a building project and creating an external appearance, the architects of the Middle Ages used universal proportions, based on the laws of human perception.
Today, psychologists have come to the conclusion that the principle of the golden ratio is nothing more than a human reaction to a certain ratio of sizes and shapes. In one experiment, a group of subjects were asked to fold a sheet of paper in such a way that the sides turned out with optimal proportions. In 85 results out of 100, people folded the sheet almost exactly according to the harmonic rule.
According to modern scientists, the indicators of the golden section are more in the field of psychology than characterize the laws of the physical world. This explains why there is such interest in him from the hoaxers. However, when constructing objects according to this rule, a person perceives them more comfortably.
Using the golden ratio in design
The principles of using a universal proportion are increasingly used in the construction of private houses. Particular attention is paid to the observance of the optimal proportions of the structure. Much attention is paid to the correct distribution of attention inside the house.
The modern interpretation of the golden section no longer refers only to the rules of geometry and form. Today, the principle of harmonic proportions obeys not only the dimensions of the facade details, the area of rooms or the length of the gables, but also the color palette used to create the interior.
It is much easier to build a harmonious structure on a modular basis. Many departments and rooms in this case are performed as separate blocks. They are designed in strict accordance with the harmonic rule. To erect a building as a set of separate modules is much easier than to create a single box.
Many firms involved in the construction of country houses, when creating a project, follow the harmonic rule. This allows customers to give the impression that the structure of the building has been worked out in detail. Such houses are usually described as the most harmonious and comfortable to use. With the optimal choice of room areas, residents psychologically feel calm.
If the house was built without taking into account harmonic proportions, you can create a layout that will be close to 1: 1.61 in terms of the ratio of wall sizes. To do this, additional partitions are installed in the rooms, or pieces of furniture are rearranged.
Similarly, the dimensions of doors and windows are changed so that the opening has a width that is 1.61 times less than the height value.
Harder to choose colors. In this case, you can observe the simplified value of the golden section - 2/3. The main color background should occupy 60% of the space of the room. Shading shade occupies 30% of the room. The remaining surface area is painted over with tones close to each other, enhancing the perception of the selected color.
The inner walls of the rooms are divided by a horizontal strip. It is located 70 cm from the floor. The height of the furniture should be in harmony with the height of the walls. This rule also applies to the distribution of lengths. For example, a sofa should have dimensions that would be at least 2/3 of the length of the wall. The area of \u200b\u200bthe room, which is occupied by pieces of furniture, should also have a certain value. It refers to the total area of the entire room as 1:1.61.
The golden ratio is difficult to apply in practice due to the presence of only one number. That is why. I design harmonious buildings, use a series of Fibonacci numbers. This provides a variety of options for shapes and proportions of building details. A series of Fibonacci numbers is also called the golden one. All values strictly correspond to a certain mathematical dependence.
In addition to the Fibonacci series, modern architecture also uses another design method - the principle laid down by the French architect Le Corbusier. When choosing this method, the starting unit of measurement is the height of the owner of the house. Based on this indicator, the dimensions of the building and the interior are calculated. Thanks to this approach, the house is not only harmonious, but also acquires individuality.
Any interior will take on a more complete look if you use cornices in it. When using universal proportions, you can calculate its size. The optimal indicators are 22.5, 14 and 8.5 cm. The eaves should be installed according to the rules of the golden section. The small side of the decorative element should be related to the larger side as it is to the combined values of the two sides. If the large side is equal to 14 cm, then the small one should be made 8.5 cm.
You can give the room comfort by dividing the wall surfaces with the help of gypsum mirrors. If the wall is divided by a curb, the height of the cornice strip should be subtracted from the remaining larger part of the wall. To create a mirror of optimal length, step back from the border and cornice same distance.
Conclusion
Houses built according to the principle of the golden section really turn out to be very comfortable. However, the price of building such buildings is quite high, since the cost of building materials increases by 70% due to atypical sizes. This approach is not at all new, since most of the houses of the last century were created based on the parameters of the owners.
Thanks to the use of the golden section method in construction and design, buildings are not only comfortable, but also durable. They look harmonious and attractive. The interior is also decorated according to a universal proportion. This allows you to wisely use the space.
In such rooms, a person feels as comfortable as possible. You can build a house using the principle of the golden section yourself. The main thing is to calculate the loads on the elements of the structure, and choose the right materials.
The golden section method is used in interior design, placing decorative elements of certain sizes in the room. This allows you to give the room comfort. Color solutions are also chosen in accordance with universal harmonic proportions.
