Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It is the most common system for the symbolic representation of numbers in the world today; the Hindu-Arabic numeral system was developed by Indian mathematicians around AD 500 using quite different forms of the numerals. From India, the system was adopted by Arabic mathematicians in Baghdad and passed on to the Arabs farther west; the current form of the numerals developed in North Africa. It was in the North African city of Bejaia that the Italian scholar Fibonacci first encountered the numerals; the use of Arabic numerals spread around the world through European trade and colonialism. The term Arabic numerals is ambiguous, it may be intended to mean the numerals used by Arabs, in which case it refers to the Eastern Arabic numerals. Although the phrase "Arabic numeral" is capitalized, it is sometimes written in lower case: for instance in its entry in the Oxford English Dictionary, which helps to distinguish it from "Arabic numerals" as the Eastern Arabic numerals.
Alternative names are Western Arabic numerals, Western numerals, Hindu–Arabic numerals, Unicode calls them digits. The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700; the development was gradual, spanning several centuries, but the decisive step was provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten, it is considered an important milestone in the development of mathematics. One may distinguish between this positional system, identical throughout the family, the precise glyphs used to write the numerals, which varied regionally; the first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD, but their dates are uncertain.
Inscriptions in Indonesia and Cambodia dating to AD 683 have been found. The numeral system came to be known to the court of Baghdad, where mathematicians such as the Persian Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825 in Arabic, the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Indian Numerals about 830, propagated it in the Arab world, their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953; the decimal point notation was introduced by Sind ibn Ali, who wrote the earliest treatise on Arabic numerals. A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus, which are the direct ancestor of the modern "Arabic numerals" used throughout the world.
Woepecke has proposed that the Western Arabic numerals were in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars. Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin. In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum. Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm; the first mentions of the numerals in the West are found in the Codex Vigilanus of 976. From the 980s, Gerbert of Aurillac used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth, he was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.
Leonardo Fibonacci, a mathematician born in the Republic of Pisa who had studied in Béjaïa, promoted the Indian numeral system in Europe with his 1202 book Liber Abaci: When my father, appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art soon pleased me above all else and I came to understand it; the numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement is the same in Arabic as well as the Indo-European languages; the reason the digits are more known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were using the digits from Libya to Morocco.
Arabs, on the other hand, call the base-10 system "Hindu numerals", referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabi
This article describes the architecture of the Muisca. The Muisca, inhabiting the central highlands of the Colombian Andes, were one of the four great civilizations of the Americas. Other than the three civilizations in present-day Mexico and Peru. While specialising in agriculture and gold-working and ceramics, their architecture was rather modest and made of non-permanent materials as wood and clay. Evidence for the Muisca architecture relies on archaeological excavations performed since the mid 20th century. In recent years larger areas showing evidence of the Early Muisca architecture have been uncovered, the biggest of them in Soacha, Cundinamarca. All of the original houses and temples have been destroyed by the Spanish conquerors and replaced with colonial architecture. Reconstructions of some houses and the most important temple in the Muisca religion. Important scholars who have contributed to the knowledge about the Muisca architecture are Gonzalo Jiménez de Quesada, who made the first contact with the Muisca, early 17th century friars Pedro Simón and Juan de Castellanos bishop Lucas Fernández de Piedrahita and modern archaeologists Eliécer Silva Celis, Sylvia Broadbent, Carl Henrik Langebaek and others.
The Altiplano Cundiboyacense, the high plateau in the Colombian Andes, has been inhabited for at least 12,400 years, with the earliest evidence in El Abra, Tibitó and Tequendama. During this era, the paleoclimate and flora and fauna were different from today, it was the end of the Pleistocene, when stadials and interstadials intercalated and the glaciers in the Eastern Ranges were advancing and retreating. When the first hunter-gatherers arrived from the north, they encountered still the Pleistocene megafauna on the highlands. During this time and age, as is evidenced in archaeological excavations at various sites on the Altiplano, the people lived in caves and rock shelters; the prehistorical period was followed by the Herrera Period dated at 800 BCE to 800 CE. It was in this era that the agricultural advancement, that started in the latest preceramic times, caused a change towards population of the plains, away from the caves and rock shelters; this led to an increase in population, modest in the early Herrera Period and more pronounced towards the end of it.
