Transcript Golden Ratio - Мостове през Историята

Golden Ratio
Art
From the Middle Ages
to modern times
Golden ratio
The golden ratio is a special number approximately equal to
1.618. 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.
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.
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 mid12th 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.
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.
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.
In Architecture
Notre Dame in Paris
The famous Cathedral of Paris has
8 golden rectangles..
Thai Mahal in India
Golden Section was also used in Thai Mahal in India.
Le Corbusier
Le Corbusier explicitly used the golden ratio
in his Modulor system for the scale of
architectural proportion.
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.
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
553.33 is 0.618, the reciprocal of
Phi!
In painting
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.
Sandro Botticelli
The Birth of the Venus
Botticelli (1445-1510) 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.
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.
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
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 (.618 - 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!
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.
The Last Supper
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.
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.
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.
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.
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.
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.
Salvador Dali
The Sacrament of the Last Supper
Pierre Mondrian
Also the paintings of nineteenthcentury 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.
References
http://goldennumber.net
http://britton.disted.camosun.bc.ca
http://jwilson.coe.uga.edu
http://en.wikipedia.org
http://library.thinkquest.org/trio/TTQ05063/phibeauty4.htm
This presentation was made by:
Safa ADAKUL
Cansu YAVUZ
Marcelo RAMOS
Martın Hrıstov Ivan Ivanov
Laura Marolleau Carmen Machado