The geometry in the Andalusian culture and its influence on the current styling

Transcription

1 The geometry in the Andalusian culture and its influence on the current styling

2 The geometry in the Andalusian culture and its influence on the current styling.

3 Index 1ºAims. 2ºStructure +Summary of the geometry s history. +2D and 3D. +Layout. +Decoration in the Arab monuments. +Influence on the current styling. +The use of psychology in choices. +Calculations. 3ºConclusions.

4 1ºAims: +Know the reasons why it s so common the use of geometric elements in art and architecture. +Study the different geometric elements. +Analyze the effects that columns make. +Identify different measures. +Visit some monuments. +Reproduce in 2D and 3D +Layout.

5 2ºStructure: +Summary of the geometry s history The beginning of the geometry dates back to Ancient Egypt, and it s the part of Maths which studies the space features. Astronomy and cartography were an useful source of resolution of geometric problems. +Geometry in the Middle Age: Maths discovered trigonometry and algebra which were related with astronomy and astrology. +Architecture: It s the art and the technique of showing and dessining buildings and spaces. Once, the architect was the boss of the building and architecture was the art of whom made the Project. It is based on: beauty, firmness and utility.

6 +Religious architecture: Christian: basilica and centralized floor. Muslim: the Mosque is the Islamic religious building The Mosque of Cordoba

7 +2D and 3D +Cordovan proportion: It has been used as the basis of the plastic composition of buildings throughout history, example is Rafael de la Hoz s proyects. In the pre-renaissance architecture was used the golden ratio.from the mathematical point of view, this ratio presents some calculations that follow a similar model of the golden ratio. This ratio is an irrational number: c = known as the Cordovan number. A good example of this is the Mosque of Cordoba.

8 +Islamic features: Fidelity to local tradition columns and Corinthian capitals. It also has the direct influences of religion: - Aniconism (rejection of images) - Abundance of large Mosques oriented to Mecca. +Different galleries: Inside the Mosque of Cordoba you can see, several galleries from the same point.

9 +Columns of the mosque. There are two types of columns with different measures. The measures of each column when we look at them from different perspectives make us not to have a real idea about them. +Layout. Aims: The ability to see every detail of the Mosque to scale. The study of Mosque with geometric shapes. Learn to appreciate different types of arches. Learn to appreciate The Mosque. + Decorations in Arab monuments. The Mosque of Cordoba is one of the greatest examples of Arabic art and culture, introduced into the Iberian Peninsula in 711; it was begun in 785. It consists of 8 buildings perpendicular to the qibla wall consisting of twelve sections

10 resting on 110 columns of different sources, supporting polychrome horseshoe arches and pillars.there are two types of arches: lower arches: horseshoe and the upper ones: semicircular. It consists of a minaret (tower), the Sahn (courtyard of the orange), the Haram (Prayer hall) and the main hall, where you can see the mihrab. The expansions let us analyze the evolution of the Cordovan art: -In 833, Abd al-rahman II tore down the wall of the qibla. -Abd al-rahman III expanded the courtyard and built the minaret. -In 961 Al-Hakam II added 12 sections, a mihrab and the octagonal dome arches. -Mansur, in 987, made an expansion to the east. The columns in the bottom allows great visibility.

11 In 1523, the Renaissance cathedral is constructed. The works took 234 years so the initial Gothic style was added Renaissance and Baroque. There is a great use of mosaics and friezes. Here are some examples of crystallographic: The plane The bow tie

12 Here we can see some examples of the elements that we could find in the Mosque: According to the Koran, Muslims could not represent humans or animals.

13 +Influence on the current styling. +Gate courtyards of Cordoba. The building of the Mudéjar house joins five different houses and galleries, corridors and stairways, with four courtyards and a tower. Until 1960 housed the headquarters of the Archaeological Museum and has recently been renovated to host the Arab House. The building released four courtyards, one of access or carriages, and two other main side, at different levels and forms homers. +Arches. An arc is the building block guideline curved or polygonal, saving the open space between two pillars or walls putting all the burden on the arch supports, by an oblique force called push. An arc consists of parts called segments, and curves can take various forms that work always in compression. This type of construction element is useful when you want to save space by relatively large pieces of gear compact.

14 Despite being a simple element, their performance was not scientifically understood until the first third of the nineteenth century. +Architecture. The Moorish architecture was a great contribution of the Arabs to the Iberian Peninsula. The architecture is understood by: Aesthetics Urbanism The construction technique The spacious homes and high ceilings are other characteristics of the Arab. The mud roof, the multiplicity of windows and doors and the existence of large homes with solar are a legacy of the Arab character. Regarding the planning, owed to the Arab urban provision of certain Arab towns in Spain, the existence of walled towns and fortresses, the latter intended for buildings of public administration very characteristic of cities in Andalusia.