Further population growth and a more stratified society is observed in archaeological analysis of the Late Muisca Period, from 1200 CE onwards. The first contact with the Muisca happened in 1537 by the troops of conquistador and explorer Gonzalo Jiménez de Quesada and his brother Hernán; the houses of the Muisca, called bohíos or malokas, were circular structures made of poles of wood and walls of clay, with a conical reed roof. A long beam of wood supported the roof in the centre of the round structure and was attached to the wooden poles; the interior of the roof was decorated with cloths with thin strokes of different colours. On the floor fine straw was placed; some bohíos those of the caciques had ceramic floors, as evidenced by findings in Mosquera. This was atypical for the Muisca houses. Although the Spanish chroniclers have reported "great populations" of the Muisca territories, the people lived in small settlements, described by the Spanish conquerors as "dispersed homesteads"; as the Maya people, the Muisca related the smaller settlements with their effective agriculture.
Houses on the Bogotá savanna were built on elevated areas to prevent them from floodings of the various rivers and swamps, characteristic of the area. Each community had their own farmlands and hunting grounds surrounding their houses; the houses were constructed around a central square with the house of the cacique in the centre. Two or more "gates" in the cercado gave access to the village; the exact number of houses in the villages requires more archaeological work. De Quesada described villages of 10 up to 100 houses; the Late Muisca Period defined as 1200-1537, is characterised by denser population and larger communities in Suba and Cota with more dispersed housing in the vicinity. Excavations in the Las Delicias neighbourhood of Bogotá, on an alluvial terrace of the Tunjuelito River in 1990, exposed six circular structures of 4.6 metres in diameter, smaller than living spaces found in other areas, e.g. in Facatativá. The occupation of these houses has been dated from the start of the Muisca Period until the colonial period.
The living space was occupied in two stages, starting from 950 BCE, followed by a next phase dated at 750 BCE. The dating has been done based on carbon, taken from the floors of the area. Ceramics, animal bones, swindles and jewellery has been found in this location too. Archaeologist Silva Celis uncovered in 1943 housing structures in Soacha with four different temporal levels with indications of population in the form of ash deposits from fires and animal bones. Various scholars agree, it has been described -by Pedro Simón among others- that at the entrance posts of the houses of the caciques human sacrifice remains were hanging and the posts smeared with blood from the victims, who were regard
The Altiplano Cundiboyacense is a high plateau located in the Eastern Cordillera of the Colombian Andes covering parts of the departments of Cundinamarca and Boyacá. The altiplano corresponds to the ancient territory of the Muisca; the Altiplano Cundiboyacense comprises three distinctive flat regions. The average altitude of the altiplano is about 2,600 metres above sea level but ranges from 2,500 metres to 4,000 metres. Altiplano in Spanish means "high plain" or "high plateau", the second part is a combination of the departments Cundinamarca and Boyacá; the limits of the Altiplano are not defined. The high plateau is enclosed by the higher mountains of the Eastern Ranges, with the Sumapaz mountains in the south and Chingaza to the east; the Tenza Valley is located to the east of the Altiplano and the Ocetá Páramo and Chicamocha Canyon are situated to the northeast. The Altiplano is subdivided into three major valleys, from northeast to southwest: Iraca Valley Ubaté–Chiquinquirá Valley Bogotá savanna The average temperature on the Altiplano Cundiboyacense is 14 °C, ranging from 0 °C to 24 °C.
The dryest months of the year are from December to March, while rain is more common in April, September and November. From June to August strong winds are present. Hail is common on the Altiplano; the Altiplano Cundiboyacense contains various Andean unique ecosystems. 60% of all páramos in the world are situated in Colombia and Boyacá has the most relative area of páramos. Boyacá is the department. To the south the Sumapaz Páramo forms a natural boundary of the Altiplano. Chingaza contains páramo vegetation. On the Altiplano the microclimate of the surroundings of Lake Iguaque produces a páramo; the Altiplano Cundiboyacense is formed as part of the uplift of the Eastern Ranges of the Colombian Andes since Neogene times. Hydrothermal activity in fractures of the forming Andean chain left its trace in the form of the many emeralds found in the western and eastern parts of the Altiplano. From the Early Cretaceous until the Eocene, the region of the present-day Altiplano was dominated by a marine environment, as part of the long inland sea of northern South America.
