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#1 Re: This is Cool » Miscellany » Today 00:08:30

2133) Metallurgy

Gist

Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys.

Summary

Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys.

Metallurgy encompasses both the science and the technology of metals, including the production of metals and the engineering of metal components used in products for both consumers and manufacturers. Metallurgy is distinct from the craft of metalworking. Metalworking relies on metallurgy in a similar manner to how medicine relies on medical science for technical advancement. A specialist practitioner of metallurgy is known as a metallurgist.

The science of metallurgy is further subdivided into two broad categories: chemical metallurgy and physical metallurgy. Chemical metallurgy is chiefly concerned with the reduction and oxidation of metals, and the chemical performance of metals. Subjects of study in chemical metallurgy include mineral processing, the extraction of metals, thermodynamics, electrochemistry, and chemical degradation (corrosion). In contrast, physical metallurgy focuses on the mechanical properties of metals, the physical properties of metals, and the physical performance of metals. Topics studied in physical metallurgy include crystallography, material characterization, mechanical metallurgy, phase transformations, and failure mechanisms.

Historically, metallurgy has predominately focused on the production of metals. Metal production begins with the processing of ores to extract the metal, and includes the mixture of metals to make alloys. Metal alloys are often a blend of at least two different metallic elements. However, non-metallic elements are often added to alloys in order to achieve properties suitable for an application. The study of metal production is subdivided into ferrous metallurgy (also known as black metallurgy) and non-ferrous metallurgy, also known as colored metallurgy.

Ferrous metallurgy involves processes and alloys based on iron, while non-ferrous metallurgy involves processes and alloys based on other metals. The production of ferrous metals accounts for 95% of world metal production.

Modern metallurgists work in both emerging and traditional areas as part of an interdisciplinary team alongside material scientists and other engineers. Some traditional areas include mineral processing, metal production, heat treatment, failure analysis, and the joining of metals (including welding, brazing, and soldering). Emerging areas for metallurgists include nanotechnology, superconductors, composites, biomedical materials, electronic materials (semiconductors) and surface engineering. Many applications, practices, and devices associated or involved in metallurgy were established in ancient India and China, such as the innovation of the wootz steel , bronze, blast furnace, cast iron, hydraulic-powered trip hammers, and double acting piston bellows.

Details

Metallurgy is the art and science of extracting metals from their ores and modifying the metals for use. Metallurgy customarily refers to commercial as opposed to laboratory methods. It also concerns the chemical, physical, and atomic properties and structures of metals and the principles whereby metals are combined to form alloys.

History of metallurgy

The present-day use of metals is the culmination of a long path of development extending over approximately 6,500 years. It is generally agreed that the first known metals were gold, silver, and copper, which occurred in the native or metallic state, of which the earliest were in all probability nuggets of gold found in the sands and gravels of riverbeds. Such native metals became known and were appreciated for their ornamental and utilitarian values during the latter part of the Stone Age.

Earliest development

Gold can be agglomerated into larger pieces by cold hammering, but native copper cannot, and an essential step toward the Metal Age was the discovery that metals such as copper could be fashioned into shapes by melting and casting in molds; among the earliest known products of this type are copper axes cast in the Balkans in the 4th millennium BCE. Another step was the discovery that metals could be recovered from metal-bearing minerals. These had been collected and could be distinguished on the basis of colour, texture, weight, and flame colour and smell when heated. The notably greater yield obtained by heating native copper with associated oxide minerals may have led to the smelting process, since these oxides are easily reduced to metal in a charcoal bed at temperatures in excess of 700 °C (1,300 °F), as the reductant, carbon monoxide, becomes increasingly stable. In order to effect the agglomeration and separation of melted or smelted copper from its associated minerals, it was necessary to introduce iron oxide as a flux. This further step forward can be attributed to the presence of iron oxide gossan minerals in the weathered upper zones of copper sulfide deposits.

Bronze

In many regions, copper-math alloys, of superior properties to copper in both cast and wrought form, were produced in the next period. This may have been accidental at first, owing to the similarity in colour and flame colour between the bright green copper carbonate mineral malachite and the weathered products of such copper-math sulfide minerals as enargite, and it may have been followed later by the purposeful selection of math compounds based on their garlic odour when heated.

Element As contents varied from 1 to 7 percent, with up to 3 percent tin. Essentially As-free copper alloys with higher tin content—in other words, true bronze—seem to have appeared between 3000 and 2500 BCE, beginning in the Tigris-Euphrates delta. The discovery of the value of tin may have occurred through the use of stannite, a mixed sulfide of copper, iron, and tin, although this mineral is not as widely available as the principal tin mineral, cassiterite, which must have been the eventual source of the metal. Cassiterite is strikingly dense and occurs as pebbles in alluvial deposits together with math and gold; it also occurs to a degree in the iron oxide gossans mentioned above.

While there may have been some independent development of bronze in varying localities, it is most likely that the bronze culture spread through trade and the migration of peoples from the Middle East to Egypt, Europe, and possibly China. In many civilizations the production of copper, math copper, and tin bronze continued together for some time. The eventual disappearance of copper-math As is difficult to explain. Production may have been based on minerals that were not widely available and became scarce, but the relative scarcity of tin minerals did not prevent a substantial trade in that metal over considerable distances. It may be that tin bronzes were eventually preferred owing to the chance of contracting As poisoning from fumes produced by the oxidation of math-containing minerals.

As the weathered copper ores in given localities were worked out, the harder sulfide ores beneath were mined and smelted. The minerals involved, such as chalcopyrite, a copper-iron sulfide, needed an oxidizing roast to remove sulfur as sulfur dioxide and yield copper oxide. This not only required greater metallurgical skill but also oxidized the intimately associated iron, which, combined with the use of iron oxide fluxes and the stronger reducing conditions produced by improved smelting furnaces, led to higher iron contents in the bronze.

Iron

It is not possible to mark a sharp division between the Bronze Age and the Iron Age. Small pieces of iron would have been produced in copper smelting furnaces as iron oxide fluxes and iron-bearing copper sulfide ores were used. In addition, higher furnace temperatures would have created more strongly reducing conditions (that is to say, a higher carbon monoxide content in the furnace gases). An early piece of iron from a trackway in the province of Drenthe, Netherlands, has been dated to 1350 BCE, a date normally taken as the Middle Bronze Age for this area. In Anatolia, on the other hand, iron was in use as early as 2000 BCE. There are also occasional references to iron in even earlier periods, but this material was of meteoric origin.

Once a relationship had been established between the new metal found in copper smelts and the ore added as flux, the operation of furnaces for the production of iron alone naturally followed. Certainly, by 1400 BCE in Anatolia, iron was assuming considerable importance, and by 1200–1000 BCE it was being fashioned on quite a large scale into weapons, initially dagger blades. For this reason, 1200 BCE has been taken as the beginning of the Iron Age. Evidence from excavations indicates that the art of iron making originated in the mountainous country to the south of the Black Sea, an area dominated by the Hittites. Later the art apparently spread to the Philistines, for crude furnaces dating from 1200 BCE have been unearthed at Gerar, together with a number of iron objects.

Smelting of iron oxide with charcoal demanded a high temperature, and, since the melting temperature of iron at 1,540 °C (2,800 °F) was not attainable then, the product was merely a spongy mass of pasty globules of metal intermingled with a semiliquid slag. This product, later known as bloom, was hardly usable as it stood, but repeated reheating and hot hammering eliminated much of the slag, creating wrought iron, a much better product.

The properties of iron are much affected by the presence of small amounts of carbon, with large increases in strength associated with contents of less than 0.5 percent. At the temperatures then attainable—about 1,200 °C (2,200 °F)—reduction by charcoal produced an almost pure iron, which was soft and of limited use for weapons and tools, but when the ratio of fuel to ore was increased and furnace drafting improved with the invention of better bellows, more carbon was absorbed by the iron. This resulted in blooms and iron products with a range of carbon contents, making it difficult to determine the period in which iron may have been purposely strengthened by carburizing, or reheating the metal in contact with excess charcoal.

