The Civil Engineering of the Incas, in which geometric configurations are shown that show that mathematics and natural sciences were known in the Inca culture. Thus, in the Andean world, 2000 years BC, there is evidence of a Proportional Geometric System of measurements, whose factor of change or variation was the mathematical relationship “PI”, synthesized in the geometric formula of the Square Cross that originated in the ancient cult to the constellation of the Southern Cross, whose existence has been verified by the discovery of the Star Geoglyph of Las Salinas de Chao, on the north coast of Peru.
His vertical aerial photography allowed the discovery of the geoglyph and later the geometric and astronomical analysis of it, the constellation of the Southern Cross is an entity and an astronomical concept linked to the problem of controlling the seasons, its cross shape is purely casual and the length of its smaller and larger arms are in the same ratio as the side of a square and its diagonal. This constellation, which with its major axis points to the south pole, is the ruler of the southern hemisphere, as is the case with the pole star in the northern hemisphere.
The Square Cross is a geometric figure used as a “COMPUTER” symbol of religious mathematical concepts in the Andean world, its presence is continuous in the sacred precincts, in the ritual objects and in the looms as in the Paracas or Inca mantle. Its shape originates from a geometric development, which takes as its starting point a unitary square that, growing by successive diagonals, allows the value of “PI” to be determined with sufficient accuracy and form a system. In the Mochica and Chavin cultures, a great waste of geometric figures is shown, in the same way in the buildings found in the city of Cusco, especially in the Fortresses of Sacsayhuamán, Ollaytambo, Pïsac and in the citadel of Machu Picchu.
From the point of view of construction technology, the Incas took advantage of the knowledge of other cultures such as the Collas the skill for stone work, the Waris the technique of agricultural terraces (andenes), the Mochicas and Chimu metallurgy. of the bronze.
Public buildings, especially those of Cusco and later times, were of course much superior constructions with excellent stone masonry and very limited use of adobe, although even the best buildings were usually thatched. All the Inca towns had their temple and their priests, the Coricancha being the great Inca ceremonial center and it was close to the main square of Cusco.
Although there were various forms of population centers in the Inca empire, they all seem to have had some common characteristics, constructions on an elevation with an element of shelter, all cities of a certain hierarchy had squares, temples, colcas or warehouses and markets for bartering. In addition, in many of them palaces were built for the Inca and his entourage. Palaces like Atahuallpa’s in Cajamarca were on the outskirts of the city.
Very little is known about engineering instruments, it is certain that the plumb line was also known and used to determine levels and measure angles and distances. Some time ago it was believed that megalithic masonry based on huge stones of irregular shape and size belonged to the pre-Inca of the Tiahuanaco period, while masonry of stone blocks of uniform size placed in regular rows was typical of the Inca period.
However, it is now assumed that the Incas used both types of construction and that almost all of the large buildings and masonry structures in the Cusco region, including Sacsayhuamán, Ollantaytambo, Machu Picchu and Cusco itself belong to the late Inca period.
The large volume of works built throughout the empire from the fourteenth century until the arrival of the Spanish (1532), was possible only through the organized effort of large groups of workers working in compliance with a peculiar system of taxation to the empire. Thanks to the mita, most of the roads, canals, dairy farms and, of course, the palaces and temples of the main cities of the Inca empire were built. The stone carved in blocks and admirably polished was the character of that architecture.
The stone they used in the constructions was extracted from the quarries and was moved by means of flat, inclined wooden rollers and levers, the instruments they had to cut the stone and carve them were black and hard pebbles selected from the rivers, they also used the blue diamond placed in a chonta handle to polish the stones, later it was carved with hammers and stone axes and bronze chisels. Ultimately it was polished with water and sand, the measuring instruments were also simple and consisted of two superimposed rulers in which certain scales have been introduced.
When studying the construction techniques of the Incas, it is difficult to imagine a place where they can be better appreciated than in the fortress of Ollantaytambo, an Inca city located in the alluvial plain of the Vilcanota River, province of Urubamba and located to the NE of the city of Cusco at 68 km from it and at 2750m.a.s.l. In the area of the fortress there is a considerable number of defensive and agricultural platforms, in them you can see the fine stone work, similar to that of the “temple of the sun” in Cusco, and perhaps of better quality. But the most significant of the Inca work are the huge slabs and stone blocks placed in the place. The largest is 5.50m long and the largest weighs almost 45 tons. Together with the other stones, with the characteristic precision of stonework, they are embedded in the rock and adjacent stones. The joint is of absolute precision, and in the case of the larger block it must have been more difficult since the stone was placed on the edge of the precipice, on a surface that was not level, but was deliberately left in its natural state.