In these warm tropical seas a fauna of ichthyosaurs and pliosaurs developed, with important finds in the Paja Formation of Villa de Leyva. During the Late Eocene-Early Oligocene epochs, South America became detached from its longest connected former member of Pangea; the isolation of the South American paleocontinent led to a large biodiversity of New World species. The dominating group of top predators and scavengers for decades of millions of years on the continent were the terror birds. Fossils of terror birds have been found throughout South America, with a major collection from current Argentina, where the biggest terror bird, roamed the paleopampas in the early Miocene; the forming Andes created a hilly landscape in the regions bordering the former sea inlet from the proto-Caribbean. Other land animals in the Tertiary were the xenungulate Etayoa bacatensis, evidence for, found in 1987 in the Bogotá Formation of the southern Altiplano; the biodiversity and former tranquility of the isolated ecosystem changed during the Pliocene, when the Panama Block emerged from the seas and formed a transferable connection with isolated North America.
This Great American Biotic Interchange led to a drastic rearrangement of South American fauna. Migrating species from North America replaced many successful South American animals, among which the terror birds; the Late Pleistocene of the Altiplano Cundiboyacense has been analysed in detail through various methods based on fossils found on the Altiplano. Pleistocene megafauna inhabited the glacial highlands of the eastern Andean chain; the climate in the glacials and stadials led to the formation of various prehistoric lakes in the valleys of the Altiplano. The Ubaté-Chiquinquirá Valley in the northwest of the Altiplano was covered with a lake, of which the current Lake Fúquene is a retreating remainder. To the extreme northeast, in Soatá, another Pleistocene lake was present; the largest paleolake in the latest Pleistocene was Lake Humboldt or Lake Bogotá covering the Bogotá savanna. The lake, some 4,000 square kilometres in size, at that time would have been seventy times larger than the biggest lake of Colombia.
Lake Tota is the remnant of a Pleistocene glacial lake higher up the Altiplano to the east. Lake Humboldt is thought to have existed until around 30,000 years ago with as modern remaining water bodies Lake Herrera, wetlands of Bogotá and the Bogotá River. Lake Humboldt had an irregular shoreline with an island in the centre; the Altiplano Cundiboyacense is regarded one of eleven archaeological regions of Colombia. The earliest evidence of human occupation in the region has been found in Pubenza, to the west of the Altiplano, dating to 16,000 years BP. On the Altiplano, the oldest findings are dated at 12,400 ± 160 years in El Abra. Younger occurrences of settlement by hunter-gatherers have been discovered at Tibitó, with an estimated age of 11,740 +/- 110 years BP and Tequendama dated at 10,920 ± 260 years BP. In the earliest ages of human population prehistoric animals as the Cuvieronius and Equus amerhippus were living on the Altiplano. Dated excavations have revealed a transition from a hunter
The Herrera Period is a phase in the history of Colombia. It is part of the Andean preceramic and ceramic, time equivalent of the North American pre-Columbian formative and classic stages and age dated by various archaeologists; the Herrera Period predates the age of the Muisca, who inhabited the Altiplano Cundiboyacense before the Spanish conquest of the Muisca and postdates the prehistory of the region in Colombia. The Herrera Period is defined as ranging from 800 BCE to 800 CE, although some scholars date it as early as 1500 BCE. Ample evidence of the Herrera Period has been uncovered on the Altiplano Cundiboyacense; the main archaeologists contributing to the present knowledge about the Herrera Period are the scholars Ana María Groot, Gonzalo Correal Urrego, Thomas van der Hammen, Carl Henrik Langebaek Rueda, Sylvia M. Broadbent, Marianne Cardale de Schrimpff; the Herrera Period is named after Lake Herrera where archaeologist Silvia Broadbent performed the first excavations on the Herrera Period in 1971.
