The desire to discover and reveal nature has led human beings to science, and the desire to change it towards the eye-pleasing shape and the beautiful has led to art. Science can be summarized as the explanation of the truths of the unknown, and art as the animation of the beautiful. Science represents truth and art represents ‘beautiful’. In science there are theories and proofs. In art, on the other hand, personal thoughts are more prominent and differ according to the person, time, society and schools.
We know that beauty, one of the dynamics of aesthetics, is related to harmony and this can be expressed with mathematical formulas. We can see with examples that the criterion of beauty in nature and in humans is expressed with mathematical concepts such as the golden ratio, symmetry and harmony.
The concept of beauty is related to an object. We describe a plant, living thing, person or work of art as beautiful. The formal qualities of the object are important in our definition of beauty. These formal attributes can be expressed with numbers. Buddha shows that beauty qualities are mathematical principles. These mathematical principles are concepts such as proportion, symmetry, order and harmony. Measures related to these concepts are formulated in various specialized fields of mathematics. Mathematics is an art characterized by order and inner harmony. By associating the mathematical order and beauty with the harmonious structure, we can bring together all kinds of art under a mathematical structure.
The idea of mathematical determination of beauty finds its first clear meaning, especially in the concept of proportion. Proportion means a pleasing interest between two sizes or parts of a whole. The idea of proportion has led artists and thinkers to seek a magical mathematical formula that will explain all the beauties in nature and art.
This search led the Italian mathematician Fibonacci, who lived between the years 1170-1250, to find the 1,1,2,3,5,8,13,21,34,… Fibonacci numbers named after him. The ratio of two consecutive numbers in the Fibonacci sequence gives approximately the value of Q=1.61804. This value is called the ‘Golden Ratio’. The golden ratio is a mathematical concept as it seems. But it is a classification of art and aesthetics as a criterion of harmony and beauty. The golden ratio is a biological fact that exists in nature without originating from human design, and humans have taken the golden ratio from nature in the field of visual creation.
Leonardo Fibonacci
Gustav Fechner (1876) captures this golden ratio with his experiments to determine the ‘threshold of aesthetics’. Obtains the result that rectangles with a ratio of sides close to the golden ratio look nicer. Such a rectangle is called a ‘golden rectangle’. Let’s draw a rectangle around the face of Leonardo Da Vinci’s famous painting Mona Lisa. It turns out that the result is a golden rectangle. Also, the painting itself is in the golden rectangle. The proportion of the horse is a symbol that fully fits the description of the picture.
Leonardo da Vinci’s portrait of the Mona Lisa was made according to the golden ratio.
We also see the golden ratio in architecture. The Parthenon temple in Greece is the most famous. The golden ratio was used in the design of Notre Dame Cathedral in Paris.
B.C. The golden ratio was used in the Sumerian tablets of the 3200s. The existence of the golden ratio emerges in the Egyptian Pyramids built by the ancient Egyptians. The pyramids are the first examples of the use of the golden ratio in architecture.
There are countless examples of the golden ratio in nature and living things. It can be found in pine cones, Echinacea purpura flowers, a tiger’s body, a fish, seashells, on plant stems, the placement of leaves, the arrangement of sunflower seeds, the spirals of galaxies, and even the features of rotating black holes.
Fibonacci sequence in sunflower
One piece of formal principle found in relation to proportion is symmetry. In symmetry, there is order between the parts of a whole. By symmetry, when viewed from a vertical axis, the whole is divided into two matching halves. Symmetrical layout is a spatial layout. Symmetry is based on grasping the two halves of a whole at the same time. Symmetry exists not only in art but also in nature. The bodies of living things are symmetrical, the leaves of trees and the wings of butterflies are symmetrical. Symmetry is one of the laws of nature. Symmetry, which is so effective in nature, is also effective in works of art in the same way and to the same extent. The pleasure of symmetry, the evaluation of symmetrical forms as beautiful is the reason why it is ingrained in the human brain.
The development of civilization in the future will be able to offer an environment open to creativity and innovation, where the relationship between aesthetics and mathematics will be used more intensively.
