EL NÚMERO ÁUREO Y
LA COLEGIATA DE SALAS
LA COLEGIATA DE SALAS
El número áureo y la colegiata de Salas from ProyectoComenius
-------------------------------------
LA
COLEGIATA SANTA Mª LA
MAYOR IN SALAS
-Piece created by
Pompeyo Leoni, a reinassance italian artist who worked for Philip II in El
Escorial and also sculpted the Mausoleum in Guadalajara between
1576 and 1582
LET’S GO TO LA
COLEGIATA !
OUR AIMS: to look
for and find the Golden Number in La
Colegiata in
Salas and collaborate in the Comenius Project.
JUSTIFICATION:
possible similarities in the architectural elements used in the
Gothic-Renaissance styles, Mannerism and Neoclassical style which predominated
sometime in the XVIII century in agreement with rationalist ideas and the
principles of reason.
LIMITATIONS: we have
only used tape-measures, pencils and calculators where we had an easy access,
always adapting ourselves to the curricular level of 1stESO.
WHAT WE DO: we want
to find the Golden Number en La
Colegiata , and so:
-we
select among the figures which contain rectangles, those which we think
are aesthetically more proportionate.
-we take
photographs of the elements we are going to study.
-we
number and identify the figures we have chosen.
-we start
to measure and take notes.
-we check the existence of the Golden Mean
CONCLUSIONS
-Our
investigation has not been very exhaustive but yet, representative.
-The
Golden number has mainly been observed in the main altarpiece and in some parts
of the Mausoleum.
-There
are many other parts which can be studied applying other principles like that
of similarity (Thales Theorem), Pythagoras Theorem …
-We can
also use other instruments of measure like the laser to obtain greater accuracy.
-The
students have become familiar with the Golden Number and have also become aware
of the artistic heritage of their village.
-but
there is still a lot of work to do …
And our
intention is to continue with the study of the Golden Number from both an
arithmetic and a geometric point of view, look for it in the buildings around
us (The Monastery in Cornellana, the Tower of the Castle, San Martin’s Church…)
and use it in our every day life, and it is for sure that we will improve a lot!!!
This
project has been carried out by the students of 1st ESO (2012 -2013) with the help of
their teachers of Mathematics and English (Enedina García and Carolina Suárez)
THE
GOLDEN RATIO IN LA
COLEGIATA IN SALAS
A presentation on a number which is as widely used as unknown.
WHAT IS THE GOLDEN NUMBER?
It is
an algebraic number
(since it is the solution to a polynomial equation) and also irrational (because it has got
infinite different decimal figures)
WHAT DOES IT MEAN GEOMETRICALLY?
Out of
this proportion we get the equation whose solution provides the Golden Ratio.
A LITTLE BIT OF MATHS HISTORY
The
Golden Ratio is nowadays represented with the Greek letter “PHI” to
acknowledge Phidias, a 5th
century B.C. sculptor , painter and architect of ancient Greece (490 - 430
B.C.) who used the Golden Ratio in his works.
The
association between this letter and the Golden Ratio did not take place until
the 20th century.
In
ancient Greece ,
it was already considered that that way of dividing a segment was logical and,
taking it into account, figures which provided proportion and beauty could be
created.
The first
person who formally studied the Golden Segment was Euclid (325 –
265 B.C.), a Greek mathematician often referred to as the “Father of Geometry”
Pythagoras (582 – 500 B.C.) and the Pythagorean School had
the star pentagon or pentagram as
its symbol, although it seems they did not know about the existence of the
Golden Ratio, at least in a conscious way, because they only worked with
fractions.
FIBONACCI
Leonardo of Pisa most commonly known as Fibonacci (1170 – 1250
A .D), spread the Hindu-Arabic numeral system in Europe .
In 1202,
he wrote the Liber Abaci.
The book advocated numeration with the digits 0 – 9, and showed the practical
importance of the new numeral system by applying it to commercial bookkeeping,
conversion of weights and measures, the calculation of interest, money-changing
and other applications.
THE ENLIGHTENMENT (end of XVII century – end of XVIII c. or beginning
of XIX c.)
Fibonacci’s
book was widely used in Europe during the Enlightenment and greatly
influenced on the European mathematical thinking since it was based on a
logical reasoning.
FIBONACCI’S SEQUENCE
Fibonacci
described his sequence 0, 1, 1, 2,
3, 5, 8, 13, 21, 34 …as the solution to an arithmetical problem on
the growth of rabbits:
“Suppose a
newborn pair of rabbits, one male and one female, is put in the wild. The
rabbits mate at the age of one month and at the end of its second month a
female can produce another pair of rabbits. Suppose that the rabbits never die
and that each female always produces one new pair, with one male and one
female, every month from the second month on. How many pairs will there
be in one year?”
ROBERT SIMPSON, SCOTTISH BOTANIST AND MATHEMATICIAN
In 1753,
he discovered that the ratios of successive numbers in the Fibonacci sequence,
when these tended to infinity, moved towards the Golden Number.
-check doing without the 1st
-1/1; 2/1; 3/2; 5/3; … 1,618033…
THE GOLDEN NUMBER - APPLICATIONS
-The Fibonacci sequence has many applications
in Computer Studies, Mathematics, The Game Theory, Biology …
-The Golden Ratio is found in multiple forms
of architecture, painting … and in objects that we very often use as we will
see below
THE GOLDEN NUMBER AND THE WORLD OF ARTS
The
proportions which follow the Golden Ratio are considered aesthetically pleasing.
Many
architects, painters, sculptors … since ancient times have created their works
basing them on the golden proportions.
THE PARTHENON in GREECE
THE VITRUVIAN MAN by LEONARDO DA VINCI
THE MONA LISA by LEONARDO DA VINCI
PYTHAGORIAN LEDA by DALI
THE PYRAMIDS in EGYPT
RUPESTRE DE MIRA IN ASIA (IV c. B.C.)
NOTRE DAME in PARIS AND THE GOLDEN RECTANGLES IN THE UNIVERSITY OF
SALAMANCA
THE FAMILY of CHARLES IV by GOYA
THE GOLDEN ROSE IN GERMANY
NATURE
Nature
hides the Golden Ratio in many of its forms: in sunflower
seeds, in galaxies and the nautilus shell, flowers and fruit.
In the case of human beings since we are a foetus. UNTIL we become a man
or a woman aesthetically “perfect”: distance between fingertips and shoulders
and elbows, length and width of the head, height and distance between our navel
and feet. Beauty standards remain …And even another Simpson (Homer in this
case), tries to follow these standards although we must make a special visual
effort.
The main
building belongs to the first part of the XVI century. The two chapels and the
bell tower were added afterwards.
-The main building is from the first half of the XVI century
-The altarpieces are from the XVII century
-The mausoleum is from the late XVI century
THE PROMOTERS
-The Valdés-Salas family as a funerary
monument
-D. Fernando Valdés-Salas, a politician and
religious man who promoted and left as his last will, the foundation of the University of Oviedo .
His name is observed in the name of our secondary school.
-The emblem of the University of Oviedo corresponds
to the coat of arms of the Valdés family
MAIN PARTS AND STYLES
-The main part: Gothic and Renaissance styles
-The two side chapels and the bell tower were
added afterwards
-The main altarpiece (beginning of the XVII
century) belongs to the Mannerism style
-The altarpiece in The Chapel of Malleza
(middle XVII century) was created by Luis Fdez de la
Vega
-The Mausoleum
THE MAUSOLEUM
-D. Fernando Valdés-Salas funerary monument
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