Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat, it is the two-dimensional analog of the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units, the standard unit of area is the square metre, the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles and circles.
Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape requires multivariable calculus. Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.
Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers. It can be proved. An approach to defining what is meant by "area" is through axioms. "Area" can be defined as a function from a collection M of special kind of plane figures to the set of real numbers which satisfies the following properties: For all S in M, a ≥ 0. If S and T are in M so are S ∪ T and S ∩ T, a = a + a − a. If S and T are in M with S ⊆ T T − S is in M and a = a − a. If a set S is in M and S is congruent to T T is in M and a = a; every rectangle R is in M. If the rectangle has length h and breadth k a = hk. Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i.e. S ⊆ Q ⊆ T. If there is a unique number c such that a ≤ c ≤ a for all such step regions S and T a = c, it can be proved that such an area function exists. Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Thus areas can be measured in square metres, square centimetres, square millimetres, square kilometres, square feet, square yards, square miles, so forth. Algebraically, these units can be thought of as the squares of the corresponding length units; the SI unit of area is the square metre, considered an SI derived unit. Calculation of the area of a square whose length and width are 1 metre would be: 1 metre x 1 metre = 1 m2and so, a rectangle with different sides would have an area in square units that can be calculated as: 3 metres x 2 metres = 6 m2; this is equivalent to 6 million square millimetres. Other useful conversions are: 1 square kilometre = 1,000,000 square metres 1 square metre = 10,000 square centimetres = 1,000,000 square millimetres 1 square centimetre = 100 square millimetres. In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units. 1 foot = 12 inches,the relationship between square feet and square inches is 1 square foot = 144 square inches,where 144 = 122 = 12 × 12.
Similarly: 1 square yard = 9 square feet 1 square mile = 3,097,600 square yards = 27,878,400 square feetIn addition, conversion factors include: 1 square inch = 6.4516 square centimetres 1 square foot = 0.09290304 square metres 1 square yard = 0.83612736 square metres 1 square mile = 2.589988110336 square kilometres There are several other common units for area. The are was the original unit of area in the metric system, with: 1 are = 100 square metresThough the are has fallen out of use, the hectare is still used to measure land: 1 hectare = 100 ares = 10,000 square metres = 0.01 square kilometresOther uncommon metric units of area include the tetrad, the hectad, the myriad. The acre is commonly used to measure land areas, where 1 acre = 4,840 square yards = 43,560 square feet. An acre is 40% of a hectare. On the atomic scale, area is measured in units of barns, such that: 1 barn = 10−28 square meters; the barn is used in describing the cross-sectional area of interaction in nuclear physics.
In India, 20 dhurki = 1 dhur 20 dhur = 1 khatha 20 khata = 1 bigha 32 khata = 1 acre In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of
Santa Cruz Department (Bolivia)
Santa Cruz, with an area of 370,621 km2, is the largest of the nine constituent departments of Bolivia occupying about one-third of the territory of the country. It is located in the eastern part of the country, sharing borders in the north and east with Brazil and with Paraguay in the south. In the 2012 census, it reported a population of 3,412,921; the capital is the city of Santa Cruz de la Sierra. The department is one of the wealthiest departments in Bolivia, with huge reserves of natural gas. Besides, it has experienced the highest increase of economic growth during the last 50 years in Bolivia and South America. According to current Constitution, the highest authority in the department lies with the governor; the former figure of prefect was appointed by the President of the Republic till 2005, when the prefect for the first time was elected by popular vote to serve for a five-year term. In 2010 the first governor was elected according to the implementation of autonomy after a struggle for a decade by the people of Santa Cruz.
Santa Cruz has a Departmental Assembly, which derives but differs from the previous Departmental Council. It is a state legislature with limited legislation powers, being able to make laws in certain subjects in exclusivity and in some others in concurrence with the state legislative branch.. The department covers a vast expanse of territory in eastern Bolivia, much of it rainforests, extending from the Andes to the border with Brazil; the department's economy depends on agriculture, with sugar, cotton and rice being grown. The amount of land cultivated by modern farming techniques is increasing in the Santa Cruz area, where weather allows for two crops a year. In recent years, the discovery of natural gas in the department has led to plans for the development of a regional natural gas industry, to boost the local economy. Bolivia’s energy minister said two proposed liquefied petroleum gas plants may allow the country to boost supplies to Brazil and Argentina by 2010, easing a shortage of the fuel after a lack of investment reduced output.
The processing plants would be built in Santa Cruz and each would produce about 200 tons of liquefied petroleum gas a day. The plants would help turn a deficit of gas into a “surplus”. In July 2004, the people voted in a nationwide referendum to allow for regulated exportation of the gas; the department hosts El Mutún, the world's second largest iron ore reserve and largest magnesium deposits are located there. Located in the Germán Busch Province in the Santa Cruz Department of Bolivia, near Puerto Suárez, El Mutún extends across the border into Brazil, where it is called the Serrania de Jacadigo. Known as the "Serrania Mutún", it has an area of about 75 square kilometers, its estimated reserves are about 40.205 billion tons of iron ore of 50% iron in hematite and magnetite form, in lesser quantities in siderite and manganese minerals. This can be compared with an estimate of the total world reserves of iron ore: 800 billion tons of crude ore containing more than 230 billion tons of iron. Santa Cruz Department covers a wide and diverse area.
