Why golden ratio is important

Adding a square equal to the length of the longest side of the rectangle gets you increasingly closer to a Golden Rectangle and the Golden Ratio.

In the Fibonacci Sequence 0, 1, 1, 2, 3, 5, 8, 13, Plotting the relationships in scale provides us with a spiral that can be seen in nature all around us. Golden Ratio in use. It's believed that the Golden Ratio has been in use for at least 4, years in human art and design, but it may be even longer than that — some people argue that the Ancient Egyptians used the principle to build the pyramids.

In more contemporary times, the Golden Ratio can be observed in music, art, and design all around you. By applying a similar working methodology you can bring the same design sensibilities to your own work. Here are just a couple of examples to inspire you:. Greek architecture. Ancient Greek architecture used the Golden Ratio to determine pleasing dimensional relationships between the width of a building and its height, the size of the portico and even the position of the columns supporting the structure.

The final result is a building that feels entirely in proportion. The neo-classical architecure movement reused these principles too. Ancient Greek architecture used the Golden Ratio to determine pleasing dimensions in buildings. The evidence for the golden rectangle being especially pleasing is pretty thin. Psychological studies showing different rectangles to groups of people seem to indicate that there was a wide range of preferences, with the ratio of the square root of two to one often being preferred over others.

Test yourself on the rectangles below to see which you prefer. According to Keith Devlin's book Devlin's angle: The myth that won't go away , the idea that the golden ratio has any relationship to aesthetics at all comes primarily from two people, of which one was misquoted, and the other resorted to invention.

The book was named after the golden ratio, but didn't argue for a theory of aesthetics based on the golden ratio, or that it should be applied to art and architecture. Such a view was misattributed to Pacioli in Pacioli was close friends with Leonardo da Vinci and it is often claimed that Leonardo himself used the golden ratio in his paintings.

There is no direct evidence of this. Perhaps the most famous of these examples is the Vitruvian Man. However the proportions in this painting do not match the golden ratio. Indeed Leonardo only mentioned whole number ratios in his works. Supposed examples of the golden ratio appearing in his pictures are in the same class as those finding the ratio in nature. Devlin attributes the "popularisation" of the golden ratio to Adolf Zeising , a 19th century German psychologist who argued that the golden ratio was a universal law that described "beauty and completeness in the realms of both nature and art [ However, Zeising's work went on to influence many others, and laid the foundations for much of the modern myth.

The so-called golden spiral superimposed on the Parthenon. There is no evidence that the golden ratio played a role in the design of this building. Another example of this myth is the claim that the golden ratio appears in the proportions of the Parthenon, part of the Acropolis in Athens.

There is no evidence of this in Greek scholarship, and the idea that the Parthenon has proportions given by the golden ratio only dates back to the s. Furthermore, the actual measurements of the Parthenon do not give proportions especially close to the golden ratio, unless you are careful with your choice of rectangles.

In fact, the Parthenon takes its harmonious appearance from the clever deployment of lines that look parallel but in fact converge or curve, so it's virtually impossible to take measurements precise enough to give exact ratios.

As the proportions of the Parthenon vary with its height it is simply not possible to find an overall proportion that agrees with the golden ratio.

The same applies to the rest of Greek architecture: there is no evidence whatsoever that the Greeks considered the golden ratio aesthetically pleasing, or used it in their art and architecture at all. It also applies to music. It is claimed that the golden ratio is important in musical composition. There is little evidence of this. However what is important in composition is the scale, and the scale is very closely linked to the twelfth root of 2.

There is very real danger in these persistent myths about the golden ratio. School children and many others are being duped into a false reality about the way that maths works. Sooner or later they will find that this reality is untrue, and will lose faith in the very real ability of maths to explain the world. Having been rather dismissive about the golden ratio I would like to conclude this section by stressing just how amazing a number the golden ratio really is - it really doesn't need all those spurious claims to make it special.

First, let's turn to natural phenomena that really are related to the golden ratio. The golden ratio is intimately related to the famous Fibonacci sequence. You can find out more about this link here.

The Fibonacci sequence certainly does appear in nature as it is both linked to the way that populations grow, and also to the way that shapes can be fitted together. For example, the sequence can be seen in the spirals on sun flowers which have to fit together in an ordered fashion, and in the leaves on some plants that need to be arranged to capture the most sunlight.