Carbon-containing iron had the further great advantage that, unlike bronze and carbon-free iron, it could be made still harder by quenching—i.e., rapid cooling by immersion in water. There is no evidence for the use of this hardening process during the early Iron Age, so that it must have been either unknown then or not considered advantageous, in that quenching renders iron very brittle and has to be followed by tempering, or reheating at a lower temperature, to restore toughness. What seems to have been established early on was a practice of repeated cold forging and annealing at 600–700 °C (1,100–1,300 °F), a temperature naturally achieved in a simple fire. This practice is common in parts of Africa even today.

By 1000 BCE iron was beginning to be known in central Europe. Its use spread slowly westward. Iron making was fairly widespread in Great Britain at the time of the Roman invasion in 55 BCE. In Asia iron was also known in ancient times, in China by about 700 BCE.

Brass

While some zinc appears in bronzes dating from the Bronze Age, this was almost certainly an accidental inclusion, although it may foreshadow the complex ternary alloys of the early Iron Age, in which substantial amounts of zinc as well as tin may be found. Brass, as an alloy of copper and zinc without tin, did not appear in Egypt until about 30 BCE, but after this it was rapidly adopted throughout the Roman world, for example, for currency. It was made by the calamine process, in which zinc carbonate or zinc oxide were added to copper and melted under a charcoal cover in order to produce reducing conditions. The general establishment of a brass industry was one of the important metallurgical contributions made by the Romans.

Precious metals

Bronze, iron, and brass were, then, the metallic materials on which successive peoples built their civilizations and of which they made their implements for both war and peace. In addition, by 500 BCE, rich lead-bearing silver mines had opened in Greece. Reaching depths of several hundred metres, these mines were vented by drafts provided by fires lit at the bottom of the shafts. Ores were hand-sorted, crushed, and washed with streams of water to separate valuable minerals from the barren, lighter materials. Because these minerals were principally sulfides, they were roasted to form oxides and were then smelted to recover a lead-silver alloy.

Lead was removed from the silver by cupellation, a process of great antiquity in which the alloy was melted in a shallow porous clay or bone-ash receptacle called a cupel. A stream of air over the molten mass preferentially oxidized the lead. Its oxide was removed partially by skimming the molten surface; the remainder was absorbed into the porous cupel. Silver metal and any gold were retained on the cupel. The lead from the skimmings and discarded cupels was recovered as metal upon heating with charcoal.

Native gold itself often contained quite considerable quantities of silver. These silver-gold alloys, known as electrum, may be separated in a number of ways, but presumably the earliest was by heating in a crucible with common salt. In time and with repetitive treatments, the silver was converted into silver chloride, which passed into the molten slag, leaving a purified gold. Cupellation was also employed to remove from the gold such contaminates as copper, tin, and lead. Gold, silver, and lead were used for artistic and religious purposes, personal adornment, household utensils, and equipment for the chase.

From 500 BCE to 1500 CE

In the thousand years between 500 BCE and 500 CE, a vast number of discoveries of significance to the growth of metallurgy were made. The Greek mathematician and inventor Archimedes, for example, demonstrated that the purity of gold could be measured by determining its weight and the quantity of water displaced upon immersion—that is, by determining its density. In the pre-Christian portion of the period, the first important steel production was started in India, using a process already known to ancient Egyptians. Wootz steel, as it was called, was prepared as sponge (porous) iron in a unit not unlike a bloomery. The product was hammered while hot to expel slag, broken up, then sealed with wood chips in clay containers and heated until the pieces of iron absorbed carbon and melted, converting it to steel of homogeneous composition containing 1 to 1.6 percent carbon. The steel pieces could then be heated and forged to bars for later use in fashioning articles, such as the famous Damascus swords made by medieval Arab armourers.

As, zinc, antimony, and nickel may well have been known from an early date but only in the alloy state. By 100 BCE mercury was known and was produced by heating the sulfide mineral cinnabar and condensing the vapours. Its property of amalgamating (mixing or alloying) with various metals was employed for their recovery and refining. Lead was beaten into sheets and pipes, the pipes being used in early water systems. The metal tin was available and Romans had learned to use it to line food containers. Although the Romans made no extraordinary metallurgical discoveries, they were responsible for, in addition to the establishment of the brass industry, contributing toward improved organization and efficient administration in mining.

Beginning about the 6th century, and for the next thousand years, the most meaningful developments in metallurgy centred on iron making. Great Britain, where iron ore was plentiful, was an important iron-making region. Iron weapons, agricultural implements, domestic articles, and even personal adornments were made. Fine-quality cutlery was made near Sheffield. Monasteries were often centres of learning of the arts of metalworking. Monks became well known for their iron making and bell founding, the products made either being utilized in the monasteries, disposed of locally, or sold to merchants for shipment to more distant markets. In 1408 the bishop of Durham established the first water-powered bloomery in Britain, with the power apparently operating the bellows. Once power of this sort became available, it could be applied to a range of operations and enable the hammering of larger blooms.

In Spain, another iron-making region, the Catalan forge had been invented, and its use later spread to other areas. A hearth type of furnace, it was built of stone and was charged with iron ore, flux, and charcoal. The charcoal was kept ignited with air from a bellows blown through a bottom nozzle, or tuyere (see figure). The bloom that slowly collected at the bottom was removed and upon frequent reheating and forging was hammered into useful shapes. By the 14th century the furnace was greatly enlarged in height and capacity.

If the fuel-to-ore ratio in such a furnace was kept high, and if the furnace reached temperatures sufficiently hot for substantial amounts of carbon to be absorbed into the iron, then the melting point of the metal would be lowered and the bloom would melt. This would dissolve even more carbon, producing a liquid cast iron of up to 4 percent carbon and with a relatively low melting temperature of 1,150 °C (2,100 °F). The cast iron would collect in the base of the furnace, which technically would be a blast furnace rather than a bloomery in that the iron would be withdrawn as a liquid rather than a solid lump.

While the Iron Age peoples of Anatolia and Europe on occasion may have accidently made cast iron, which is chemically the same as blast-furnace iron, the Chinese were the first to realize its advantages. Although brittle and lacking the strength, toughness, and workability of steel, it was useful for making cast bowls and other vessels. In fact, the Chinese, whose Iron Age began about 500 BCE, appear to have learned to oxidize the carbon from cast iron in order to produce steel or wrought iron indirectly, rather than through the direct method of starting from low-carbon iron.

After 1500

During the 16th century, metallurgical knowledge was recorded and made available. Two books were especially influential. One, by the Italian Vannoccio Biringuccio, was entitled De la pirotechnia (Eng. trans., The Pirotechnia of Vannoccio Biringuccio, 1943). The other, by the German Georgius Agricola, was entitled De re metallica. Biringuccio was essentially a metalworker, and his book dealt with smelting, refining, and assay methods (methods for determining the metal content of ores) and covered metal casting, molding, core making, and the production of such commodities as cannons and cast-iron cannonballs. His was the first methodical description of foundry practice.

Agricola, on the other hand, was a miner and an extractive metallurgist; his book considered prospecting and surveying in addition to smelting, refining, and assay methods. He also described the processes used for crushing and concentrating the ore and then, in some detail, the methods of assaying to determine whether ores were worth mining and extracting. Some of the metallurgical practices he described are retained in principle today.

Ferrous metals

From 1500 to the 20th century, metallurgical development was still largely concerned with improved technology in the manufacture of iron and steel. In England, the gradual exhaustion of timber led first to prohibitions on cutting of wood for charcoal and eventually to the introduction of coke, derived from coal, as a more efficient fuel. Thereafter, the iron industry expanded rapidly in Great Britain, which became the greatest iron producer in the world. The crucible process for making steel, introduced in England in 1740, by which bar iron and added materials were placed in clay crucibles heated by coke fires, resulted in the first reliable steel made by a melting process.

