1.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
2.
Gallon
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The gallon is a unit of measurement for liquid capacity in both the US customary units and the British imperial systems of measurement. Three significantly different sizes are in current use, the imperial gallon defined as 4, while there is no official symbol for the gallon, gal is in common use. The gallon currently has one definition in the system. Historically, there were many definitions and redefinitions, there were more than a few systems of liquid measurements in the pre-1884 United Kingdom. The imperial fluid ounce is defined as 1⁄160 of a gallon, there are four quarts in a gallon. The US gallon is legally defined as 231 cubic inches, which is exactly 3.785411784 liters, a US liquid gallon of water weighs about 8.34 pounds or 3.78 kilograms at 62 °F, making it about 16. 6% lighter than the imperial gallon. There are four quarts in a gallon, two pints in a quart and 16 US fluid ounces in a US pint, which makes the US fluid ounce equal to 1⁄128 of a US gallon. For example, the volume of products and alcoholic beverages are both referenced to 60 °F in government regulations. This dry measure is one-eighth of a US Winchester bushel of 2150.42 cubic inches, the US dry gallon is not used in commerce, and is not listed in the relevant statute, which jumps from the dry quart to the peck. The Imperial gallon is used in life in the United Kingdom. Gallons used in fuel economy expression in Canada are Imperial gallons, the gallon was removed from the list of legally defined primary units of measure catalogued in the EU directive 80/181/EEC, for trading and official purposes, with effect from 31 December 1994. Under the directive the gallon could still be used – but only as a supplementary or secondary unit, Ireland also passed legislation in response to the EU directive with the effective date being 31 December 1993. Though the gallon has ceased to be the legally defined primary unit, it can still be used in both the UK and Ireland as a supplementary unit. The Imperial gallon continues to be used as a unit of measure in Anguilla, Antigua and Barbuda, the Bahamas, the British Virgin Islands, the Cayman Is. Dominica, Grenada, Montserrat, Myanmar, St. Kitts & Nevis, St. Lucia, and St. Vincent & the Grenadines. Other than the United States, the US gallon is used in Liberia, Belize, Colombia, The Dominican Republic, Ecuador, El Salvador, Guatemala, Haiti, Honduras, Nicaragua, and Peru. The United Arab Emirates started selling gasoline by the litre in 2010, along with Guyana, the two former had used the Imperial gallon, and the latter the US gallon until they switched. Antigua and Barbuda plan to switch over to using litres by 2015
3.
Three-dimensional space
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Three-dimensional space is a geometric setting in which three values are required to determine the position of an element. This is the meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space, when n =3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol ℝ3 and this serves as a three-parameter model of the physical universe in which all known matter exists. However, this space is one example of a large variety of spaces in three dimensions called 3-manifolds. Furthermore, in case, these three values can be labeled by any combination of three chosen from the terms width, height, depth, and breadth. In mathematics, analytic geometry describes every point in space by means of three coordinates. Three coordinate axes are given, each perpendicular to the two at the origin, the point at which they cross. They are usually labeled x, y, and z, below are images of the above-mentioned systems. Two distinct points determine a line. Three distinct points are either collinear or determine a unique plane, four distinct points can either be collinear, coplanar or determine the entire space. Two distinct lines can intersect, be parallel or be skew. Two parallel lines, or two intersecting lines, lie in a plane, so skew lines are lines that do not meet. Two distinct planes can either meet in a line or are parallel. Three distinct planes, no pair of which are parallel, can meet in a common line. In the last case, the three lines of intersection of each pair of planes are mutually parallel, a line can lie in a given plane, intersect that plane in a unique point or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line, a hyperplane is a subspace of one dimension less than the dimension of the full space. The hyperplanes of a space are the two-dimensional subspaces, that is
4.
Solid
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Solid is one of the four fundamental states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume, unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to other, either in a regular geometric lattice or irregularly. The branch of physics deals with solids is called solid-state physics. Materials science is concerned with the physical and chemical properties of solids. Solid-state chemistry is concerned with the synthesis of novel materials, as well as the science of identification. The atoms, molecules or ions which make up solids may be arranged in a repeating pattern. Materials whose constituents are arranged in a regular pattern are known as crystals, in some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Almost all common metals, and many ceramics, are polycrystalline, in other materials, there is no long-range order in the position of the atoms. These solids are known as amorphous solids, examples include polystyrene, whether a solid is crystalline or amorphous depends on the material involved, and the conditions in which it was formed. Solids which are formed by slow cooling will tend to be crystalline, likewise, the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed. While many common objects, such as an ice cube or a coin, are chemically identical throughout, for example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is an organic material consisting primarily of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties, the forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride is made up of sodium and chlorine. In diamond or silicon, the atoms share electrons and form covalent bonds, in metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding, metals typically are strong, dense, and good conductors of both electricity and heat
5.
