Transcript Golden Ratio - Мостове през Историята

Golden Ratio
Art
Renaissance
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.
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.
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.
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.
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.
References
http://goldennumber.net
http://britton.disted.camosun.bc.ca
http://jwilson.coe.uga.edu
http://en.wikipedia.org
Safa ADAKUL
Cansu YAVUZ
Marcelo RAMOS