One difficulty with the bloomery process for the production of soft bar iron was that, unless the temperature was kept low (and the output therefore small), it was difficult to keep the carbon content low enough so that the metal remained ductile. This difficulty was overcome by melting high-carbon pig iron from the blast furnace in the puddling process, invented in Great Britain in 1784. In it, melting was accomplished by drawing hot gases over a charge of pig iron and iron ore held on the furnace hearth. During its manufacture the product was stirred with iron rabbles (rakes), and, as it became pasty with loss of carbon, it was worked into balls, which were subsequently forged or rolled to a useful shape. The product, which came to be known as wrought iron, was low in elements that contributed to the brittleness of pig iron and contained enmeshed slag particles that became elongated fibres when the metal was forged. Later, the use of a rolling mill equipped with grooved rolls to make wrought-iron bars was introduced.

The most important development of the 19th century was the large-scale production of cheap steel. Prior to about 1850, the production of wrought iron by puddling and of steel by crucible melting had been conducted in small-scale units without significant mechanization. The first change was the development of the open-hearth furnace by William and Friedrich Siemens in Britain and by Pierre and Émile Martin in France. Employing the regenerative principle, in which outgoing combusted gases are used to heat the next cycle of fuel gas and air, this enabled high temperatures to be achieved while saving on fuel. Pig iron could then be taken through to molten iron or low-carbon steel without solidification, scrap could be added and melted, and iron ore could be melted into the slag above the metal to give a relatively rapid oxidation of carbon and silicon—all on a much enlarged scale. Another major advance was Henry Bessemer’s process, patented in 1855 and first operated in 1856, in which air was blown through molten pig iron from tuyeres set into the bottom of a pear-shaped vessel called a converter. Heat released by the oxidation of dissolved silicon, manganese, and carbon was enough to raise the temperature above the melting point of the refined metal (which rose as the carbon content was lowered) and thereby maintain it in the liquid state. Very soon Bessemer had tilting converters producing 5 tons in a heat of one hour, compared with four to six hours for 50 kilograms (110 pounds) of crucible steel and two hours for 250 kilograms of puddled iron.

Neither the open-hearth furnace nor the Bessemer converter could remove phosphorus from the metal, so that low-phosphorus raw materials had to be used. This restricted their use from areas where phosphoric ores, such as those of the Minette range in Lorraine, were a main European source of iron. The problem was solved by Sidney Gilchrist Thomas, who demonstrated in 1876 that a basic furnace lining consisting of calcined dolomite, instead of an acidic lining of siliceous materials, made it possible to use a high-lime slag to dissolve the phosphates formed by the oxidation of phosphorus in the pig iron. This principle was eventually applied to both open-hearth furnaces and Bessemer converters.

As steel was now available at a fraction of its former cost, it saw an enormously increased use for engineering and construction. Soon after the end of the century it replaced wrought iron in virtually every field. Then, with the availability of electric power, electric-arc furnaces were introduced for making special and high-alloy steels. The next significant stage was the introduction of cheap oxygen, made possible by the invention of the Linde-Frankel cycle for the liquefaction and fractional distillation of air. The Linz-Donawitz process, invented in Austria shortly after World War II, used oxygen supplied as a gas from a tonnage oxygen plant, blowing it at supersonic velocity into the top of the molten iron in a converter vessel. As the ultimate development of the Bessemer/Thomas process, oxygen blowing became universally employed in bulk steel production.

Light metals

Another important development of the late 19th century was the separation from their ores, on a substantial scale, of aluminum and magnesium. In the earlier part of the century, several scientists had made small quantities of these light metals, but the most successful was Henri-Étienne Sainte-Claire Deville, who by 1855 had developed a method by which cryolite, a double fluoride of aluminum and sodium, was reduced by sodium metal to aluminum and sodium fluoride. The process was very expensive, but cost was greatly reduced when the American chemist Hamilton Young Castner developed an electrolytic cell for producing cheaper sodium in 1886. At the same time, however, Charles M. Hall in the United States and Paul-Louis-Toussaint Héroult in France announced their essentially identical processes for aluminum extraction, which were also based on electrolysis. Use of the Hall-Héroult process on an industrial scale depended on the replacement of storage batteries by rotary power generators; it remains essentially unchanged to this day.

Welding

One of the most significant changes in the technology of metals fabrication has been the introduction of fusion welding during the 20th century. Before this, the main joining processes were riveting and forge welding. Both had limitations of scale, although they could be used to erect substantial structures. In 1895 Henry-Louis Le Chatelier stated that the temperature in an oxyacetylene flame was 3,500 °C (6,300 °F), some 1,000 °C higher than the oxyhydrogen flame already in use on a small scale for brazing and welding. The first practical oxyacetylene torch, drawing acetylene from cylinders containing acetylene dissolved in acetone, was produced in 1901. With the availability of oxygen at even lower cost, oxygen cutting and oxyacetylene welding became established procedures for the fabrication of structural steel components.

The metal in a join can also be melted by an electric arc, and a process using a carbon as a negative electrode and the workpiece as a positive first became of commercial interest about 1902. Striking an arc from a coated metal electrode, which melts into the join, was introduced in 1910. Although it was not widely used until some 20 years later, in its various forms it is now responsible for the bulk of fusion welds.

Metallography

The 20th century has seen metallurgy change progressively, from an art or craft to a scientific discipline and then to part of the wider discipline of materials science. In extractive metallurgy, there has been the application of chemical thermodynamics, kinetics, and chemical engineering, which has enabled a better understanding, control, and improvement of existing processes and the generation of new ones. In physical metallurgy, the study of relationships between macrostructure, microstructure, and atomic structure on the one hand and physical and mechanical properties on the other has broadened from metals to other materials such as ceramics, polymers, and composites.

Metallurgy and mining

This greater scientific understanding has come largely from a continuous improvement in microscopic techniques for metallography, the examination of metal structure. The first true metallographer was Henry Clifton Sorby of Sheffield, England, who in the 1860s applied light microscopy to the polished surfaces of materials such as rocks and meteorites. Sorby eventually succeeded in making photomicrographic records, and by 1885 the value of metallography was appreciated throughout Europe, with particular attention being paid to the structure of steel. For example, there was eventual acceptance, based on micrographic evidence and confirmed by the introduction of X-ray diffraction by William Henry and William Lawrence Bragg in 1913, of the allotropy of iron and its relationship to the hardening of steel. During subsequent years there were advances in the atomic theory of solids; this led to the concept that, in nonplastic materials such as glass, fracture takes place by the propagation of preexisting cracklike defects and that, in metals, deformation takes place by the movement of dislocations, or defects in the atomic arrangement, through the crystalline matrix. Proof of these concepts came with the invention and development of the electron microscope; even more powerful field ion microscopes and high-resolution electron microscopes now make it possible to detect the position of individual atoms.

Another example of the development of physical metallurgy is a discovery that revolutionized the use of aluminum in the 20th century. Originally, most aluminum was used in cast alloys, but the discovery of age hardening by Alfred Wilm in Berlin about 1906 yielded a material that was twice as strong with only a small change in weight. In Wilm’s process, a solute such as magnesium or copper is trapped in supersaturated solid solution, without being allowed to precipitate out, by quenching the aluminum from a higher temperature rather than slowly cooling it. The relatively soft aluminum alloy that results can be mechanically formed, but, when left at room temperature or heated at low temperatures, it hardens and strengthens. With copper as the solute, this type of material came to be known by the trade name Duralumin. The advances in metallography described above eventually provided the understanding that age hardening is caused by the dispersion of very fine precipitates from the supersaturated solid solution; this restricts the movement of the dislocations that are essential to crystal deformation and thus raises the strength of the metal. The principles of precipitation hardening have been applied to the strengthening of a large number of alloys.