Gas
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Gas is one of the four fundamental states of matter. A pure gas may be made up of atoms, elemental molecules made from one type of atom. A gas mixture would contain a variety of pure gases much like the air, what distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer, the interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam, the gaseous state of matter is found between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention, high-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these states of matter see list of states of matter. The only chemical elements which are stable multi atom homonuclear molecules at temperature and pressure, are hydrogen, nitrogen and oxygen. These gases, when grouped together with the noble gases. Alternatively they are known as molecular gases to distinguish them from molecules that are also chemical compounds. The word gas is a neologism first used by the early 17th-century Flemish chemist J. B. van Helmont, according to Paracelsuss terminology, chaos meant something like ultra-rarefied water. An alternative story is that Van Helmonts word is corrupted from gahst and these four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a relationship among these properties expressed by the ideal gas law. Gas particles are separated from one another, and consequently have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another, transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of boiling points for compounds formed by ionic and covalent bonds leads us to this conclusion, the drifting smoke particles in the image provides some insight into low pressure gas behavior
6.
Plasma (physics)
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Plasma is one of the four fundamental states of matter, the others being solid, liquid, and gas. Yet unlike these three states of matter, plasma does not naturally exist on the Earth under normal surface conditions, the term was first introduced by chemist Irving Langmuir in the 1920s. However, true plasma production is from the separation of these ions and electrons that produces an electric field. Based on the environmental temperature and density either partially ionised or fully ionised forms of plasma may be produced. The positive charge in ions is achieved by stripping away electrons from atomic nuclei, the number of electrons removed is related to either the increase in temperature or the local density of other ionised matter. Plasma may be the most abundant form of matter in the universe, although this is currently tentative based on the existence. Plasma is mostly associated with the Sun and stars, extending to the rarefied intracluster medium, Plasma was first identified in a Crookes tube, and so described by Sir William Crookes in 1879. The nature of the Crookes tube cathode ray matter was identified by British physicist Sir J. J. The term plasma was coined by Irving Langmuir in 1928, perhaps because the glowing discharge molds itself to the shape of the Crookes tube and we shall use the name plasma to describe this region containing balanced charges of ions and electrons. Plasma is a neutral medium of unbound positive and negative particles. Although these particles are unbound, they are not ‘free’ in the sense of not experiencing forces, in turn this governs collective behavior with many degrees of variation. The average number of particles in the Debye sphere is given by the plasma parameter, bulk interactions, The Debye screening length is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, when this criterion is satisfied, the plasma is quasineutral. Plasma frequency, The electron plasma frequency is compared to the electron-neutral collision frequency. When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics, for plasma to exist, ionization is necessary. The term plasma density by itself refers to the electron density, that is. The degree of ionization of a plasma is the proportion of atoms that have lost or gained electrons, even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma. The degree of ionization, α, is defined as α = n i n i + n n, where n i is the number density of ions and n n is the number density of neutral atoms
7.
Liquid
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A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a constant volume independent of pressure. As such, it is one of the four states of matter. A liquid is made up of tiny vibrating particles of matter, such as atoms, water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container, most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, a distinctive property of the liquid state is surface tension, leading to wetting phenomena. The density of a liquid is usually close to that of a solid, therefore, liquid and solid are both termed condensed matter. On the other hand, as liquids and gases share the ability to flow, although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is in form as interstellar clouds or in plasma form within stars. Liquid is one of the four states of matter, with the others being solid, gas. Unlike a solid, the molecules in a liquid have a greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, a liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, if liquid is placed in a bag, it can be squeezed into any shape. These properties make a suitable for applications such as hydraulics. Liquid particles are bound firmly but not rigidly and they are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its point, the cohesive forces that bind the molecules closely together break. If the temperature is decreased, the distances between the molecules become smaller, only two elements are liquid at standard conditions for temperature and pressure, mercury and bromine. Four more elements have melting points slightly above room temperature, francium, caesium, gallium and rubidium, metal alloys that are liquid at room temperature include NaK, a sodium-potassium metal alloy, galinstan, a fusible alloy liquid, and some amalgams
8.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
9.
Metre
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The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
10.