Lake Herrera is one of the many remnants of the ancient Lake Humboldt, a Pleistocene lake that existed on the Bogotá savanna. The lake with an approximate surface area of 280 hectares is situated at an altitude of 2,550 metres within the boundaries of the Cundinamarca municipality Mosquera, close to Madrid and Bojacá; the site of Lake Herrera is close to the archaeological site of Aguazuque. The region of the Herrea Period and Muisca Confederation, the Altiplano Cundiboyacense; the earliest evidence for inhabitation are found in El Tequendama. This lithic period is defined as from 12,400 to 1000 BCE. Sites are Aguazuque and Checua. Agriculture started around 5000 years before present which led to the development of more complex societies, of which the Herrera Period is one of many in the Andean civilizations. Early evidence of inhabitation has been found in Zipacón and is dated at 3270 BCE. From the Herrera Period ceramic has been found; the oldest ceramic evidence found dates to 2500 BP, except for one piece found near Tocarema and dated at 2750 BP.
The people from the Herrera Period performed agriculture, as evidenced in among others the Thomas van der Hammen Reserve, named after Dutch geologist and botanist Thomas van der Hammen. The Late Herrera Period coincides with the Nahuange Period of the Tairona. Archaeological evidence of the Herrera Period has been found in numerous places on the Altiplano Cundiboyacense, among others in Sopó, Usme, Iza, Gámeza, Facatativá, Moniquirá, Chía, Chiscas, Soatá, Jericó, Covarachía, Sativanorte and El Cocuy; the site in Soacha is one of the most important finds from the Herrera Period, dating from 400 BCE onwards, into the age of the Muisca. At the site the remains of 2200 individual people, 274 complete ceramic pots, stone tools, seeds of cotton, maize and curuba, 634 fragmented and intact spindles and 100 tunjos not used for offerings have been found in Soacha. Over the years and based on new findings, various authors have defined periods of Herrera and Muisca. Regional variations exist, listed below.
Muisca Confederation Aguazuque, Lake Herrera, Tequendama Argüello García, Pedro María. 2015. Subsistence economy and chiefdom emergence in the Muisca area. A study of the Valle de Tena, 1–193. University of Pittsburgh. Accessed 2016-07-08. Cardale de Schrimpff, Marianne. 1985. En busca de los primeros agricultores del Altiplano Cundiboyacense - Searching for the first farmers of the Altiplano Cundiboyacense, 99–125. Banco de la República. Accessed 2016-07-08. Correal Urrego, Gonzalo. 1990. Aguazuque: Evidence of hunter-gatherers and growers on the high plains of the Eastern Ranges, 1-316. Banco de la República: Fundación de Investigaciones Arqueológicas Nacionales. Accessed 2016-07-08. Kruschek, Michael H.. 2003. The evolution of the Bogotá chiefdom: A household view, 1-271. University of Pittsburgh. Accessed 2016-07-08. Langebaek Rueda, Carl Henrik. 1995. Arqueología Regional en el Territorio Muisca: Juego de Datos del Proyecto Valle de Fúquene - Regional Archaeology in the Muisca Territory: A Study of the Fúquene and Susa Valleys, 1-215.