Additional Information

Metallurgy plays a pivotal role in many industries like aviation, public transportation and electronics — industries that require making things.

From the production of mighty machinery and sturdy construction materials to the creation of intricate electrical systems, metals take center stage. With their exceptional mechanical strength, remarkable thermal conductivity and impressive electrical properties, metals are the lifeblood of technological advancements.

Through skilled hands, metallurgy unlocks the potential of metals, shaping them into essential components that power our modern world. Metallurgists extract, refine and meticulously craft to meet the ever-evolving demands of industries, driving innovation and propelling us into the future.

What Is Metallurgy?

Metallurgy is the study and manipulation of metals and their properties. It is a field of science that focuses on understanding how metals behave and finding ways to improve their properties for different applications. Metallurgists work with widely used metals — like iron, aluminum, copper and steel — in various industries.

One important part of the field is extracting metals from their natural sources, such as ores. An ore is a naturally occurring rock or mineral that contains a valuable material, such as metal or gemstones, which can be extracted and processed for various industrial purposes.

Once extraction is complete, ores can be purified to remove impurities and improve their quality. Think of purification in metallurgy like filtering water. Just as you remove impurities and contaminants from water to make it clean and safe to drink, metallurgists use different methods to remove unwanted substances from metals or ores, making them pure and of higher quality for their intended use.

Metallurgists also study the structure of metals at a microscopic level. They examine how atoms are arranged in metals and how this arrangement affects their properties, like strength, hardness, and conductivity. By understanding the structure, metallurgists can modify metals through processes like heating and cooling, known as heat treatment, to improve their properties.

Metallurgists develop new alloys by combining different metals or adding other elements. Think of it as mixing different paint colors to create a vibrant masterpiece that is stronger, more durable, or corrosion-resistant. Stainless steel, for example, is an alloy that combines iron's strength with chromium's corrosion resistance, making it perfect for shiny kitchen appliances and sturdy construction materials. It's like having the best of both worlds in one metal combo!

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#2 Re: Dark Discussions at Cafe Infinity » crème de la crème » Yesterday 18:17:29

1442) William Alfred Fowler

Summary

William Fowler (born August 9, 1911, Pittsburgh, Pennsylvania, U.S.—died March 14, 1995, Pasadena, California) was an American nuclear astrophysicist who, with Subrahmanyan Chandrasekhar, won the Nobel Prize for Physics in 1983 for his role in formulating a widely accepted theory of element generation.

Fowler studied at the Ohio State University (B.S., 1933) and at the California Institute of Technology (Ph.D., 1936), where he became an assistant professor in 1939 and a full professor in 1946. His theory of element generation, which he developed with Sir Fred Hoyle, Margaret Burbidge, and Geoffrey Burbidge in the 1950s, suggests that in stellar evolution elements are synthesized progressively from light elements to heavy ones, in nuclear reactions that also produce light and heat. With the collapse of more massive stars, the explosive rebound known as supernova occurs; according to theory, this phase makes possible the synthesis of the heaviest elements.

Fowler also worked in radio astronomy, proposing with Hoyle that the cores of radio galaxies are collapsed “superstars” emitting strong radio waves and that quasars are larger versions of these collapsed superstars.

Fowler received the National Medal of Science (1974) and the Legion of Honour (1989).

Details

William Alfred Fowler (August 9, 1911 – March 14, 1995) was an American nuclear physicist, later astrophysicist, who, with Subrahmanyan Chandrasekhar, was awarded the 1983 Nobel Prize in Physics. He is known for his theoretical and experimental research into nuclear reactions within stars and the energy elements produced in the process and was one of the authors of the influential B2FH paper.

Early life

On 9 August 1911, Fowler was born in Pittsburgh. Fowler's parents were John MacLeod Fowler and Jennie Summers Watson. Fowler was the eldest of his siblings, Arthur and Nelda.

The family moved to Lima, Ohio, a steam railroad town, when Fowler was two years old. Growing up near the Pennsylvania Railroad yard influenced Fowler's interest in locomotives. In 1973, he travelled to the Soviet Union just to observe the steam engine that powered the Trans-Siberian Railway plying the nearly 2,500-kilometre (1,600 mi) route that connects Khabarovsk and Moscow.

Education

In 1933, Fowler graduated from the Ohio State University, where he was a member of the Tau Kappa Epsilon fraternity. In 1936, Fowler received a Ph.D. in nuclear physics from the California Institute of Technology in Pasadena, California.

Career

In 1936, Fowler became a research fellow at Caltech. He was elected to the United States National Academy of Sciences in 1938. In 1939, Fowler became an assistant professor at Caltech.

Although an experimental nuclear physicist, Fowler's most famous paper was his collaboration with Margaret and Geoffrey Burbidge, "Synthesis of the Elements in Stars" Significantly, Margaret Burbidge was first author, Geoffrey Burbidge second, Fowler third, and Cambridge cosmologist Fred Hoyle. That 1957 paper in Reviews of Modern Physics categorized most nuclear processes for origin of all but the lightest chemical elements in stars. It is widely known as the B2FH paper. Though the theory of Stellar Nucleosynthesis established in the paper was later cited by the Nobel Committee as the reason for his 1983 Nobel in Physics, Margaret Burbidge did not share in the award.

In 1942, Fowler became an associate professor at Caltech. In 1946, Fowler became a Professor at Caltech. Fowler, along with Lee A. DuBridge, Max Mason, Linus Pauling, and Bruce H. Sage, was awarded the Medal for Merit in 1948 by President Harry S. Truman.

Fowler succeeded Charles Lauritsen as director of the W. K. Kellogg Radiation Laboratory at Caltech, and was himself later succeeded by Steven E. Koonin. Fowler was awarded the National Medal of Science by President Gerald Ford.

Fowler was Guggenheim Fellow at St John's College, Cambridge in 1962–63. He was elected to the American Philosophical Society in 1962, won the Henry Norris Russell Lectureship of the American Astronomical Society in 1963, elected to the American Academy of Arts and Sciences in 1965, won the Vetlesen Prize in 1973, the Eddington Medal in 1978, the Bruce Medal of the Astronomical Society of the Pacific in 1979, and the Nobel Prize in Physics in 1983 (shared with Subrahmanyan Chandrasekhar) for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe .

Fowler's doctoral students at Caltech included Donald D. Clayton.

Personal life

A lifelong fan of steam locomotives, Fowler owned several working models of various sizes.

Fowler's first wife was Adriane Fay (née Olmsted) Fowler (1912–1988). They had two daughters, Mary Emily and Martha.

In December 1989, Fowler married Mary Dutcher (1919–2019), an artist, in Pasadena, California. On 11 March 1995, Fowler died from kidney failure in Pasadena, California. He was 83.

Additional Information

Stars in the universe form from clouds of gas and dust. When these clouds are pulled together by gravitational force, energy is released in the form of heat. And when a high enough temperature is reached, reactions among the atomic nuclei in the star’s interior begin. These reactions are what causes radiation from stars. In the 1950s William Fowler showed how these nuclear reactions also account for how various elements are formed. These processes have created the elements that make up our earth and other heavenly bodies in the universe.