To understand the construction techniques used, it is necessary to examine three points:
1. the techniques to extract the stone from the quarry; 2. your transportation; 3. Your linking on the site. In all these operations, the physical limitations of the available equipment must be taken into account. The use of metal instruments is unlikely. Pack animals were not available, only man performed this task. With regard to transportation, use has been made of Alder trunks (Agnus jorullensis: sauco or quishuar) 9m long and 15 cm in diameter, a tree that grows on the banks of rivers and streams, the eucalyptus trees that are seen today they are not native to the area, they were introduced in the 17th century.
The large almost rectangular slabs were cut into smaller pieces by a procedure that consisted of hitting the stone until forming a continuous V-shaped groove, which ran parallel to its cleavage. In some cases in this slot there were cavities or wedge-shaped notches, almost 8 cm long and 2 cm deep, these cavities may have been made to place stone wedges that would help split the rock and force it to open along Along the marked grooves, it is also probable that the larger cavities would have served for the water to be placed in such a way that, on cold nights, when it froze, it caused the widening and enlargement of the cracks and could be quickly divided.
It is in transportation where you can best admire the ingenuity of the Incas. In Ollantaytambo they faced the tremendous problem of carrying immense stones, the largest of which weighed about 75 tons, they were carried from the top of a hill to the valley, crossing the river, and then carried up to the fortress and placed in position. desired, after having cut them conveniently. The whole process can be explained using deductions that correspond to the field of engineering, due to the nature of the roads there is no possibility that they have been pulled on some type of sled, they must have been transported on rollers placed on a prepared surface, placing three or four logs along its backfill surface.
This is suggested not only by the flat faces of the large stones, but also by the well-preserved nature of the road. This is a very brief description of the construction technology of the Incas using stone, the evidence of engineering confirms the extraordinary technical skill used to achieve their unsurpassed structures. They were not only masters in the handling of materials, but also true engineers. Their ingenuity safely places them among the great builders of all time.
The planning, construction and maintenance of road, hydraulic and building works form a set of pragmatic technological processes that are identified with the personality of the Incas to subdue nature and put it at their service. The construction materials were mud, stone, wood and vegetable fibers, the Incas did not know the brick, they did not burn the clay even though they did it to obtain ceramics. The Inca road network is remarkable, only the admirable Roman road network is in the same category, it integrated the empire and served both for the administration and transmission of information as well as for the circulation of people and animals in times of peace and war, both they built roads to the ends of the conquered domains.
The difference is that the Incas, not having wheeled vehicles, did not need such good pavements, nor such wide roads, nor such resistant bridges; they used steps in the sections of strong slope, the paved roads or not, they were an important element of the Andean culture from the most ancient times. The road network was a system that included infrastructure – roads, bridges and dairy farms; Warehouses located at distances compatible with daily travel, services, and supplies. The total length of the road system has been estimated at 40,000 kilometers. It was made up of two large north-south longitudinal roads, one coastal and the other Andean.
The coastal route ran from Quito in the north to the Maule River, about a hundred kilometers south of what is today Santiago de Chile, and to Mendoza in Argentina, on the east side. In addition, there were connecting roads for the longitudinal roads that ran from east to west along the slopes of the coastal valleys, as is obvious, the road calls for bridges. Without roads it would have been almost impossible to conquer regions so distant from the city of Cusco, nor administered after its conquest. The Inca roads caused great admiration to the Spaniards, as has been indicated there were two main roads from north to south, one along the coast and the other that crossed the highlands, these two roads were crossed by transversal roads, while others Minor roads led to every village in the empire, roads known as Ccapan Ñan.
Small rivers were crossed by bridges of various types, depending on various local conditions, the smallest being built with a series of logs or with large stones supported by masonry abutments. But the type of bridge that attracts the most attention is the suspension bridge, which was generally used to cross narrow and deep ravines. These bridges were made by stretching 5 large cables across the clearing that were firmly anchored to a beam embedded in masonry piles at each end, the cables were long and thin braided fiber, reaching about forty centimeters in diameter, these three form the floor and the other two served as handrails, these were repaired every year technology that is still preserved today.
In Peru, irrigation works were of the greatest importance, especially in the coastal region. Among the most important and admirable engineering works, the irrigation ditches and canals stand out. They were built with the optimal slope and with a layout adapted to the hills; these works came to have many kilometers in length. The channels of the Incas exceed in efficiency, the water was conducted to the fields by means of small ditches whose flow could be regulated with gates formed by stone slabs, in Cusco the drainage and water supply were very well resolved, the currents Flowing through the city were confined within walls and the smaller beds were paved with stones, the water was carried into the buildings by stone-lined conduits.
In the good lands for agriculture, the banks of the rivers were straightened and narrowed in order to increase and preserve the arable land. The Incas built some stone baths with permanent running water, relief models were made, one of these hydraulic works is the Tipón in Cusco which is a true hydraulic laboratory.
The most important technological advance of the ancient Peruvians was probably the improvement of agriculture, it involved the improvement of water technology, irrigation and agricultural technology, in the Andes a very sophisticated technological set of artificial terraces was perfected and developed, called platforms or andenería, which allowed the use of the fertile part of the Andes