In practice, when choosing a sheet (picture) format, the “classic” proportions of the sides of a rectangle are often used, in which the ratio of the smaller side to the larger one is 0.6180339, and the larger to the smaller one is 1.6180339. These numbers have been called golden since ancient times, and the ratio of magnitudes necessary to obtain them is known as golden ratio or the golden ratio.
The basis of the doctrine of the harmony of the world, expressed in numerical terms, was laid by the ancient Greek mathematician Pythagoras (VI century BC). He presented the golden section as one of the laws that mathematically accurately determines the most beautiful and harmonious ratio of the parts of the whole, divided into two unequal halves.
The construction of a rectangle is based on the ratio of the parts of the segment in the proportions of the golden section. With the help of diagonals, it is divided into its component parts, in which the dynamics of proportional figures is formed - a square, a rectangle, as well as right-angled and isosceles triangles.
Thus, using diagonals, you can get a sequential row of increasing rectangles, with an aspect ratio of 1:√2, 1:√3, 1:√4, 1:√5, derived from a square.
With a side of √4, a rectangle with a double square is formed. With a side of √3, two right-angled triangles are formed, in which the common hypotenuse is the diagonal of the rectangle, equal to twice the value of the smaller leg (i.e., the side of the square), and they have sharp corners 30 and 60 degrees.
The diagonal is also used in the construction of successively increasing squares, creating a "dynamic" development of their size.
In this construction, the side of each subsequent square is related to the side of the previous one, as the diagonal of the square is to its own side. These transformations are sometimes referred to as "active square".
The geometric system of dynamic proportions of the square, rectangle and triangle was the basis for the creation of architectural structures in early period ancient egypt. In addition, in the conditions of the primitive technique of architectural construction in those distant times, it was constantly required to restore the perpendicular to the line, which was then carried out using a rope with 12 knots. With the use of such a device, a right-angled triangle was obtained with a side-to-side ratio of 3: 4: 5, which later became known as the Egyptian one. Currently, right angles are built on its basis and perpendiculars are drawn to the end of the segment.
Since ancient times, the golden ratio has been used in the practice of constructing various images. This contributes to the creation of harmonious images and balance of proportions in everything that surrounds. The proportions of the golden section are present in mathematics, and especially in geometry, in fine arts, in everyday life and in nature, in the plant and animal world.
The golden ratio has been widely developed in mathematics. So, in the 16th century, the Italian scientist Fibonacci built a mathematical series of numbers, in which the next number determines the sum of the previous two - 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. In addition, another dependence of these numbers is established, in which the ratio of each subsequent to the previous one is expressed by the number 1.618 ..., and the previous one to the next - 0.618. Thus, in this mathematical series, an interconnection of numbers is formed, containing the proportions of the golden section.
Especially often the golden ratio is used in geometry when dividing a circle into equal parts and constructing regular polygons.
In a stellated polygon - a five-pointed star, each point of intersection of its sides divides them into two unequal parts in the proportions of the golden section.
Since ancient times, the golden ratio has been used in various types visual arts- architecture, sculpture, painting. The Parthenon is a classic example of the application of the golden ratio in architecture.
Especially widely used in his work was the ratio of the golden section of Leonardo da Vinci, which he called the "divine proportion".
The ancient statues of Greek art, reflecting the proportions of an ideally shaped human body, also obey the numerical harmony of the golden section.
The golden ratio is used in the inscription of letters and numbers in various fonts.
The golden ratio is often used in determining the size of a rectangle given its larger or smaller side. If a rectangular picture has a length (AB), then its height (AC) is determined by the following construction:
First, an arc equal to half of it is drawn from the end of the segment (B) to the intersection with the perpendicular (AO=OB=VD). The resulting point D is connected by a straight line to the other end of the segment (A). Then, from point D, an arc with a radius of VD is drawn to the intersection with this straight line and point E is marked. An arc drawn from the end of segment A with a radius of AE determines point C along a vertical straight line and the required height of the picture AC.
If the height of the picture (AC) is given, then its length (AB) is determined by another construction. First, a square ASDE is built with a side equal to AC. Then, from the middle of the side of the square (O), an arc with a radius of OD is drawn and a point B is obtained on a horizontal straight line, which will determine the desired length of the side of the rectangular picture AB.
On a rectangle with golden proportions, you can build any size similar sheet format.
To do this, it is placed on a sheet of paper in one of its corners (A) and a diagonal is drawn in it. Then from point A they postpone given size horizontal or vertical side of the sheet format and draw a perpendicular through its end until it intersects with the diagonal, which will determine the second side of the rectangle.