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#3 Jokes » Grape Jokes - I » Yesterday 17:51:58

Jai Ganesh
Replies: 0

Q: What did the green grape say to the purple grape?
A: Breathe! Breathe!
* * *
Q: Why aren't grapes ever lonely?
A: Because they come in bunches!
* * *
Q: What is purple and long?
A: The grape wall of China.
* * *
Q: What did the grape say when he got stepped on?
A: He let out a little wine.
* * *
Q: "What's purple and huge and swims in the ocean?"
A: "Moby Grape."
* * *

#4 Dark Discussions at Cafe Infinity » Chance Quotes - III » Yesterday 17:09:49

Jai Ganesh
Replies: 0

Chance Quotes - III

1. I think it's no secret that I've tried to take chances in my career and also in my life, and I believe to not live in fear. - Nicolas Cage

2. When a person cannot deceive himself the chances are against his being able to deceive other people. - Mark Twain

3. Far and away the best prize that life has to offer is the chance to work hard at work worth doing. - Theodore Roosevelt

4. A lie gets halfway around the world before the truth has a chance to get its pants on. - Winston Churchill

5. I will prepare and some day my chance will come. - Abraham Lincoln

6. Every existing thing is born without reason, prolongs itself out of weakness, and dies by chance. - Jean-Paul Sartre

7. Atheism is so senseless. When I look at the solar system, I see the earth at the right distance from the sun to receive the proper amounts of heat and light. This did not happen by chance. - Isaac Newton

8. No man will be a sailor who has contrivance enough to get himself into a jail; for being in a ship is being in a jail, with the chance of being drowned... a man in a jail has more room, better food, and commonly better company. - Samuel Johnson

9. We are not the same persons this year as last; nor are those we love. It is a happy chance if we, changing, continue to love a changed person. - W. Somerset Maugham

10. Forgiveness says you are given another chance to make a new beginning. - Desmond Tutu

11. America is the land of the second chance - and when the gates of the prison open, the path ahead should lead to a better life. - George W. Bush

12. If you are given a chance to be a role model, I think you should always take it because you can influence a person's life in a positive light, and that's what I want to do. That's what it's all about. - Tiger Woods.

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#7 Re: Jai Ganesh's Puzzles » Doc, Doc! » Yesterday 15:16:24

Hi,

#2562. What does the medical term Granuloma mean?

#8 Re: Jai Ganesh's Puzzles » General Quiz » Yesterday 14:44:27

Hi,

#9785. Name the American retail businesswoman, writer, and television personality (born August 3, 1941). She gained success through a variety of business ventures, encompassing publishing, broadcasting, merchandising and e-commerce.

#9786. Name the American businesswoman who has been the chair and chief executive officer (CEO) of General Motors since January 15, 2014 (born December 24, 1961). She is the first female CEO of a 'Big Three' automaker.

#10 Re: Introductions » hello everyone!!! » Yesterday 13:47:17

Hi MathAppreciator,

Welcome to the forum!

#11 Re: This is Cool » Miscellany » Yesterday 00:10:52

2132) Chemistry

Gist

Chemistry is a branch of natural science that deals principally with the properties of substances, the changes they undergo, and the natural laws that describe these changes.

Summary

Chemistry, the science that deals with the properties, composition, and structure of substances (defined as elements and compounds), the transformations they undergo, and the energy that is released or absorbed during these processes. Every substance, whether naturally occurring or artificially produced, consists of one or more of the hundred-odd species of atoms that have been identified as elements. Although these atoms, in turn, are composed of more elementary particles, they are the basic building blocks of chemical substances; there is no quantity of oxygen, mercury, or gold, for example, smaller than an atom of that substance. Chemistry, therefore, is concerned not with the subatomic domain but with the properties of atoms and the laws governing their combinations and how the knowledge of these properties can be used to achieve specific purposes.

The great challenge in chemistry is the development of a coherent explanation of the complex behaviour of materials, why they appear as they do, what gives them their enduring properties, and how interactions among different substances can bring about the formation of new substances and the destruction of old ones. From the earliest attempts to understand the material world in rational terms, chemists have struggled to develop theories of matter that satisfactorily explain both permanence and change. The ordered assembly of indestructible atoms into small and large molecules, or extended networks of intermingled atoms, is generally accepted as the basis of permanence, while the reorganization of atoms or molecules into different arrangements lies behind theories of change. Thus chemistry involves the study of the atomic composition and structural architecture of substances, as well as the varied interactions among substances that can lead to sudden, often violent reactions.

Chemistry also is concerned with the utilization of natural substances and the creation of artificial ones. Cooking, fermentation, glass making, and metallurgy are all chemical processes that date from the beginnings of civilization. Today, vinyl, Teflon, liquid crystals, semiconductors, and superconductors represent the fruits of chemical technology. The 20th century saw dramatic advances in the comprehension of the marvelous and complex chemistry of living organisms, and a molecular interpretation of health and disease holds great promise. Modern chemistry, aided by increasingly sophisticated instruments, studies materials as small as single atoms and as large and complex as DNA (deoxyribonucleic acid), which contains millions of atoms. New substances can even be designed to bear desired characteristics and then synthesized. The rate at which chemical knowledge continues to accumulate is remarkable. Over time more than 8,000,000 different chemical substances, both natural and artificial, have been characterized and produced. The number was less than 500,000 as recently as 1965.

Intimately interconnected with the intellectual challenges of chemistry are those associated with industry. In the mid-19th century the German chemist Justus von Liebig commented that the wealth of a nation could be gauged by the amount of sulfuric acid it produced. This acid, essential to many manufacturing processes, remains today the leading chemical product of industrialized countries. As Liebig recognized, a country that produces large amounts of sulfuric acid is one with a strong chemical industry and a strong economy as a whole. The production, distribution, and utilization of a wide range of chemical products is common to all highly developed nations. In fact, one can say that the “iron age” of civilization is being replaced by a “polymer age,” for in some countries the total volume of polymers now produced exceeds that of iron.

Details

Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during reactions with other substances. Chemistry also addresses the nature of chemical bonds in chemical compounds.

In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both basic and applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties of the soil on the Moon (cosmochemistry), how medications work (pharmacology), and how to collect DNA evidence at a crime scene (forensics).

Chemistry has existed under various names since ancient times. It has evolved, and now chemistry encompasses various areas of specialisation, or subdisciplines, that continue to increase in number and interrelate to create further interdisciplinary fields of study. The applications of various fields of chemistry are used frequently for economic purposes in the chemical industry.

Etymology

The word chemistry comes from a modification during the Renaissance of the word alchemy, which referred to an earlier set of practices that encompassed elements of chemistry, metallurgy, philosophy, astrology, astronomy, mysticism, and medicine. Alchemy is often associated with the quest to turn lead or other base metals into gold, though alchemists were also interested in many of the questions of modern chemistry.

The modern word alchemy in turn is derived from the Arabic word al-kīmīā. This may have Egyptian origins since al-kīmīā is derived from the Ancient Greek, which is in turn derived from the word Kemet, which is the ancient name of Egypt in the Egyptian language. Alternately, al-kīmīā may derive from 'cast together'.

Modern principles

The current model of atomic structure is the quantum mechanical model. Traditional chemistry starts with the study of elementary particles, atoms, molecules, substances, metals, crystals and other aggregates of matter. Matter can be studied in solid, liquid, gas and plasma states, in isolation or in combination. The interactions, reactions and transformations that are studied in chemistry are usually the result of interactions between atoms, leading to rearrangements of the chemical bonds which hold atoms together. Such behaviors are studied in a chemistry laboratory.

The chemistry laboratory stereotypically uses various forms of laboratory glassware. However glassware is not central to chemistry, and a great deal of experimental (as well as applied/industrial) chemistry is done without it.

A chemical reaction is a transformation of some substances into one or more different substances. The basis of such a chemical transformation is the rearrangement of electrons in the chemical bonds between atoms. It can be symbolically depicted through a chemical equation, which usually involves atoms as subjects. The number of atoms on the left and the right in the equation for a chemical transformation is equal. (When the number of atoms on either side is unequal, the transformation is referred to as a nuclear reaction or radioactive decay.) The type of chemical reactions a substance may undergo and the energy changes that may accompany it are constrained by certain basic rules, known as chemical laws.

Energy and entropy considerations are invariably important in almost all chemical studies. Chemical substances are classified in terms of their structure, phase, as well as their chemical compositions. They can be analyzed using the tools of chemical analysis, e.g. spectroscopy and chromatography. Scientists engaged in chemical research are known as chemists. Most chemists specialize in one or more sub-disciplines. Several concepts are essential for the study of chemistry; some of them are:

Matter

In chemistry, matter is defined as anything that has rest mass and volume (it takes up space) and is made up of particles. The particles that make up matter have rest mass as well – not all particles have rest mass, such as the photon. Matter can be a pure chemical substance or a mixture of substances.