Metric system
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The metric system is an internationally agreed decimal system of measurement. Many sources also cite Liberia and Myanmar as the other countries not to have done so. Although the originators intended to devise a system that was accessible to all. Control of the units of measure was maintained by the French government until 1875, when it was passed to an intergovernmental organisation. From its beginning, the features of the metric system were the standard set of interrelated base units. These base units are used to larger and smaller units that could replace a huge number of other units of measure in existence. Although the system was first developed for use, the development of coherent units of measure made it particularly suitable for science. Although the metric system has changed and developed since its inception, designed for transnational use, it consisted of a basic set of units of measurement, now known as base units. At the outbreak of the French Revolution in 1789, most countries, the metric system was designed to be universal—in the words of the French philosopher Marquis de Condorcet it was to be for all people for all time. However, these overtures failed and the custody of the metric system remained in the hands of the French government until 1875. In languages where the distinction is made, unit names are common nouns, the concept of using consistent classical names for the prefixes was first proposed in a report by the Commission on Weights and Measures in May 1793. The prefix kilo, for example, is used to multiply the unit by 1000, thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as,1 mg =0, however,1935 extensions to the prefix system did not follow this convention, the prefixes nano- and micro-, for example have Greek roots. During the 19th century the prefix myria-, derived from the Greek word μύριοι, was used as a multiplier for 10000, prefixes are not usually used to indicate multiples of a second greater than 1, the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the unit of volume. The base units used in the system must be realisable. Each of the units in SI is accompanied by a mise en pratique published by the BIPM that describes in detail at least one way in which the base unit can be measured. In practice, such realisation is done under the auspices of a mutual acceptance arrangement, in the original version of the metric system the base units could be derived from a specified length and the weight of a specified volume of pure water
11.
Cube
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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids and it has 6 faces,12 edges, and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid and it is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron and it has cubical or octahedral symmetry. The cube has four special orthogonal projections, centered, on a vertex, edges, face, the first and third correspond to the A2 and B2 Coxeter planes. The cube can also be represented as a tiling. This projection is conformal, preserving angles but not areas or lengths, straight lines on the sphere are projected as circular arcs on the plane. In analytic geometry, a surface with center and edge length of 2a is the locus of all points such that max = a. For a cube of length a, As the volume of a cube is the third power of its sides a × a × a, third powers are called cubes, by analogy with squares. A cube has the largest volume among cuboids with a surface area. Also, a cube has the largest volume among cuboids with the same linear size. They were unable to solve this problem, and in 1837 Pierre Wantzel proved it to be impossible because the root of 2 is not a constructible number. The cube has three uniform colorings, named by the colors of the faces around each vertex,111,112,123. The cube has three classes of symmetry, which can be represented by coloring the faces. The highest octahedral symmetry Oh has all the faces the same color, the dihedral symmetry D4h comes from the cube being a prism, with all four sides being the same color. The lowest symmetry D2h is also a symmetry, with sides alternating colors. Each symmetry form has a different Wythoff symbol, a cube has eleven nets, that is, there are eleven ways to flatten a hollow cube by cutting seven edges. To color the cube so that no two adjacent faces have the color, one would need at least three colors
12.
Arithmetic
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Arithmetic is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations between them—addition, subtraction, multiplication and division. Arithmetic is an part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are still used to refer to a wider part of number theory. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations as early as 2000 BC and these artifacts do not always reveal the specific process used for solving problems, but the characteristics of the particular numeral system strongly influence the complexity of the methods. The hieroglyphic system for Egyptian numerals, like the later Roman numerals, in both cases, this origin resulted in values that used a decimal base but did not include positional notation. Complex calculations with Roman numerals required the assistance of a board or the Roman abacus to obtain the results. Early number systems that included positional notation were not decimal, including the system for Babylonian numerals. Because of this concept, the ability to reuse the same digits for different values contributed to simpler. The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs. For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, Greek numerals were used by Archimedes, Diophantus and others in a positional notation not very different from ours. Because the ancient Greeks lacked a symbol for zero, they used three separate sets of symbols, one set for the units place, one for the tens place, and one for the hundreds. Then for the place they would reuse the symbols for the units place. Their addition algorithm was identical to ours, and their multiplication algorithm was very slightly different. Their long division algorithm was the same, and the square root algorithm that was taught in school was known to Archimedes. He preferred it to Heros method of successive approximation because, once computed, a digit doesnt change, and the square roots of perfect squares, such as 7485696, terminate immediately as 2736. For numbers with a part, such as 546.934. The ancient Chinese used a positional notation. Because they also lacked a symbol for zero, they had one set of symbols for the place