When we look at a beautiful landscape, we are covered all around. Then we pay attention to details. A babbling river or a majestic tree. We see a green field. We notice how the wind hugs him gently and the juror sways the grass from side to side. We can feel the aroma of nature and hear the birds singing... Everything is harmonious, everything is interconnected and gives a sense of peace, a sense of beauty. Perception goes in stages in slightly smaller shares. Where will you sit on the bench: on the edge, in the middle, or anywhere? Most will answer that a little further from the middle. An approximate number in bench proportion from your body to the edge would be 1.62. So it is in the cinema, in the library - everywhere. We instinctively create harmony and beauty, which I call the “Golden Section” all over the world.
The Golden Ratio in Mathematics
Have you ever wondered if it is possible to define the measure of beauty? It turns out that mathematically it is possible. Simple arithmetic gives the concept of absolute harmony, which is displayed in impeccable beauty, thanks to the principle of the Golden Section. The architectural structures of other Egypt and Babylon were the first to conform to this principle. But Pythagoras was the first to formulate the principle. In mathematics, this division of the segment is slightly more than half, or rather 1.628. This ratio is represented as φ =0.618= 5/8. A small segment \u003d 0.382 \u003d 3/8, and the entire segment is taken as one.
A:B=B:C and C:B=B:A 
Great writers, architects, sculptors, musicians, people of art, and Christians who draw pictograms (five-pointed stars, etc.) with its elements in temples, escaping evil spirits, and people studying exact sciences, problem solving cybernetics.
Golden section in nature and phenomena.
Everything on earth taking shape grows up, sideways or in a spiral. Archimedes paid close attention to the latter, having drawn up an equation. A cone, a shell, a pineapple, a sunflower, a hurricane, a web, a DNA molecule, an egg, a dragonfly, a lizard are arranged along the Fibonacci series ... 
Ticirius proved that our entire Universe, space, galactic space, everything is planned based on the Golden Principle. Absolutely in everything living and not living you can read the highest beauty. 
The golden ratio in man.
The bones are thought out by nature, also according to the proportion 5 / 8. This excludes people's reservations about “big bones”. Most body parts in ratios apply to the equation. If all parts of the body obey the Golden formula, then the external data will be very attractive and ideally folded. 
Segment from the shoulders to the top of the head and its size = 1:1.618
Segment from the navel to the top of the head and from the shoulders to the top of the head = 1:1.618
Segment from the navel to the knees and from them to the feet = 1: 1.618
The segment from the chin to the extreme point of the upper lip and from it to the nose \u003d 1: 1.618 
All facial distances give a general idea of the ideal proportions that attract the eye.
Fingers , palm , also obey the law . It should also be noted that the segment of the spread arms with the torso is equal to the height of a person. Why , all organs , blood , molecules correspond to the Golden formula . True harmony inside and outside of our space.
Parameters from the physical side of the surrounding factors.
Sound volume. Highest point sound that causes discomfort and pain in the auricle = 130 decibels. This number can be divided by the proportion 1.618, then it turns out that the sound of a human scream will be = 80 decibels.
Using the same method, moving on, we get 50 decibels, which is typical for the normal volume of human speech. And the last sound that we get thanks to the formula is the pleasant sound of a whisper = 2.618.
According to this principle, it is possible to determine the optimal-comfortable, minimum and maximum number of temperature, pressure, humidity. The simple arithmetic of harmony is embedded in our entire environment.
The golden ratio in art.
In architecture, the most famous buildings and structures: Egyptian pyramids, Mayan pyramids in Mexico, Notre Dame de Paris, Greek Parthenon, Petrovsky Palace, and others. 
In music: Arensky, Beethoven, Havan, Mozart, Chopin, Schubert, and others.
In painting: almost all the paintings of famous artists are painted according to the section: the versatile Leonardo da Vinci and the inimitable Michelangelo, Shishkin and Surikov are so close in writing, the ideal of the purest art is the Spaniard Raphael, and the Italian Botticelli, who gave the ideal of female beauty, and many, many others.
In poetry: the ordered speech of Alexander Sergeevich Pushkin, especially “Eugene Onegin” and the poem “Shoemaker”, the poetry of the wonderful Shota Rustaveli and Lermontov, and many other great masters of the word.
In sculpture: a statue of Apollo Belvedere, Olympian Zeus, beautiful Athena and graceful Nefertiti, and other sculptures and statues.
Photography uses the “rule of thirds”. The principle is this: the composition is divided into 3 equal parts vertically and horizontally, the key points are located either on the intersection lines (horizon) or at the intersection points (object). Thus the proportions are 3/8 and 5/8. 