In the west lies a series of temperate Sub-Andean ranges and valleys while to the north and south lies two different lowlands areas. To the northeast lies the flat Llanos Chiquitanos areas and beyond these the Serranías Chiquitanas ranges. In the far east the departments have small parts of the huge Pantanal wetland; the first settlers of Santa Cruz were Spaniards that accompanied Ñuflo de Chávez, as well as Guarani, some Flemings, Portuguese and Italians working for the Spanish crown. Among the first settlers there were Sephardic Jews converted to Christianity who were persecuted by the Inquisition in Spain. Santa Cruz has a multicultural population: 60% are Castizos with both Mestizo and European ascendants, 30% are Natives 10% are Whites of European descent, of whom about a quarter are so-called "Russian" Mennonites of German tradition and descent. At 416 meters above sea level, it is warm and tropical most of the year. Winters are short and last only 2–3 months but can get cold suddenly. "Surazos" can drop the temperature by as much as 30 degrees overnight.
This extreme cold lasts only a few days at a time and the beautiful, sub-tropical Santa Cruz is pleasant throughout most of the year. Here the climate varies by geographical zone: temperate to cold in the western sierras and warm to hot and humid as one descends into the extensive plains; the Department of Santa Cruz is divided into 15 provinces. During the stages of the Chaco war between Paraguay and Bolivia, as the Paraguayan army approached Santa Cruz department, local nationalists backed by a Paraguay-based independence movement sought to create a separate independent state in Santa Cruz department. A referendum on autonomy was held in Santa Cruz department in 2008. Eastern departments in Bolivia, including Santa Cruz, have majority of the natural gas reserves. Bolivian president Evo Morales is planning to introduce legislation to tackle the poverty in the country using tax revenues from richer departments like Santa Cruz. Additionally, Morales's attempts to change the constitution were opposed by the opposition governors who run five of Bolivia's nine regions.
85.6 percent voted in favour of autonomy, because the referendum was illegal, Evo morales started prosecuting people that were supporters of colonialism and serfdom. Kaa-Iya del Gran
Florida is a province in the Santa Cruz Department, Bolivia. Its capital is Samaipata; the province was created by law on December 15, 1924. The province is divided into four municipalities; the archaeological site of Fort Samaipata, declared a UNESCO World Heritage Site in 1998 and Amboró National Park are the principal tourist attractions of the province. Laguna Volcán Las Cuevas. There are several pools and beaches where the locals swim and disport themselves
Pucará is a small town in Bolivia
La Higuera is a small village in Bolivia located in the Province of Vallegrande, in the Department of Santa Cruz. It is situated in the La Higuera Canton belonging to the Pucará Municipality; the village is situated some 150 km southwest of Santa Cruz de la Sierra and 15 southwest of Pucará. La Higuera lies at an elevation of 1950 m, its population is 119 indigenous Guaraní people. On October 8, 1967, the Argentine Marxist revolutionary Che Guevara was captured by the CIA-assisted Bolivian Army in the nearby ravine Quebrada del Churo, ending his campaign to create a continental revolution in South America. Che Guevara was held in the schoolhouse, where he was killed the next day; the body was brought to Vallegrande, where it was placed on display and afterwards secretly buried under an airstrip. "Tourists from all over the world visit La Higuera on pilgrimage. A Frenchman has opened a hostel at the telegraph office where the guerrilla fighters made their last attempt to establish contact with the outside world.
Next door, Cuban doctors provide treatment to the destitute farm workers free of charge. Images of the revolutionary hang in the villagers' huts, many people pray to "Santo Ernesto", said to bring about miracles." A monument to "El Che" and a memorial in the former schoolhouse are the major tourist attraction for this area. La Higuera is a stop on the "Ruta del Che", inaugurated in 2004. Che Guevara Legacy Lives on in Bolivia BBC News, August 24, 2004 Bolivian Town Recalls Che Assassination Prensa Latina, October 8, 2008 Che Sat Here: The Making of a Martyr by Alex Ayala Ugarte, Virginia Quarterly Review, Winter 2009 Issue Che Guevara's 81st birthday Marked in Bolivia Ahora, June 15, 2009
The density, or more the volumetric mass density, of a substance is its mass per unit volume. The symbol most used for density is ρ, although the Latin letter D can be used. Mathematically, density is defined as mass divided by volume: ρ = m V where ρ is the density, m is the mass, V is the volume. In some cases, density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials have different densities, density may be relevant to buoyancy and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material water.
Thus a relative density less than one means. The density of a material varies with pressure; this variation is small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid; this causes it to rise relative to more dense unheated material. The reciprocal of the density of a substance is called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density. In a well-known but apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy.
Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated and compared with the mass. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!". As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment; the story first appeared in written form in Vitruvius' books of architecture, two centuries after it took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. From the equation for density, mass density has units of mass divided by volume; as there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use.
