1. Golden Ratio
Art
From the Middle Ages to modern times

2. Golden ratio
The golden ratio is a special number approximately equal to If you divide a line into two parts so that: the longer part divided by the smaller part is also equal to the whole length divided by the longer part then you will have the golden ratio. The golden section is also a term that describes a unique measurement phenomenon in nature wherein the off-centered proportional finite value of about 5 to 8 represents a measurement with infinite values.

3. Many artists, architects and mathematicians believed (and still believing) this proportion is aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.

4. The Middle Ages art mainly consists of Romanesque and Gothic art.
Romanesque art developed between about 1000 and 1300 in conjunction with the rise of monasticism in Western Europe.
The style developed initially in France, but spread to Christian Spain, England, Flanders, Germany, Italy, and elsewhere to become the first medieval style found all over Europe.
Gothic art was a Gothic art developed in France out of in the mid-12th century and spread to all of Western Europe, but took over art more completely north of the Alps, never quite effacing more classical styles in Italy. In many areas, especially Germany, Late Gothic art continued well into the 16th century, before being subsumed into Renaissance art.

5. The Renaissance marks the period of European history at the close of the Middle Ages and the rise of the Modern world. It represents a cultural rebirth from the 14th through the middle of the 17th centuries. Early Renaissance, mostly in Italy, bridges the art period during the fifteenth century, between the Middle Ages and the High Renaissance in Italy. It is generally known that Renaissance matured in Northern Europe later, in 16th century.

6. After this period Golden Section was not more used in art until present times when painters and architects began again to project their works according to this proportion.

7. In Architecture

8. Notre Dame in Paris
The famous Cathedral of Paris has 8 golden rectangles..

9. Thai Mahal in India
Golden Section was also used in Thai Mahal in India.

10. Le Corbusier
Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion.

11. The UN Building
In the United Nations building, the width of the building compared with the height of every ten floors is a Golden Ratio.

12. CN Tower in Toronto
The CN Tower in Toronto, the tallest tower and freestanding structure in the world, contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of is 0.618, the reciprocal of Phi!

13. In painting

14. Piero della Francesca Baptism of Christ
It portrays Christ being baptised by John, his head surmounted by a dove representing the Holy Spirit. Christ, John's hand, the bird and the bowl form an axis which divides the painting in two symmetrical parts. A second division is created by the tree on the left, which instead divides it according to the golden ratio.

15. Sandro Botticelli The Birth of the Venus
Botticelli ( ) had to be fascinated by the golden proportion, since used it for his "Birth of Venus. " In fact if you measure the height of the navel height overall, their relationship will be 0.618, as well as between the distance between the neck of the femur and the knee and the length of the entire leg or the relationship between the elbow and the tip of the middle finger and arm length.

16. Leonardo
Da Vinci
He explored the human body involving in the ratios of the lengths of various body parts. He called this ratio the "divine proportion" and featured it in many of his paintings and used this ratio very impressive.

17. Leonardo Da Vinci explored the human body involving in the ratios of the lengths of various body parts. He called this ratio the "divine proportion" and featured it in many of his paintings.
Old Man
Vitruvian Man
Mona Lisa

18. The Annunciation
Using the left side of the painting as a side, create a square on the left of the painting by inserting a vertical line. Notice that you have created a square and a rectangle. The rectangle turns out to be a Golden Rectangle, of course. Also, draw in a horizontal line that is 61.8% of the way down the painting ( the inverse of the Golden Ratio). Draw another line that is 61.8% of the way up the painting. Try again with vertical lines that are 61.8% of the way across both from left to right and from right to left. You should now have four lines drawn across the painting. Notice that these lines intersect important parts of the painting, such as the angel, the woman, etc. Coincidence? I think not!

19. The Last Supper
 In The Last Supper golden rectangles can be seen. He applied golden section from the dimensions of the table which Jesus sat, to the wall and window.

20. The Last Supper

21. Mona Lisa
Measure the length and the width of the painting itself. The ratio is, of course, Golden. Draw a rectangle around Mona's face (from the top of the forehead to the base of the chin, and from left cheek to right cheek) and notice that this, too, is a Golden rectangle.

22. Albrecht Durer
At this time in Northern Europe Albrecht Durer worked on similar problems. According to one of his letters he met Luca Pacioli in Italy. Albrecht Durer  developed detailed theory about proportions of the human body. Important place in his work was taken by the hold golden ratio. He found that the growth of man is divided of golden ratio from waist line.

23. Georges Seurat Bathers
The horizon falls exactly at the golden section of the height of the painting.  The trees and people are placed at golden sections of smaller sections of the painting.

24. Circus Sideshow (Parade de Cirque)
Seurat’s painting which is following Circus Sideshow has a large number of the golden rectangle. This painting rely on the principle of the golden ratio. The people’s who are on the left side of the picture, above the waist per unit (1.618), down 1 unit.

25. Edward Burne Jones Golden Stairs
Golden sections appear in the stairs and the ring of the trumpet carried by the fourth woman from the top.  The lengths of the gowns from the sash below the breast to the bottom hem hits the phi point at their knees.  The width of the interior door at the back of the top of the stairs is a golden section of the width of the top of the opening of the skylight. 

26. The Sacrament of the Last Supper
Salvador Dali
The Sacrament of the Last Supper
Following Da Vinci's lead, Dali positioned the table exactly at the golden section of the height of his painting.  He positioned the two disciples at Christ's side at the golden sections of the width of the composition.
In addition, the windows in the background are formed by a large dodecahedron.  Dodecahedrons consist of 12 pentagons, which exhibit phi relationships in their proportions.

27. The Sacrament of the Last Supper
Salvador Dali
The Sacrament of the Last Supper

28. Pierre Mondrian
Also the paintings of nineteenth- century painter Pierre Mondrian are important. He was the author of numerous abstract paintings, dominated by the use of geometric shapes. In this context, is clearly visible the setting that Mondrian Art based on the combination of the whole painting squares and rectangles gold.

29. References http://goldennumber.net http://britton.disted.camosun.bc.ca

30. Martın Hrıstov Ivan Ivanov Laura Marolleau Carmen Machado
This presentation was made by:
Safa ADAKUL
Cansu YAVUZ
Marcelo RAMOS
Martın Hrıstov Ivan Ivanov
Laura Marolleau Carmen Machado