Center for Comparative Arch, University of Pittsburgh. Accessed 2016-07-08. Nieto Escalante, Juan Antonio. 2010. Geografía de Colombia - Geography of Colombia, 1-367. Instituto Geográfico Agustín Codazzi. Reyes Zambrano, Pedro. 1995. El páramo: un ecosistema de alta montaña - The páramo: an ecosystem of the high mountains, 1-168. Accessed 2016-07-08. Boada Rivas, Ana María. 2006. Patrones de asentamiento regional y sistemas de agricultura intensiva en Cota y Suba, Sabana de Bogotá - Regional settlement patterns and intensive agricultural systems in Cota and Suba, Bogotá savanna, 1–181. Banco de la República. Accessed 2016-07-08. Lleras Pérez, Roberto. 1989. Arqueología del alto Valle de Tenza - Archaeology of the upper Tenza Valley, 1–148. Banco de la República. Accessed 2016-07-08. Peña León, Germán Alberto. 1991. Exploraciones arqueológicas en la cuenca media del Río Bogotá - Archaeological explorations in the Bogotá River basin, 1–138. Banco de la República. Accessed 2016-07-08. Huge team of archaeologists work to recover treasures from 3000-Year-Old site in Colombia - Ancient Origins
This article describes the economy of the Muisca. The Muisca were the original inhabitants of the Altiplano Cundiboyacense, the high plateau in the Eastern Ranges of central present-day Colombia, their rich economy and advanced merchant abilities were known by the indigenous groups of the area and described by the Spanish conquistadores whose primary objective was the acquisition of the mineral resources of Tierra Firme. The Muisca economy was self-sufficient regarding the basic supplies, thanks to the advanced technologies of the agriculture on raised terraces by the people; the system of trade was well established providing both the higher social classes and the general population abundances of gold, marine snails, coca and other luxury goods. Markets were held every four to eight days in various settlements throughout the Muisca Confederation and special markets were organised around festivities where merchants from far outside the Andes were trading their goods with the Muisca. Apart from agriculture, the Muisca were well developed in the production of different crafts, using the raw materials traded with surrounding indigenous peoples.
Famous are the tumbaga objects made by the Muisca. Cotton mantles and nets were made by the Muisca women and traded for valuable goods, tropical fruits and small cotton cloths were used as money; the Muisca were unique in South America for having real coins of called tejuelos. Mining was an important source of income for the Muisca, who were called "The Salt People" because of their salt mines in Zipaquirá, Nemocón and Tausa. Like their western neighbours, the Muzo -who were called "The Emerald People"- they mined emeralds in their territories in Somondoco. Carbon was found throughout the region of the Muisca in Eocene sediments and used for the fires for cooking and the production of salt and golden ornaments; as the clear objective of the Spanish colonisers was to gain access to the rich mineral resources and the golden figures made by the Muisca, many primary accounts of the Muisca economy have been considered biased, misinterpreted or outright false by scholars. Pedro de Aguado, Pedro Simón, Juan de Castellanos, Juan de los Barrios, first conquistador Gonzalo Jiménez de Quesada and many others have written about the economy of the Muisca.
Research, in many cases nuancing or refuting the scriptures of the early Spanish writers, has been conducted by Carl Henrik Langebaek, Marianne Cardale de Schrimpff, Sylvia Broadbent, Jorge Gamboa Mendoza, Javier Ocampo López and others. In the times before the Spanish conquest of the Muisca, the central part of present-day Colombia; the central authorities of Bacatá in the south and Hunza in the north were called zipa and zaque respectively. Other rulers were the iraca priest in sacred City of the Sun Sugamuxi, the Tundama of Tundama and various other caciques; the Muisca spoke Chibcha, in their own language called Muysccubun. The Muisca, different from the other three great civilisations of the Americas. Roads were present to connect the settlements with each other and with the surrounding indigenous groups, of which the Guane and Lache to the north, the Panche and Muzo to the west and Guayupe and Tegua to the east were the most important; the Muisca were polytheistic and their religion and mythology was connected with the natural area they were inhabiting.
They had a thorough understanding of astronomical parameters and developed a complex luni-solar calendar. According to the calendar they had specific times for sowing and the organisation of festivals where they sang and played music and drank their national drink chicha in great quantities; the Muisca mummified the most respected members of their community and the mummies were not buried, yet displayed in their temples, in natural locations such as caves and carried on their backs during warfare to impress their enemies. Their art is the most famous remnant of their culture, as living spaces and other existing structures have been destroyed by the Spanish who colonised the Muisca territories. A primary example of their fine goldworking is the Muisca raft, together with more objects made of gold, tumbaga and cotton displayed in the Museo del Oro in Bogotá, the ancient capital of the southern Muisca. Accounts of the Spanish conquistadores show the Muisca had a advanced and specialised economy based on a variety of sources of income.