As a result it is possible to observe ratios close to the golden ratio arising in certain natural phenomena find out more here. These phenomena include the distribution of drones to female bees in a bee-hive, which is linked to the way that bees reproduce over many generations find out more here.

So it is indeed possible to see the golden ratio in the garden, and there are very good mathematical reasons for this. Fibonacci thought of his sequence when considering the population growth of idealised rabbits.

See this article to find out more. But perhaps even more interesting are the many fascinating mathematical properties of the golden ratio. These are explored in various Plus articles , but I would like to point out one that is particularly fascinating and which really sets the golden ratio apart from other numbers: its extreme irrationality.

Irrational numbers are numbers that can't be represented by fractions and that have an infinite decimal expansion that doesn't end in a repeating block. This very fact means that it is hard to observe irrational numbers in nature. The golden ratio has the amazing property of being the most irrational number of them all. This means that not only is it not possible to represent it exactly as a fraction, it isn't even possible to approximate it easily by a fraction. See this article for the mathematical details.

The difficulty of approximating the golden ratio by a fraction makes it a very useful number to mathematicians and scientists studying the process of synchronisation. This occurs when a system with a natural frequency is forced by one of a different frequency, and adopts the forcing frequency.

One example is the synchronisation of the human body to the daily frequency of sunlight. A second example is the Earth's climate which synchronises to the natural cycles of the orbit around the Sun. However, synchronisation can itself be a problem, leading to unwanted resonances in a system such as a suspension bridge vibrating severely if a marching band walks over it.

By choosing two frequencies in the ratio of we can avoid synchronisation due to the extreme irrationality of the golden ratio. This very useful property appears to be exploited by the brain and insect species as well as climate scientists and even people who manufacture aircraft. So the golden ratio does have a starring role, but not one that you often read about in the mythology associated with it.

This is a great pity! It is a lovely paradox that the most interesting thing about the golden ratio is that it isn't a ratio. This article is based on a talk in Budd's ongoing Gresham College lecture series see video above. You can see other articles based on the talk here. He is particularly interested in applying mathematics to the real world and promoting the public understanding of mathematics.

He has co-written the popular mathematics book Mathematics Galore! Sangwin, and features in the book 50 Visions of Mathematics ed. Sam Parc. The claim about the golden ratio in music actually refers to form, not to frequency though that doesn't stop people from making music with tunings related to the golden ratio, but anyway. The claim is that if you have some work with an AB form, the A and B sections will ideally have durations in the golden ratio, etc.

I think it's claimed that this proportion can be specifically found in the music of Mozart. Golden Ratio is widely practised in the variois drum beats in Carnatic music. They follow rule called 'Hemachandra series - about byears prior to Fibonacci himself'. Also see Melakarta rules structure in Carnatic music.

Would love to having a discussion on it. The smaller part goes into the larger as the larger goes into the whole. So the small portion is a ratio of the larger Portion in the same ratio that the larger portion goes into a whole. Great article that exposes the whole "golden ratio" baloney! One comment, though: you cannot say "degrees are measured in radians", as in the next-to-last paragraph of the section titled "Spirals, Golden and Otherwise"; it is like saying "meters are measured in feet".

Note that in Lego bricks the golden ratio is to be found in several aspects, including the relationship of the studs and tubes. It has been claimed as a significant contributor to their commercial success, although it may be that the system was in part inspired by Le Corbusier architectural designs. Can't we use 2 consecutive Fibonacci numbers in the higher range to approximate the golden ratio? Even your fingers follow the Golden Ratio.

The human eye is used to seeing this magical number and we subconsciously react positively to it. As designers, we can use this number to our advantage. Even small tweaks to the way you crop an image or develop a layout can dramatically improve how your users interact with your design.

Watch it now. Emily has written for some of the top tech companies, covering everything from creative copywriting to UX design. When she's not writing, she's traveling the world next stop: Japan! Design A guide to the Golden Ratio for designers 4 min read. Link copied to clipboard. Top Stories. Photo credit: Mostafa Amin and Brandology Studio.

Photo credit: Kazi Mohammed Erfan. Get awesome design content in your inbox each week Give it a try—it only takes a click to unsubscribe. Thanks for signing up! Get Started Designing Better.