Atom

The atom is the basic unit of chemistry. It consists of a dense core called the atomic nucleus surrounded by a space occupied by an electron cloud. The nucleus is made up of positively charged protons and uncharged neutrons (together called nucleons), while the electron cloud consists of negatively charged electrons which orbit the nucleus. In a neutral atom, the negatively charged electrons balance out the positive charge of the protons. The nucleus is dense; the mass of a nucleon is approximately 1,836 times that of an electron, yet the radius of an atom is about 10,000 times that of its nucleus.

The atom is also the smallest entity that can be envisaged to retain the chemical properties of the element, such as electronegativity, ionization potential, preferred oxidation state(s), coordination number, and preferred types of bonds to form (e.g., metallic, ionic, covalent).

Element

A chemical element is a pure substance which is composed of a single type of atom, characterized by its particular number of protons in the nuclei of its atoms, known as the atomic number and represented by the symbol Z. The mass number is the sum of the number of protons and neutrons in a nucleus. Although all the nuclei of all atoms belonging to one element will have the same atomic number, they may not necessarily have the same mass number; atoms of an element which have different mass numbers are known as isotopes. For example, all atoms with 6 protons in their nuclei are atoms of the chemical element carbon, but atoms of carbon may have mass numbers of 12 or 13.

The standard presentation of the chemical elements is in the periodic table, which orders elements by atomic number. The periodic table is arranged in groups, or columns, and periods, or rows. The periodic table is useful in identifying periodic trends.

Compound

A compound is a pure chemical substance composed of more than one element. The properties of a compound bear little similarity to those of its elements. The standard nomenclature of compounds is set by the International Union of Pure and Applied Chemistry (IUPAC). Organic compounds are named according to the organic nomenclature system. The names for inorganic compounds are created according to the inorganic nomenclature system. When a compound has more than one component, then they are divided into two classes, the electropositive and the electronegative components. In addition the Chemical Abstracts Service has devised a method to index chemical substances. In this scheme each chemical substance is identifiable by a number known as its CAS registry number.

Molecule

A molecule is the smallest indivisible portion of a pure chemical substance that has its unique set of chemical properties, that is, its potential to undergo a certain set of chemical reactions with other substances. However, this definition only works well for substances that are composed of molecules, which is not true of many substances (see below). Molecules are typically a set of atoms bound together by covalent bonds, such that the structure is electrically neutral and all valence electrons are paired with other electrons either in bonds or in lone pairs.

Thus, molecules exist as electrically neutral units, unlike ions. When this rule is broken, giving the "molecule" a charge, the result is sometimes named a molecular ion or a polyatomic ion. However, the discrete and separate nature of the molecular concept usually requires that molecular ions be present only in well-separated form, such as a directed beam in a vacuum in a mass spectrometer. Charged polyatomic collections residing in solids (for example, common sulfate or nitrate ions) are generally not considered "molecules" in chemistry. Some molecules contain one or more unpaired electrons, creating radicals. Most radicals are comparatively reactive, but some, such as nitric oxide (NO) can be stable.

The "inert" or noble gas elements (helium, neon, argon, krypton, xenon and radon) are composed of lone atoms as their smallest discrete unit, but the other isolated chemical elements consist of either molecules or networks of atoms bonded to each other in some way. Identifiable molecules compose familiar substances such as water, air, and many organic compounds like alcohol, sugar, gasoline, and the various pharmaceuticals.

However, not all substances or chemical compounds consist of discrete molecules, and indeed most of the solid substances that make up the solid crust, mantle, and core of the Earth are chemical compounds without molecules. These other types of substances, such as ionic compounds and network solids, are organized in such a way as to lack the existence of identifiable molecules per se. Instead, these substances are discussed in terms of formula units or unit cells as the smallest repeating structure within the substance. Examples of such substances are mineral salts (such as table salt), solids like carbon and diamond, metals, and familiar silica and silicate minerals such as quartz and granite.

One of the main characteristics of a molecule is its geometry often called its structure. While the structure of diatomic, triatomic or tetra-atomic molecules may be trivial, (linear, angular pyramidal etc.) the structure of polyatomic molecules, that are constituted of more than six atoms (of several elements) can be crucial for its chemical nature.

Substance and mixture

A chemical substance is a kind of matter with a definite composition and set of properties. A collection of substances is called a mixture. Examples of mixtures are air and alloys.

Mole and amount of substance

The mole is a unit of measurement that denotes an amount of substance (also called chemical amount). One mole is defined to contain exactly 6.02214076×{10}^{23} particles (atoms, molecules, ions, or electrons), where the number of particles per mole is known as the Avogadro constant. Molar concentration is the amount of a particular substance per volume of solution, and is commonly reported in mol/{dm}^3.

Additional Information

Chemistry is the scientific study of matter, its properties, composition, and interactions. It is often referred to as the central science because it connects and bridges the physical sciences, such as physics and biology. Understanding chemistry is crucial for comprehending the world around us, from the air we breathe to the food we eat and the materials we use in everyday life.

Chemistry has many sub-disciplines such as analytical chemistry, physical chemistry, biochemistry, and more. Chemistry plays a crucial role in various industries, including pharmaceuticals, materials science, environmental science, and energy production, making it a cornerstone of modern science and technology

The area of science devoted to studying nature and also composition, properties, elements, and compounds that form matter as well as looking into their reactions forming new substances is chemistry. Chemistry has also been categorized further based on the particular areas of study.

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#12 This is Cool » Minkowski space » 2024-04-24 21:27:17

Jai Ganesh
Replies: 0

Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) combines inertial space and time manifolds with a non-inertial reference frame of space and time into a four-dimensional model relating a position (inertial frame of reference) to the field.

The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds".

Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events. Minkowski space differs from four-dimensional Euclidean space insofar as it treats time differently than the three spatial dimensions.

In 3-dimensional Euclidean space, the isometry group (maps preserving the regular Euclidean distance) is the Euclidean group. It is generated by rotations, reflections and translations. When time is appended as a fourth dimension, the further transformations of translations in time and Lorentz boosts are added, and the group of all these transformations is called the Poincaré group. Minkowski's model follows special relativity, where motion causes time dilation changing the scale applied to the frame in motion and shifts the phase of light.

Spacetime is equipped with an indefinite non-degenerate bilinear form, called the Minkowski metric, the Minkowski norm squared or Minkowski inner product depending on the context. The Minkowski inner product is defined so as to yield the spacetime interval between two events when given their coordinate difference vector as an argument. Equipped with this inner product, the mathematical model of spacetime is called Minkowski space. The group of transformations for Minkowski space that preserves the spacetime interval (as opposed to the spatial Euclidean distance) is the Poincaré group (as opposed to the Galilean group).

Hermann Minkowski

Hermann Minkowski (born June 22, 1864, Aleksotas, Russian Empire [now in Kaunas, Lithuania]—died Jan. 12, 1909, Göttingen, Germany) was a German mathematician who developed the geometrical theory of numbers and who made numerous contributions to number theory, mathematical physics, and the theory of relativity. His idea of combining the three dimensions of physical space with that of time into a four-dimensional “Minkowski space”—space-time—laid the mathematical foundations for Albert Einstein’s special theory of relativity.

The son of German parents living in Russia, Minkowski returned to Germany with them in 1872 and spent his youth in the royal Prussian city of Königsberg. A gifted prodigy, he began his studies at the University of Königsberg and the University of Berlin at age 15. Three years later he was awarded the “Grand Prix des Sciences Mathématiques” by the French Academy of Sciences for his paper on the representation of numbers as a sum of five squares. During his teenage years in Königsberg he met and befriended another young mathematical prodigy, David Hilbert, with whom he worked closely both at Königsberg and later at the University of Göttingen.