The SI unit of kilogram per cubic metre and the cgs unit of gram per cubic centimetre are the most used units for density. One g/cm3 is equal to one thousand kg/m3. One cubic centimetre is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are more practical and US customary units may be used. See below for a list of some of the most common units of density. A number of techniques as well as standards exist for the measurement of density of materials; such techniques include the use of a hydrometer, Hydrostatic balance, immersed body method, air comparison pycnometer, oscillating densitometer, as well as pour and tap. However, each individual method or technique measures different types of density, therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question; the density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is measured with a scale or balance.
To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object. If the body is not homogeneous its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ = d m / d V, where d V is an elementary volume at position r; the mass of the body t
Bolivia the Plurinational State of Bolivia is a landlocked country located in western-central South America. The capital is Sucre; the largest city and principal industrial center is Santa Cruz de la Sierra, located on the Llanos Orientales a flat region in the east of Bolivia. The sovereign state of Bolivia is a constitutionally unitary state, divided into nine departments, its geography varies from the peaks of the Andes in the West, to the Eastern Lowlands, situated within the Amazon Basin. It is bordered to the north and east by Brazil, to the southeast by Paraguay, to the south by Argentina, to the southwest by Chile, to the northwest by Peru. One-third of the country is within the Andean mountain range. With 1,098,581 km2 of area, Bolivia is the fifth largest country in South America, the 27th largest in the world and the largest landlocked country in the Southern Hemisphere; the country's population, estimated at 11 million, is multiethnic, including Amerindians, Europeans and Africans.
The racial and social segregation that arose from Spanish colonialism has continued to the modern era. Spanish is the official and predominant language, although 36 indigenous languages have official status, of which the most spoken are Guarani and Quechua languages. Before Spanish colonization, the Andean region of Bolivia was part of the Inca Empire, while the northern and eastern lowlands were inhabited by independent tribes. Spanish conquistadors arriving from Cuzco and Asunción took control of the region in the 16th century. During the Spanish colonial period Bolivia was administered by the Royal Audiencia of Charcas. Spain built its empire in large part upon the silver, extracted from Bolivia's mines. After the first call for independence in 1809, 16 years of war followed before the establishment of the Republic, named for Simón Bolívar. Over the course of the 19th and early 20th century Bolivia lost control of several peripheral territories to neighboring countries including the seizure of its coastline by Chile in 1879.
Bolivia remained politically stable until 1971, when Hugo Banzer led a coup d'état which replaced the socialist government of Juan José Torres with a military dictatorship headed by Banzer. Banzer's regime cracked down on leftist and socialist opposition and other forms of dissent, resulting in the torture and deaths of a number of Bolivian citizens. Banzer was ousted in 1978 and returned as the democratically elected president of Bolivia from 1997 to 2001. Modern Bolivia is a charter member of the UN, IMF, NAM, OAS, ACTO, Bank of the South, ALBA and USAN. For over a decade Bolivia has had one of the highest economic growth rates in Latin America, it is a developing country, with a medium ranking in the Human Development Index, a poverty level of 38.6%, one of the lowest crime rates in Latin America. Its main economic activities include agriculture, fishing and manufacturing goods such as textiles, refined metals, refined petroleum. Bolivia is rich in minerals, including tin and lithium. Bolivia is named after Simón Bolívar, a Venezuelan leader in the Spanish American wars of independence.
The leader of Venezuela, Antonio José de Sucre, had been given the option by Bolívar to either unite Charcas with the newly formed Republic of Peru, to unite with the United Provinces of Rio de la Plata, or to formally declare its independence from Spain as a wholly independent state. Sucre opted to create a brand new state and on 6 August 1825, with local support, named it in honor of Simón Bolívar; the original name was Republic of Bolívar. Some days congressman Manuel Martín Cruz proposed: "If from Romulus comes Rome from Bolívar comes Bolivia"; the name was approved by the Republic on 3 October 1825. In 2009, a new constitution changed the country's official name to "Plurinational State of Bolivia" in recognition of the multi-ethnic nature of the country and the enhanced position of Bolivia's indigenous peoples under the new constitution; the region now known as Bolivia had been occupied for over 2,500 years. However, present-day Aymara associate themselves with the ancient civilization of the Tiwanaku culture which had its capital at Tiwanaku, in Western Bolivia.
The capital city of Tiwanaku dates from as early as 1500 BC when it was a small, agriculturally based village. The community grew to urban proportions between AD 600 and AD 800, becoming an important regional power in the southern Andes. According to early estimates, the city covered 6.5 square kilometers at its maximum extent and had between 15,000 and 30,000 inhabitants. In 1996 satellite imaging was used to map the extent of fossilized suka kollus across the three primary valleys of Tiwanaku, arriving at population-carrying capacity estimates of anywhere between 285,000 and 1,482,000 people. Around AD 400, Tiwanaku went from being a locally dominant force to a predatory state. Tiwanaku expanded its reaches into the Yungas and brought its culture and way of life to many other cultures in Peru and Chile. Tiwanaku was not a violent culture in many respects. In order to expand its reach, Tiwanaku exercised great political astuteness, creating colonies, fostering trade agree