15 Regarding the construction technique, the Arabs were also pioneers in how to build not only homes of mud was more practical, aesthetic and advanced but were also teachers in the war constructs as strong. Manifestations of architectural styles all go out to meet Walker at Segovia. A lesson in architectural history at every corner, emblematic examples of civil architecture (Roman aqueduct, Roman farmhouse, Renaissance palaces...), military (Alcázar, Wall), religious (Gothic Cathedral, Romanesque portico, convents and monasteries) dazzle in this city of Stone and Light. As early as the Iron Age, about 500 BC found traces of weapons and boars from the Celtiberian culture that Rome will end and present us his emblem, the Aqueduct: Built to supply water to the city.

16 In 410 starts the arrival of the barbarians to Spain. In 711 the Muslims invaded the Peninsula besieging the city and destroying several arches of the Aqueduct. +Moorish architecture in Spain. One thing that really surprised to visitors is that the Muslim has bequeathed. The great Mosque of Cordoba is one of the most admired monuments; the other is, of course, The Alhambra of Granada, a palace surprisingly well-preserved in its original state. When speaking of Moorish Spain, Arab, or Muslim, we talk about a feature of the history of European art that can be confusing. For a while Europe was still in the feudal era, after the fall of the Roman Empire, to evolve in their Visigothic and Romanesque and Gothic lines later, Spain enters this chapter of history with an African invasion from the south, reaches nearly all the Peninsula. On the other hand, when the Arabs arrived in the Iberian Peninsula, his style was

17 distinctly African but, after 800 years it settled logically hispanicizing, were progressively away from African trends that centuries ago had brought with them. Then created a sui generis style. This unique style reaches its climax in the Caliphate style, rendered in Córdoba, and which had the greatest exponent of the Mosque. These 800 years of history would be characterized by a very mixed Spain, which would co-exist in peace three populations with different religions, Jewish, Muslims and Christians. As in Muslim territory freedom of religion for Jews and Christians could continue living in peace and according to their customs, in the reconquered territories, until the time of the Catholic Monarchs respected, Muslims and Jews also allow continue to live according to their traditions in reconquered territory. It is precisely this feature that creates this unique fusion of styles so characteristically Hispanic, where

18 we see monuments of Moorish, Mudejar, and all possible combinations (Gothic- Mudejar). The word comes from the Arabic mustab Mozarabic 'rab meaning that wants to look Arab, so Christians who remained in conquered territory was called staying true to their religion. On the other hand the word comes from the Moorish mudeyyen Arabic, which means that you are allowed to remain. It was Muslims living in Spanish-Christian territory. Again its architectural style is called the same way, and can be defined as that between the s. XI to XV, in which Christian elements (Romanesque and Gothic) structures, materials and decorative elements are mixed with Muslim. +Psychology behind the decoration. +Why do we like proportions? The answer is in our brain, in our natural beginnings.

19 Evolution has made the natural geometric elements become "normal" to us. This is common to all animals on Earth. In the case of humans, we have advanced on evolution so we don t see the "odd shapes" as dangerous. We have become accustomed to these shapes imitating the nature, all that is out of the ordinary is rejected. +Calculations. This chapter aims to support all mathematical calculations with all the observed. Let s start with the columns, which have frustum cone. Its aim is giving the structure more stability because the generatrix is inclined inwardly and the center of gravity is below the half of the half of the column, so it is much firmer, and also it makes them look higher.

20 X and Y are almost equal,3 meters y The first hypothesis was that the false parallelism of the generating tricks the human eye. x So being the generators of the column congruent in reality, the brain understands that the solid figure is higher than it appears. To prove it we took the measures of the contours of the columns at different heights. We got this:

21 Height Contour Diameter Radio 15 cm cm cm cm 133 cm cm cm 130 cm cm To be sure that it is a frustum cone we check it and we can see that the equality is not exactly fulfilled. So we can think that the contour loss is proportional to the gain of height, therefore we are talking about a frustum cone. Now, we re going to study the optical effect of this hypothesis: -Let's assume we are located two meters from the column and the observer is located one meter above the ground. The perception of the width is determined by the angle between the tangent from the observer to the column. -The distance from the observer to the center of the upper circle comes out of a right triangle:

22 x 300cm 200cm = cm. -The distance from the observer to the point where the tangent touches the upper circumference of the column is: x 300cm cm cm

23 -To know the height of the column, we use the same right triangle as before. -The distance from the observer to the center of the column also depends on the height. Due to the loss of contour of the columns as the height increases, our eyes detect the loss of width like a cylindrical column of almost 4 meters high, and not a truncated cone of 3 meters. 3º Conclusions. Our proyect tries to approach a mathematical view of art, architecture and decoration present in three Arab monuments which have been witnesses of Al Andalus in our land: the Mosque of Cordoba, the Alhambra in Granada and Arab Baths in Jaen. We first made a visit to the Mosque of Cordoba in which we tried to find these geometric elements that allow us to deep in the importance they had to Maths for

24 Arabs to make these buildings, and the intention they had with their use. Then we tried to reproduce the geometric patterns we detected in these buildings and see how his influence has spread so that it has permeated modern decorative styles.