After earning his doctorate in 1885, Minkowski taught mathematics at the Universities of Bonn (1885–94), Königsberg (1894–96), Zürich (1896–1902), and Göttingen (1902–09). Together with Hilbert, he pursued research on the electron theory of the Dutch physicist Hendrik Lorentz and its modification in Einstein’s special theory of relativity. In Raum und Zeit (1907; “Space and Time”) Minkowski gave his famous four-dimensional geometry based on the group of Lorentz transformations of special relativity theory. His major work in number theory was Geometrie der Zahlen (1896; “Geometry of Numbers”). His works were collected in David Hilbert (ed.), Gesammelte Abhandlungen, 2 vol. (1911; “Collected Papers”).

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#13 Re: Dark Discussions at Cafe Infinity » crème de la crème » 2024-04-24 17:36:45

1441) John Vane

Summary

Sir John Robert Vane (born March 29, 1927, Tardebigg, Worcestershire, England—died November 19, 2004, Farnborough, Hampshire) was an English biochemist who, with Sune K. Bergström and Bengt Ingemar Samuelsson, won the Nobel Prize for Physiology or Medicine in 1982 for the isolation, identification, and analysis of prostaglandins. These are biochemical compounds that influence blood pressure, body temperature, allergic reactions, and other physiological phenomena in mammals.

Vane graduated from the University of Birmingham in 1946 and earned a doctorate at the University of Oxford in 1953. He spent several years on the faculty of Yale University (1953–55) in the United States before returning to England to join the Institute of Basic Medical Sciences of the University of London. In 1973 he became research director of the Wellcome Research Laboratories in Beckenham, Kent, a post he held until 1985. In 1986 Vane founded the William Harvey Research Institute, attached to St. Bartholomew’s Hospital in London, which funded cardiovascular research. He remained with the institute, in various positions, until his death.

As part of his Nobel Prize-winning work, Vane demonstrated that aspirin inhibits the formation of prostaglandins associated with pain, fever, and inflammation, thus providing a physiological rationale for the effectiveness of the world’s most widely used drug. He also discovered prostacyclin, an important prostaglandin that plays a vital role in the process of blood coagulation.

Vane, the recipient of numerous honours, was elected a fellow of the Royal Society in 1974 and was made an honorary member of the American Academy of Arts and Sciences in 1982. He was knighted in 1984.

Details

Sir John Robert Vane (29 March 1927 – 19 November 2004) was a British pharmacologist who was instrumental in the understanding of how aspirin produces pain-relief and anti-inflammatory effects and his work led to new treatments for heart and blood vessel disease and introduction of ACE inhibitors. He was awarded the Nobel Prize in Physiology or Medicine in 1982 along with Sune Bergström and Bengt Samuelsson for "their discoveries concerning prostaglandins and related biologically active substances".

Education and early life

Born in Tardebigge, Worcestershire, John Vane was one of three children and grew up in suburban Birmingham. His father, Maurice Vane, was the son of Jewish Russian immigrants and his mother, Frances Vane, came from a Worcestershire farming family. He attended a local state school from age 5, before moving on to King Edward's School in Edgbaston, Birmingham. An early interest in chemistry was to prove the inspiration for studying the subject at the University of Birmingham in 1944.

During his undergraduate studies, Vane became disenchanted with chemistry but still enjoyed experimentation. When Maurice Stacey, the Professor of Chemistry at Birmingham, was asked by Harold Burn to recommend a student to go to Oxford and study pharmacology, Vane jumped at the chance and moved to Burn's department in 1946. Under Burn's guidance, Vane found motivation and enthusiasm for pharmacology, writing: "[the] laboratory gradually became the most active and important centre for pharmacological research in the U.K. and the main school for training of young pharmacologists." Vane completed a Bachelor of Science degree in pharmacology and briefly went to work at the University of Sheffield, before coming back to Oxford to complete his Doctor of Philosophy degree in 1953[4] supervised by Geoffrey Dawes.

Career and research

After completing his DPhil, Vane worked as an assistant professor the Department of Pharmacology at Yale University before moving back to the United Kingdom to take up a post as a senior lecturer in the Institute of Basic Medical Sciences at the University of London in 1955.

University of London

Vane held a post at the University of London for 18 years, progressing from senior lecturer to Professor of Experimental Pharmacology in 1966 (at the Royal College of Surgeons). During that time he developed certain bioassay techniques and focussed his research on both angiotensin-converting enzyme and the actions of aspirin, eventually leading to the publication with Priscilla Piper of the relationship between aspirin and the prostaglandins that earned him the Nobel Prize in Physiology or Medicine in 1982.

Wellcome Foundation

In 1973, Vane left his academic post at the Royal College of Surgeons and took up the position as Director of Research at the Wellcome Foundation, taking a number of his colleagues with him who went on to form the Prostaglandin Research department. Under the leadership of Salvador Moncada, this group continued important research that eventually led to the discovery of prostacyclin.

Return to academia

In 1985, Vane returned to academic life and founded the William Harvey Research Institute at the Medical College of St Bartholomew's Hospital (now Barts and The London School of Medicine and Dentistry. At the William Harvey Research Institute, Vane's work focused on selective inhibitors of COX-2, and the interplay between nitric oxide and endothelin in the regulation of vascular function.

Awards and honours

Vane was elected a Fellow of the Royal Society (FRS) in 1974. He was also awarded honorary doctorate degrees from Jagiellonian University Medical College (formerly Copernicus Academy of Medicine) in 1977, Paris Descartes University in 1978, Mount Sinai School of Medicine in 1980 and the University of Aberdeen in 1983. He was awarded the Lasker Award in 1977 for the discovery of prostacyclin and was knighted in 1984 for his contributions to science. In 2000, Vane received the Golden Plate Award of the American Academy of Achievement.

Personal life

John Vane married, in 1948, (Elizabeth) Daphne Page and had 2 daughters. He died on 19 November 2004 in Princess Royal University Hospital, Kent, from long-term complications arising from leg and hip fractures he sustained in May of that year. Lady Vane died in 2021.

Additional Information

Prostaglandins are hormone-like substances that govern several important processes in the body. They also come into play when the body is under attack. In 1971 John Vane showed that acetylsalicylic acid, a substance found in pain-relieving and fever-reducing medications like aspirin, works by inhibiting the formation of prostglandins. In 1976 Vane discovered the prostacyclin prostglandin, which expands the smallest blood vessels and, unlike certain other prostglandins, inhibits the formation of blood particles called platelets that cause blood to coagulate.

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#14 Jokes » Corn Jokes - III » 2024-04-24 16:58:52

Jai Ganesh
Replies: 0

Q: What do you call a mythical veggie?
A: A unicorn.
* * *
Q: What do corn use for money?
A: Corn "Bread."
* * *
Q: What has ears but cannot hear?
A: A field of corn.
* * *
If corn oil comes from corn, what does baby oil come from?
* * *
Don't tell a secrets in a cornfield. There a too many ears.
* * *

#15 Re: Science HQ » Outer Space » 2024-04-24 16:46:31

Introduction

Through space exploration humans have learned a great deal about the planets, stars, and other objects in space. More than 5,000 spacecraft have been launched into space to gather information since 1957. They include spacecraft with humans on board, space probes, and satellites. The Soviet Union (now Russia) and the United States were originally the main countries exploring space. Many other countries are now involved.

Astronauts

Astronauts (called cosmonauts in Russia and taikonauts in China) go through a thorough training program. They study math and science in classrooms. They learn to operate their spacecraft by using computer-controlled simulators. These devices present astronauts with conditions that they will later experience during actual flight. Astronauts also must improve their physical fitness. They make special trips in airplanes to get used to the feeling of weightlessness.

Humans cannot survive in outer space on their own. The environment is not the same as it is on Earth. Astronauts therefore travel in space in tightly sealed compartments. They bring their own supply of oxygen with them. Once in space, astronauts may conduct scientific experiments. They also may make repairs to their spacecraft or other equipment in space. They wear heavy space suits for work outside the spacecraft.