There are many tricks in according to the Golden Ratio that should be analyzed in detail. I will describe them in detail in the next one. 
Modern web design includes 2 features that must be clearly observed: aesthetics and the right scope. If you follow these concepts, web design can be considered successful.
As for aesthetics, here we mean that when drawing this or that image of an object, we use many different manipulations: creating a grid, layout, using typographic techniques in order to get a good structure of the object. It is important to maintain a sense of harmony, order and visual balance in any graphic processing. The Golden Ratio and the Rule of Three will help us with this.
You have probably heard of these terms before. And, perhaps, you have an idea in which specific projects they can be used. The "Golden Ratio" and the "Rule of Three" are used to change the image and present it in at its best than it actually is. Such technologies help to improve even the most primitive picture.
Let's take a closer look at these features and find out in which areas of web design they can be applied.
What is the "Golden Ratio" and how did it appear?
This term may not be clear at first glance. Why "Golden"? Why use this technology? To date, it still remains a mystery who invented the "Golden Section", where this name came from. However, it is known that the technology has been used for 2400 years. It is also worth noting that the golden ratio is used in various branches of science: in astronomy, mathematics, architecture, music, painting and many others.
The golden ratio is formed from a simple mathematical equation that shows a ratio. In its simplest mathematical form, this relationship looks like this:
As you can see, this is a unique equation that separates the relationship between two line sizes and proportions. In decimal, b divided by a equals 1.618033... if a>b. In the example below, let's say that b is 5. Then the equation will look like this:
You may have heard of the Fibonacci sequence before. How does it actually work? For example, there is a series of numbers in which any given number created by adding the previous two. Starting from 0, the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… etc:
The written expression is represented as a formula: xn = xn-1 + xn-2 .
The sequence is closely related to the golden ratio, because if you take any two consecutive numbers and divide by the previous one, the fraction will be very close to the golden ratio. As the value of the number increases, the fraction gets even closer to the golden ratio. For example, 8/5 is 1.6, 34/21 is 1.619, and so on.
"Golden Spiral" Rectangle
So, you must have seen similar equations. But why do designers use geometry in their designs? Why is overlaying shapes necessary? The scheme is called the Fibonacci Spiral. It is actually quite simple and is the most optimal for many. geometric shapes. The spiral is created using quarter circles that are drawn inside an array of squares based on the Fibonacci sequence.
The diagram below shows an example:
It turns out that each subsequent radius is greater than the previous one by a number close to the golden ratio. The resulting spiral is used in many areas, most often in drawing and architecture, but it can also be observed in natural phenomena.
"Rule of Three"
This rule is one of the variants of the golden spiral and is often used when cropping photos and videos. Used to trim frames and give them an aesthetic look. To apply the "Rule of Three", you need to divide the image by 9 equal parts. Draw 2 horizontal lines and 2 vertical lines. It is important to place them evenly. The point is to align focus with the leftmost vertical divider. The horizon or "vanishing point" must be level with the horizontal divider.
Application of the "Golden Spiral"
As already noted, the Fibonacci sequence is closely related to the golden ratio. The application of the golden section is performed using a traced spiral. The image shows an example of use this method. So, we see a rectangle, the base of which extends from the woman's right wrist to her left elbow.
The rectangle expands vertically until it reaches the crown. If we draw squares inside the golden rectangle, all the important parts of the woman are on the edges of the inner squares: her chin, eyes and lips. Leonardo da Vinci used the golden ratio many times in his work. Below are examples of the golden spiral in nature and space.
Application in web design
Many designers make the mistake of thinking that by simply dividing or multiplying by 1.61... you can get a harmonious proportion. This is far from true, it is just the basis of the process. You can't just use this or that number and get the magic proportion. However, there are certain ways that help to get the golden ratio. Some artists tend to think that the golden ratio theory is a myth. Here is another example of how the golden ratio works. Let's take a prototype site and consider the application of the golden ratio on it.
Looks pretty simple, right? Yes, in fact it is. The design is based on a 960 pixel grid. The design is represented using the golden ratio. If you use 1 golden spiral that spans 960px, you can see how the header, logo, etc. were positioned.
We move our spiral lower and rely on its dimensions
It turns out a kind of cascade of spirals in which the main design elements are inscribed in rectangles with a golden ratio
A grid based on the golden ratio has a number of proportional relationships within it that are clearly proportional within a rectangle. At the bottom of this article, I have attached a PSD file that contains my example, you can try using it in your project to experiment with the golden ratio.
