02golden ratio

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Art

Golden Ratio

From the Middle Agesto modern times



Golden ratioThe golden ratio is a special number approximately equal to1.618. If you divide a line into two parts so that: the longer

part divided by the smaller part is also equal to the wholelength divided by the longer part, then you will have thegolden ratio. The golden section is also a term that describesa unique measurement phenomenon in nature wherein theoff-centered proportional finite value of about 5 to 8represents a measurement with infinite values.



Many artists, architects and mathematicians believed (andstill believe) this proportion is aesthetically pleasing.

Mathematicians have studied the golden ratio because ofits unique and interesting properties.



The Middle Ages art mainly consists of Romanesque and Gothic art.Romanesque art developed between about 1000 and 1300 inconjunction 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 becomethe 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, LateGothic art continued well into the 16th century, before being

subsumed into Renaissance art.



The Renaissance marks the period of European history atthe 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, mostlyin 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.



After this period the Golden Section was not more used inart until present times when painters and architects beganagain to project their works according to this proportion.



In Architecture



Notre Dame in Paris

The famous Cathedral of Paris has8 golden rectangles..



Thai Mahal in India

Golden Section was also used in Thai Mahal in India.



Le Corbusier

Le Corbusier explicitly used the golden ratioin his Modulor system for the scale ofarchitectural proportion.



The UN Building

In the United Nations building,the width of the buildingcompared with the height of

every ten floors is a Golden Ratio.



CN Tower in Toronto

The CN Tower in Toronto, thetallest tower and freestandingstructure in the world, containsthe golden ratio in its design. Theratio of observation deck at 342meters to the total height of553.33 is 0.618, the reciprocal ofPhi!



In painting



Piero della Francesca

It portrays Christ being baptisedby John, his head surmounted by

a dove representing the HolySpirit. Christ, John's hand, thebird and the bowl form an axis

which divides the painting in twosymmetrical parts. A second

division is created by the tree onthe left, which instead divides itaccording to the golden ratio.

Baptism of Christ



Sandro BotticelliThe Birth of the Venus

Botticelli (1445-1510) had to befascinated by the golden

proportion, since he used it forhis "Birth of Venus. " In fact ifyou measure the height of the

navel height overall, theirrelationship will be 0.618, as

well as between the distancebetween the neck of the femurand the knee and the length of

the entire leg or therelationship between the

elbow and the tip of the middlefinger and arm length.



LeonardoDa Vinci

He explored the human body involving in the ratiosof the lengths of various body parts. He called this

ratio the "divine proportion" and featured it inmany of his paintings and used this ratio very

impressive.



Leonardo Da Vinci explored the human body involving in theratios 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



Using the left side of the painting as a side, create a square on the left of thepainting 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 (.618 - theinverse 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 fromleft to right and from right to left. You should now have four lines drawn acrossthe painting. Notice that these lines intersect important parts of the painting,

such as the angel, the woman, etc. Coincidence? I think not!

The Annunciation



In The Last Supper golden rectangles can be seen. Heapplied golden section from the dimensions of the

table which Jesus sat, to the wall and window.

The Last Supper



The Last Supper



Measure the length and the widthof the painting itself. The ratio is,

of course, Golden. Draw a

rectangle around Mona's face(from the top of the forehead tothe base of the chin, and from leftcheek to right cheek) and notice

that this, too, is a Golden

rectangle.

Mona Lisa



At this time in Northern

Europe Albrecht Durer workedon similar problems. According

to one of his letters he met LucaPacioli in Italy.

Albrecht Durer developeddetailed theory about proportions of

the human body. Important placein his work was taken by

the hold golden ratio. He found thatthe growth of man is

divided of golden ratio fromwaist line.

Albrecht Durer



Georges SeuratBathers

The horizon falls exactly at the

golden section of the height ofthe painting. The trees andpeople are placed at golden

sections of smaller sections of the

painting.



Circus Sideshow (Parade de Cirque)

Seurat’s painting which is

following Circus Sideshow has alarge number of the golden

rectangle. This painting rely onthe principle of the golden ratio.The people who are on the leftside of the picture, above the

waist per unit (1.618), down 1 unit.



Edward Burne Jones

Golden Stairs

Golden sections appear in the stairsand the ring of the trumpet carried

by the fourth woman from thetop. The lengths of the gowns from

the sash below the breast to thebottom hem hits the phi point at

their knees. The width of the interiordoor at the back of the top of the

stairs is a golden section of the widthof the top of the opening of the

skylight.



Salvador Dali

In addition, the windows in the background are formed by a largedodecahedron. Dodecahedrons consist of 12 pentagons, which

exhibit phi relationships in their proportions.

The Sacrament of the Last Supper

Following Da Vinci'slead, Dali positionedthe table exactly atthe golden sectionof the height of his

painting. He

positioned the twodisciples at Christ'sside at the golden

sections of thewidth of the

composition.



Salvador DaliThe Sacrament of the Last Supper



Pierre Mondrian

Also the paintings of nineteenth-

century painter Pierre Mondrianare important.

He was the author of numerousabstract paintings, dominated

by the use of geometric shapes.In this context, is clearly visiblethe setting that Mondrian Artbased on the combination of the

whole painting squares andrectangles gold.



http://jwilson.coe.uga.edu

http://britton.disted.camosun.bc.ca

http://goldennumber.net

http://en.wikipedia.org

References

http://library.thinkquest.org/trio/TTQ05063/phibeauty4.htm

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