The main foundation of their economy was the agricultural development using raised terraces on the fertile plains and valleys of the Altiplano Cundiboyacense. The caciques did not control the production directly. Excavations at the archaeological site El Infiernito did not provide evidence of a power structure based on economical differences. Social complexity and advanced status of economies are measured based on the specialisation in craft production; the specialised crafts form an economical advantage and sign of social prestige over competing communities. This has been theorised in the case of the Muisca economy, yet certain research restricted to the Bogotá area has found little evidence to support that thesis. Explanations for the lack of archaeological evidence on wealth differences and relations between higher social classes and wealth have been given in the fo
Hindu–Arabic numeral system
The Hindu–Arabic numeral system is a positional decimal numeral system, is the most common system for the symbolic representation of numbers in the world. It was invented between the 4th centuries by Indian mathematicians; the system was adopted in Arabic mathematics by the 9th century. Influential were the books of Al-Kindi; the system spread to medieval Europe by the High Middle Ages. The system is based upon ten glyphs; the symbols used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages; these symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe, Eastern Arabic numerals used in the Middle East, the Indian numerals used in the Indian subcontinent. The Hindu-Arabic numerals were invented by mathematicians in India. Perso-Arabic mathematicians called them "Hindu numerals", they came to be called "Arabic numerals" in Europe, because they were introduced to the West by Arab merchants.
The Hindu–Arabic system is designed for positional notation in a decimal system. In a more developed form, positional notation uses a decimal marker, a symbol for "these digits recur ad infinitum". In modern usage, this latter symbol is a vinculum. In this more developed form, the numeral system can symbolize any rational number using only 13 symbols. Although found in text written with the Arabic abjad, numbers written with these numerals place the most-significant digit to the left, so they read from left to right; the requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from the Brahmi numerals; the symbols used to represent the system have split into various typographical variants since the Middle Ages, arranged in three main groups: The widespread Western "Arabic numerals" used with the Latin and Greek alphabets in the table, descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb.
The "Arabic–Indic" or "Eastern Arabic numerals" used with Arabic script, developed in what is now Iraq. A variant of the Eastern Arabic numerals is used in Urdu; the Indian numerals in use with scripts of the Brahmic family in India and Southeast Asia. Each of the dozen major scripts of India has its own numeral glyphs; as in many numbering systems, the numerals 1, 2, 3 represent simple tally marks. After three, numerals tend to become more complex symbols. Theorists believe that this is because it becomes difficult to instantaneously count objects past three; the Brahmi numerals at the basis of the system predate the Common Era. They replaced the earlier Kharosthi numerals used since the 4th century BC. Brahmi and Kharosthi numerals were used alongside one another in the Maurya Empire period, both appearing on the 3rd century BC edicts of Ashoka. Buddhist inscriptions from around 300 BC use the symbols that became 1, 4, 6. One century their use of the symbols that became 2, 4, 6, 7, 9 was recorded.
These Brahmi numerals are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, there were rather separate numerals for each of the tens. The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, younger than the Brahmi numerals; the place-value system is used in the Bakhshali Manuscript. Although date of the composition of the manuscript is uncertain, the language used in the manuscript indicates that it could not have been composed any than 400; the development of the positional decimal system takes its origins in Hindu mathematics during the Gupta period. Around 500, the astronomer Aryabhata uses the word kha to mark "zero" in tabular arrangements of digits; the 7th century Brahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role of zero. The Sanskrit translation of the lost 5th century Prakrit Jaina cosmological text Lokavibhaga may preserve an early instance of positional use of zero.
These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti's Chronology of the scholars. The numeral system came to be known to both the Persian mathematician Khwarizmi, who wrote a book, On the Calculation with Hindu Numerals in about 825, the Arab mathematician Al-Kindi, who wrote four volumes, On the Use of the Hindu Numerals around 830; these earlier texts did not use the Hindu numerals. Kushyar ibn L
This article describes the astronomy of the Muisca. The Muisca, one of the four advanced civilisations in the Americas before the Spanish conquest of the Muisca, had a thorough understanding of astronomy, as evidenced by their architecture and calendar, important in their agriculture. Various astronomical sites have been constructed on the Altiplano Cundiboyacense, the territories of the Muisca in the central Colombian Andes, but few remain today. Many archaeoastronomical places have been destroyed by the Spanish conquistadores and replaced by their catholic churches. El Infiernito, outside Villa de Leyva, is the best known of the remaining sites; the Temple of the Sun in sacred City of the Sun Sugamuxi has been reconstructed. Important scholars who have contributed to the knowledge of the Muisca astronomy were José Domingo Duquesne and Alexander von Humboldt in the late 18th and early 19th century and modern researchers as Eliécer Silva Celis, Manuel Arturo Izquierdo Peña, Carl Henrik Langebaek and Juan David Morales.
