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This project has been funded with support from the European Commission. This web site reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Geographical Areas

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Douro International Natural Park
Miranda do Douro
Geography, Math, Chemistry, Biology, Physics, Geology
The Douro International Natural Park (PNDI) is located in both regions of Trás-os-Montes and Beira (NE Portugal) and occupies an area of 85,150 ha, encompassing the municipalities of Miranda do Douro, Mogadouro, Freixo to Freixo de Espada à Cinta and Figueira Castelo Rodrigo. The Douro River, formerly of violent waters, was transformed into a succession of lentic reservoirs of dams. The Park covers the border stretch of the Douro river, including its valley and adjacent plateau surfaces, and extends south through the valley of its tributary, the river Agueda. This granitic area, where the valley already resembles the "Douro wine region", is characterized by its microclimate, with low rainfall and mild winter temperatures, and called Terra Quente Transmontana (hot land). The major natural values of the region include native vegetation cover of different oak species: Quercus pyrenaica and Quercus faginea in areas of higher altitude and Quercus rotundifolia and Quercus suberin the drier land. There are also Juniperus oxicedrus and Celtisa ustralis in tight valleys and rocky spurs of the Douro and, near the tributaries, alder (Alnus glutinosa), willow (Salix spp.) and ash trees (Fraxinus angustifolia). The most common shrubs are Cytisus striatus and Cistus ladanifer. The fauna in the PNDI is distinguished by its number of species and their conservation status (i.e. critically endangered, endangered and vulnerable). In terms of birds, several species like Milvus milvus, Oenanthe leucura, Neophron percnopterus (symbol of the PNDI, the Egyptian Vulture), Circus pygargus, Aquila chrysaetos, Hieraaetus fasciatus, Pyrrhocorax pyrrhocorax, Ciconia nigra and Falco peregrinus are threatened. The majority of these birds have their preferred habitat on cliffs. As far as mammals are concerned, the bats (Rhinolophus euryale, Myothis blythii), the wolf Canis lupus), the wildcat (Felis silvestris), among others, are vulnerable. In the group of reptiles, Emys orbicularis and Vipera latastei can also be cited.


Deciduous vegetation In this region summer is hot and winter is harsh, so it is common to find deciduous vegetation coating either walls or patios of buildings which creates effects of luminosity and darkness that brings consequences in the temperature balance. In the summer, the leaves of deciduous plants provide shadow and absorb the solar radiation as a result these places become fresher. In the winter, the lack of the leaves let the houses or patios get solar radiation which leads to a higher temperature.
Uncoated Stone House In this area, both shale and granite used to be the most popular materials concerning traditional buildings in the past. The regular pattern of weather conditions of this particular region presents thermal high temperatures which may occur either during the year or during the day. Therefore, the construction in uncoated stone is advantageous due to the thickness of the walls that not only provides a large heat storage capacity but it also causes a delay in its transmission, known as thermal inertia. These materials, shale and granite, play an important role in the housing thermal comfort.
A Gabled house In this picture we can see a Miranda do Douro typical gabled house, whose roof only has two gables. This house is exposed to North/South direction. The larger area is facing South, so that it can take advantage from solar energy. By maximizing solar gains, it becomes a major contributor to the building heating. On the other hand, the smaller area towards North, much more darkening, enables the decreasing of thermal loss in the building.
Balconies towards South The solar orientation of the balconies and their depth provide an efficient use of solar radiation. The balconies are mostly towards South in order to get a longer exposure to the sun. The sun blinds in the eaves are used to protect the entrance of the building from the solar radiation, in the summer, by darkening the balcony and keeping it fresher. In winter, as the sun is lower in the horizon, the walls and the windows are exposed to the solar radiation which makes it possible to take advantage of that solar radiation. Consequently, there is a rise of the temperature inside the house.
Dovecots The traditional dovecots are constructions that belong to the typical northeast countryside landscape in Trás-os-Montes, Portugal. They are also a good example of the Bioclimatic architecture. Portuguese Dovecots have a roof of a single plane which allows the capture of thermal energy. One may call your attention to the fact that these constructions are placed towards southeast so that they can capture the morning sunlight which empowers both the health and the fitness of the doves. To the north where the coldest and windy area is located, the front end of the dovecot is curve since this kind of shape reduces the surface that is exposed to the cold and wind. On the top of the dovecots you can find either quartz white stones or pinnacles in granite or shale that protect the doves from the wind and call their attention, as well.
Tessellations I Inaugurated in November 1960, the dam of Miranda do Douro is located in the international stretch of the River Douro. The use of hydroelectric power is composed of the dam, which includes a flood spillway in its central part, the underground station, control buildings also for discharge and substation, located on the right bank. In our visit to the substation building, we found a white and green pavement, consisting of quadrilaterals, example of a frieze. The friezes are characterised by the repetition of a motif along a direction. In a frieze, bearing in mind that it is extended indefinitely in both directions, the infinite repetition of the motif is expressed by the existence of translational symmetries that makes the frieze globally invariant. In addition to the (geometry) translation, there are still other types of symmetry: reflection and glide reflection.
