The Mathematics of ArtThe Mathematics of Art "Music is a hidden mathematical problem of the soul, - Leibniz “Art without math would not” – Luca Pacioli
The Mathematics of ArtThe Mathematics of Art For many people, mathematics is a course consisting only of symbols and rules where educational experiences are challenged together. Certainly rules and symbols are part of mathematics but they are never all. Math which we encounter in many fields of our lives such as art, music, architecture, basic sciences, is in a successive harmony even if we do not realize it and the real fun part of mathematics starts here.
The Mathematics of ArtThe Mathematics of Art There is an artistic value aesthetics and beauty in the internal discipline and harmony of mathematics. It is intertwined with art with its applications in art branches such as architecture, music, and painting. Just as there is a harmony of color in painting, a pattern between words in poetry, a uniformity of meaning in mathematics, there is an order between operations, beauty, and harmony in thinking in solving the problem and theorem.
The Mathematics of ArtThe Mathematics of Art In the 1950s a group of researchers in Turkey Hagia Sophia, Sultanahmet and Süleymaniye mosques are viewed as architectural masterpieces. When they see that the structures of these structures are loose during the study they are surprised how these structures have survived against earthquakes for centuries. Then they go to study the Selimiye Mosque in Edirne. A Japanese scientist looks at the dome and says that it is against the rules of mathematics and physics to see the dome standing there and that like buildings in Istanbul the ground is loose. They concerned about the demolition of the minarets of the mosque and they considered fixing the foundation of the minarets with the latest technology metal clamps. When they open the foundation of the minarets they come across similar cuffs they intend to put. It is said that the architect Sinan Selimiye solved an equation with 13 unknowns to place the dome of that mosque at that width. Thus it is seen that mathematics lies based on the dome and minarets.
Golden RatioGolden Ratio One of the situations in which mathematics and art are most related is the "golden ratio". Golden ratio; The gold is a constant number also known as the average the golden portion and the perfect proportion and its value is 1,61803…. In ancient times painters and sculptors pondered how ideal human-size should be and defined ideal human size. ``The ratio of the length to the length from the navel to the foot is equal to the ratio of the length from the navel to the foot to the length from the navel to the bedside.´´
Golden RatioGolden Ratio The golden ratio is an important number in biology, mathematics and art history. Leonardo da Vinci and Corbusier took measurements of the human body determined according to the golden ratio. Neufert which is one of the most important reference books of today's architects is based on the human body determined according to the golden ratio.
Mathematics and MusicMathematics and Music •In ancient Greece, music was accepted as one of the four main branches of mathematics. According to the program of Pythagoras (586 BC) (Quadrivium) Music; Arithmetic, Geometry and Astronomy are accepted at the same level. Pyhagoras (6th century BC) revealed that different sounds of different lengths of a wire were obtained. It is the basis of the musical series used today. Pythagoras divided a 12- unit wire into two and obtained an octave. The resulting 6-unit length (1/2 of the wire) is an octave treble of the 12-unit length. Pythagoras found a range of 5 units with a length of 8 units (2/3 of the wire) and a range of 4 units with a length of 9 units (3/4 of the wire). • According to Pythagoras ratios, the difference between 5 and 4 gives the full tone. 2/3:3/4=8/9 (5T- 4T=2M ) the multiplication of the full voice by 8/9 gives us a tone treble of that voice. •Let our main voice be “do”. •1/2 of the east gives us an octave treble of the east, 2/3 of the sound of “left, 3/4 of the sound“, 8/9 of the sound of “re,, 64/81 of the sound of” mi ”.
Mathematics and MusicMathematics and Music •When you go this way; Do, re, mi, fa, sol, la, si, do sounds respectively; 1, 8/9, 64/81, 3/4, 2/3, 16/27, 128/243 and 1/2. •Pythagoras obtained 8 full tones with 1 of 8/9 of the string, but when adding 6 full tones to a note, almost the octave of that note was obtained, which is called the “Pythagoras coma. 
Mathematics and MusicMathematics and Music •Another important figure in music is the mathematician Fibonacci. Rabbit farm problem:1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987… the sum of the last two numbers gives us the next number. Note that the ratio of two consecutive numbers (the ratio of the smaller number to the larger number) converges to the same number. 0, 61803398… (golden ratio) •Pythagoras ranges also follow the golden ratio rule. •Bella Bartok is a composer who uses the golden ratio. •There are various opinions about whether Mozart uses gold. •19th century. J. Fourier examined the nature of the musical series. “Fourier proved that all musical sounds from musical instruments and human beings can be defined by mathematical expressions, and that this can be done by periodic sine functions.