Wall Art & The Golden Ratio Working Together

The ancient Egyptians were the foremost to apply mathematics in artwork. It seems almost certain that they ascribed magical properties to the golden section, and utilized it in the creation of their huge pyramids. As the golden section is discovered in the design and beauty of nature, it can also be utilized to achieve appeal and balance in the design of wall art. This is only a tool though, and not a rule, for painting. Pythagoras, the Greek mathematician and philosopher, was particularly involved by the golden section, and proved that it was the origins for the proportions of the human figure. He showed that the human body is built with each section in a indisputable golden proportion to all the other constituent parts. Pythagoras' discoveries of the proportions of the human figure had a amazing effect on Greek wall art. Every part of their major buildings, down to the smallest detail of beautification, was built upon this proportion. The golden section was used commonly by Leonardo Da Vinci. Note how all the important dimensions of the room and the table in Da Vinci's "The Last Supper" were centred on the golden section, which was recognized in the Renaissance period as The Divine Proportion. A golden rectangle fits so perfectly around the central figure that it is often considered the artist intentionally painted the figure to conform to those proportions. Knowing Leonardo's attraction to mathematical patterns and the Fibonacci sequence, this is fairly likely. Salvador Dalí explicitly used the golden section in his work of art, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A enormous dodecahedron, with edges in golden ratio to one another, is balanced above and behind Jesus and dominates the painting. Michelangelo's David used the same hypothesis, denoting the naval as the arithmetical epicentre of the Golden Ratio.

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Mathematics - The Concept

Some of us may find mathematics difficult where others of us a passion. Mathematics can be found in our everyday lives and is a subject which we cannot avoid: in our purchases, in cooking ingredients, when making automobiles, the stock market - every time anything is given a value, measured or calculated. Its practical application is indisputable. So what is mathematics after all?
Mathematics is a science of numbers, equations, functions and graphs and its most important components are the individual, purely mathematical fields, such as arithmetic, algebra, mathematical analyses and geometry.
If we pose the question what at all mathematics is, we will certainly invoke a passionate discussion even among philosophers. As the Frenchman Jean-Baptist le Rond d¢ Alembert once said: "Mathematics is a type of game which helps us discover the secrets of nature but which keeps us in total darkness."
This explanation brings us to the very heart of the matter because mathematics is an artificial product; a tool created by man itself. It of itself is not able to pass any judgement concerning the world and one can spend many years solving numerous mathematical tasks while learning absolutely nothing of the world around them. Instead, one can find oneself "drowning in their own gravy" because the system of tools used in mathematics was invented by mankind itself. However, if we use mathematics to help us organise the world in a better way, it can serve as a great scientific tool. It can also help to shed light on the previously mentioned darkness of knowledge.
With the help of mathematics, researchers and scientists began to prove scientific knowledge around the 16th century. Today, every scientific assertion requires proof. "From the moment when mankind set out the task to prove the most simplest of assertions, it was shown that many of them were proven wrong," commented Bertrand Russel (1872-1970), a British philosopher and mathematician. This statement hit the hammer on the nail because many assertions which were considered as more than true have now been proved untenable.
Many earlier beliefs about the world relied on faith, speculation and dubitation. If Galieleo Galilei were not able to prove his beliefs about the solar system, then, next to the church's assertion that the sun revolves around the earth, his statement that in fact the earth revolves around the sun would be nothing more than heresy.
Bertrand Russel referred to mathematics as "the only science in which we never know what we are talking about and never know whether that which we assert is actually true." This is because that which is "true" can only relate to reality.
In practice and experience, mathematics becomes useful the moment when it is applied to reality. In the end, who would be interested in the fact that two times two equals four if someone were to propose that two times two tastes like oranges, which we would rather prefer. In this case, it would be nothing more than a game of numbers and use of free time.
                                   

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