Pavements II In the area surrounding the dam of Miranda do Douro, near the substation building, we found some examples of flat surface tessellations. The tessellation of a flat surface is a set of polygons that cover the surface without glitches or overlays. The tessellations obtained from the repetition of a single polygon are pure or monotone. If the paving is made up of congruent regular polygons, this means that it has the same size and shape. The following images illustrate two examples of pure and regular tessellations: the first image is an example of one made up of equilateral triangles, while the second represents a path made by slabs with the shape of regular hexagons. Note that you can only pave the surface when using equilateral triangles, squares or hexagons.
Rotations The Control Building for the hydroelectric plant of Miranda do Dourois located on the right bank of the Douro River, in which all the maneuvers of the electro- and hydromechanic equipment are concentrated. In the control room, we found these clocks that are part of a broad set of instruments that allow the operation and control of the dam. The hour hand and the minute hand of the clocks describe a rotation movement around a fixed point (rotation center). Each minute corresponds to an amplitude of six degrees, clockwise (negative), i.e. when one hour goes by, the minute hand makesa 360° rotation.
Traditional costumes of the Lands of Miranda During the visit to the artisan/craftsmanAureliano Ribeiro, in the village of Constantim, we collected images of traditional costumes from the region of Miranda, made of woven wool (or “burel”, i.e. coarse woollen cloth) and richly embellished by geometric motifs. We can recognize several isometries in the embroideries that decorate the pieces. An isometry is a geometric transformation that preserves the distance between points and the amplitude of the angles. (Geometric) translations, rotations and reflections are examples of isometries used in the creation of these true works of art, traditionally used on feast days or by folklore groups.
Mirandese Honor Cloak The Mirandese Honor Cloak is a piece of great ethnographic value, used once by ox herders to protect themselves from rain and cold. Made of woven wool, today it is used in official ceremonies and has a prominent place in the social, cultural and political life of Mirandese people, given its peculiarity and the fact of being unique in this ethnographic landscape. The cloak consists of two parts – the cloak itself and the hood. This is made up of the peak, the edges of the brims and the opening??, which are adorned, on their back part, with finely cut woven wool, sewn by hand on the background using black wool fabrics. Based on the proportionality between its parts, the ornaments are based on geometric figures arranged in parallel lines, where the symmetries extend through the front part of the piece.
Oxcart wheel In a predominantly rural region as Miranda do Douro, the use of instruments and vehicles linked to agriculture and livestock were common in the everyday life of the population. From the Neolithic period to the end of the 20th century, oxcarts were used as a means of transport for heavy loads. Hay, potatoes, bread and all the crops came to the villages along with the distinctive sound of the \"song\" of the wheels. Built with the wood of the common ash or of elms and iron, the wheels of the oxcart are a good example of rotational symmetry. Divided into nine circular sectors, each with 40º of amplitude, it is possible to rotate the object around its center, leaving it unchanged (the transformed figure corresponds to the initial figure), through several rotations.
Instruments - Drum and Cash The drum and the box observed in the village of Constantim belong to the membranophone family and, along with bagpipes, serve to make the circle danses or play together with the Pauliteiros (groups of men who dance at the sound of traditional music using sticks) in their traditional Mirandese dances. The body of the drum and of the box has a cylindrical shape and itis also the part that makes the sound produced by the drumsticksresonate. The laws of proportionality are present in the construction of drums and boxes, so as to produce particular musical notes, since most produce sounds without a specific height. The ropes that help tune the instruments are disposed according to geometric transformations, such as translation and reflection.
Miranda do Douro Cathedral Situated in the middle of the town of Miranda do Douro, Miranda\'s Cathedral is a Renaissance monument built in the 16th century (1552). Inside you can admire the high altar, a fabulous Renaissance altar piece composed of 56 biblical images and the image of the Jesus Child of the top hat. Classified as a national monument, it has monumental Mannerist and Baroque wood carvings. The main facade is symmetrical and regular and flanked by two grand rectangular towers which are topped by a balustrade where a Baroque wrought-iron cross stands. In this cross, we can identify different isometries: translation, reflection, glide reflection and rotation (tower clocks).
Stained Glass of the Cathedral of Miranda do Douro The multiple rectilinear windows present in the Cathedral of Miranda do Douro are the lighting system inside the temple. In one of them, we can observe this stained-glass window in different shades of green. Stained-glass is a type of panel composed of pieces of colored glass or paintings on glass which generally represent scenes or characters. In this case, it consists of pieces of colored glass and it is possible to observe two polygons paving the surface (Archimedean or semi-regular tessellation): squares and hexagons. We have, therefore, several isometries: translation, rotation, and reflection (vertical axis and horizontal axis).
Ruins of the Bishop\'s Palace In front of the Cathedral lies a garden, where the remains of the monumental 16th century granite cloister are found, badly damaged by a fire in the early 18th century. The Bishops’Palace and the Seminar were built in 1601 andtheiropulence was not inferiortothat of the“Sé” (main cathedral), whose Renaissance styleit tried to imitate. The Palace was disposedaround a central courtyard, surroundedby a cloister in recessed arches, on monolithic columns. The galleries on the ground floor are still visible, with its segmental arches supported by rectangular pillars. Only the ground floor and a large arcade remain of the cloister. In this arcade,we can identify two isometries: translation and reflection. The cistern in the garden has an octagonal shape.