The Muisca were an advanced civilisation, who inhabited the Altiplano Cundiboyacense and as southeastern part of that the Bogotá savanna before the Spanish conquest of the Muisca, of what became known as Colombia today. The onset of the Muisca Period is set at 800 AD, following the Herrera Period, the reign of the Muisca lasted until the arrival of the Spanish in 1537. On the fertile plains of the Andean high plateau the Muisca developed a rich economy consisting of agricultural technologies of drainage and irrigation, fine crafts of gold and ceramics and textiles and a religious and mythological society; the political organisation was rather loose. Trading and pilgrimage routes were built through the hills of the Altiplano; the most important and still remaining archaeological site of the Muisca, dates to the pre-Muisca Herrera Period. It is an astronomical site where at solstices the Sun lines up the shadows of the stone pillars with the sacred Lake Iguaque, where according to the Muisca religion the mother goddess Bachué was born.
Additionally, the site used to be a place of pilgrimage where the Muisca gathered and interchanged goods. Archaeologist Carl Henrik Langebaek noted that the festivities performed at El Infiernito date back to the Early Muisca Period and that no evidence was found those celebrations existed in the Herrera Period; the true alignments of the pillar shadows are 271 degrees. The eastern alignment points to the Morro Negro hill. El Infiernito at the equinoxes announced the rainy seasons on the Altiplano. Astronomy was an important factor in the organisation of the Muisca, both in terms of cycles of harvest and sowing and in the construction of their architecture; the temples and houses were built with an east–west orientation. In the textiles of the people, the symbols for the Sun and Moon are visible, it is probable that the deities in the religion of the Muisca represented weavers of the Earth and the terrain. The Muisca used gold for their art and rituals and the gold was considered "Semen of the Sun".
At the ritual of the installation of the new zipa in Lake Guatavita, depicted in the famous Muisca raft, the new zipa would cover his naked body with gold dust and jump in the lake. Music was played and he was surrounded by four priests, representing two children of the Sun and two children of the Moon; the religion of the Muisca contained various deities who were based on cosmological and environmental factors. The supreme being of the Muisca, Chiminigagua represented the birth of the Universe who had sent two birds to create light and shape the Earth, his children were the god of the Sun. Both deities served as the basis for the complex lunisolar Muisca calendar, having different divisions for synodic and sidereal months; the days were equal to the Gregorian calendar days and the three different years were composed of sets of different months. One of the most important religious figures in the Muisca religion was Bochica, the bearded messenger god. According to the myths, Bochica walked from Pasca to Iza.
The line connecting those two places in the southeastern part of the Altiplano with the northwestern part has an azimuth of 45 degrees. The line between the city of Bacatá with the constructed Temple of the Sun in Sugamuxi has an azimuth of 45 degrees; the length between the two places is 110 kilometres which equals to one degree of the circumference of the Earth. Continuing this trajectory to the northeast, it lines up with the highest peak of the Sierra Nevada del Cocuy. Throughout the territories of the Muisca Confederation there have existed numerous temples and other sites of the Muisca. Today few of those remain. A reconstruction of the Sun Temple of Sugamuxi has been built in the Archaeology Museum, the Moon Temple of Chía has been destroyed, El Infiernito exists still from pre-Muisca times and the Cojines del Zaque are two stones located in Tunja; the Cojines were built aligned like the Goranchacha Temple. On the sites of the temples, the Spanish colonisers built their churches; the Cojines are aligned with an azimuth of 106 degrees to the cross quarter of the Sun, passing over the present-day San Francisco church to the sacred hill of Romiquira.
Seen from Bolívar Square in Bogotá, the Sun at the June solstice rises over Monserrate, called by the Muisca quijicha caca or "grandmother's foo