The Race into Space

In the 1900s scientists developed rockets that could travel fast enough to escape the pull of the force called gravity. Gravity is a force on Earth that pulls objects toward the center of the planet. The development of powerful rockets allowed the Soviet Union to launch the first artificial satellite on October 4, 1957. It was called Sputnik 1, and it orbited around Earth. On November 3, 1957, the Soviet Union sent a dog into orbit. On April 12, 1961, the Russian cosmonaut Yury Gagarin became the first human to circle Earth in space. In 1963 Valentina Tereshkova became the first woman in space.

The National Aeronautics and Space Administration (NASA) took charge of the U.S. effort. The first U.S. satellite was launched on January 31, 1958. On May 5, 1961, astronaut Alan B. Shepard, Jr., became the first American to enter space. Shepard flew for only 15 minutes and did not complete an orbit around Earth. On February 20, 1962, John H. Glenn, Jr., completed three orbits around Earth. On July 20, 1969, astronaut Neil Armstrong became the first human to walk on the Moon.

Space Stations

Space stations are spacecraft that stay in orbit for a long period of time. Scientists can spend days or even months at a station doing experiments. The Soviet Union began launching space stations in 1971, and the United States followed in 1973. But these stations did not stay in space long. The Soviet station Mir stayed in orbit much longer, from 1986 to 2001.

In the 1990s the United States and 15 other countries agreed to build and operate a large space station together. The new project was called the International Space Station (ISS). Assembly of the ISS began in 1998. The first crew began to live in the station in November 2000.

Space Shuttles

In 1981 the United States launched the first reusable spacecraft, called a space shuttle. The main section had wings and was called the orbiter. Attached to the orbiter were rockets, fuel tanks, and oxygen tanks. These boosted the craft through the thickest part of Earth’s atmosphere. When their fuel was used up, the boosters fell into the ocean, where they could be recovered. At the end of a mission, the orbiter returned to Earth and landed like an airplane.

The first shuttle missions were successful. Astronaut Sally Ride became the first U.S. woman in space on June 18, 1983. But in January 1986 the shuttle Challenger exploded 73 seconds after liftoff. All seven crew members were killed. NASA stopped the shuttle program to study the cause of the explosion.

The United States returned to space in September 1988 with the launching of the shuttle Discovery. In 1990 Discovery put the Hubble Space Telescope into orbit around Earth. This telescope sends clear images of space back to Earth. But then in February 2003 the shuttle Columbia broke apart as it was returning to Earth. The seven crew members on board were killed. The shuttle program did not resume until 2005.

NASA ended the shuttle program in 2011. Later missions to space were expected to use Russian spacecraft or new spacecraft built by U.S. companies.

Space Probes

Space probes are vehicles that carry scientific equipment but no passengers. Some make one-way voyages into deep space. Probes are controlled from Earth by radio. They send back their findings the same way.

In the late 1950s the Soviet Union and the United States launched their first deep-space probes. Probes eventually landed on the planets Mars and Venus and flew past the planets Jupiter, Saturn, Uranus, and Neptune. They collected information on the planets’ atmospheres, moons, and ring systems. In the early 2000s scientists sent several new probes to explore Mars and other planets and objects in space.

#16 Dark Discussions at Cafe Infinity » Chance Quotes - II » 2024-04-24 16:33:43

Jai Ganesh
Replies: 0

Chance Quotes - II

1. Luck always favours the brave. And you must remember that brave are the people who follow their heart; brave are the people who take chances in life. Which also means you have to say no sometimes. I believe the power of no is greater than yes. - Preity Zinta

2. But we also believe in taking risks, because that's how you move things along. - Melinda Gates

3. I am a great believer in luck, and I find the harder I work the more I have of it. - Stephen Leacock

4. Some folk want their luck buttered. - Thomas Hardy

5. And when I was saying I want to become number one of the world and I was 7, 8 years old, most of the people were laughing to me. Because you know, it seemed like I have one percent chances to do that. And I've done it. - Novak Djokovic

6. I just do whatever it is that I believe I should do, regardless of the risks to my life. - Corazon Aquino

7. I guess I've always been attracted to people who stand out as individuals - people who are adventurous and take chances. - Carmen Electra

8. The true statesman is the one who is willing to take risks. - Charles de Gaulle

9. I'm the one who will take chances, not worry about the backlash. - Magic Johnson

10. I like entrepreneurial people; I like people who take risks. - Billie Jean King

11. God's dice always have a lucky roll. - Sophocles

12. Luck affects everything. Let your hook always be cast; in the stream where you least expect it there will be a fish. - Ovid.

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#19 Re: Jai Ganesh's Puzzles » General Quiz » 2024-04-24 15:06:02

Hi,

#9783. Name the Canadian-American executive, non-profit leader, and prominent women's-issues supporter based in New York City (born 1959). In April 2014, she became president and CEO of Grameen America, a nonprofit microfinance organization founded by Nobel Peace Prize winner, Muhammad Yunus. From 1999 until 2012, she served as the first female CEO and chairman of Avon Products, Inc., a multi-level marketing company. She was also the first woman to serve as Chairman of the Cosmetic, Toiletry & Fragrance Association, and Chairman of the World Federation of Direct Selling Associations.

#9784. Name the American businesswoman and politician, known primarily for her tenure as chief executive officer (CEO) of Hewlett-Packard (HP) from 1999 to 2005 (born September 6, 1954). She was the first woman to lead a Fortune Top-20 company.

#20 Re: Jai Ganesh's Puzzles » Doc, Doc! » 2024-04-24 14:23:18

Hi,

#2561. What does the medical term Testicular artery mean?

#23 Re: This is Cool » Miscellany » 2024-04-24 00:08:56

2131) Amputation

Gist

Amputation is the loss or removal of a body part such as a finger, toe, hand, foot, arm or leg. It can be a life changing experience affecting your ability to move, work, interact with others and maintain your independence.

Summary

Amputation is the removal of a limb by trauma, medical illness, or surgery. As a surgical measure, it is used to control pain or a disease process in the affected limb, such as malignancy or gangrene. In some cases, it is carried out on individuals as a preventive surgery for such problems. A special case is that of congenital amputation, a congenital disorder, where fetal limbs have been cut off by constrictive bands. In some countries, judicial amputation is currently used to punish people who commit crimes. Amputation has also been used as a tactic in war and acts of terrorism; it may also occur as a war injury. In some cultures and religions, minor amputations or mutilations are considered a ritual accomplishment. When done by a person, the person executing the amputation is an amputator. The oldest evidence of this practice comes from a skeleton found buried in Liang Tebo cave, East Kalimantan, Indonesian Borneo dating back to at least 31,000 years ago, where it was done when the amputee was a young child.

Details

Amputation is the surgical removal of all or part of a limb or extremity such as an arm, leg, foot, hand, toe, or finger.

About 1.8 million Americans are living with amputations. Amputation of the leg -- either above or below the knee -- is the most common amputation surgery.

Reasons for Amputation

There are many reasons an amputation may be necessary. The most common is poor circulation because of damage or narrowing of the arteries, called peripheral arterial disease. Without adequate blood flow, the body's cells cannot get oxygen and nutrients they need from the bloodstream. As a result, the affected tissue begins to die and infection may set in.

Other causes for amputation may include:

* Severe injury (from a vehicle accident or serious burn, for example)
* Cancerous tumor in the bone or muscle of the limb
* Serious infection that does not get better with antibiotics or other treatment
* Thickening of nerve tissue, called a neuroma
* Frostbite

The Amputation Procedure

An amputation usually requires a hospital stay of five to 14 days or more, depending on the surgery and complications. The procedure itself may vary, depending on the limb or extremity being amputated and the patient's general health.

Amputation may be done under general anesthesia (meaning the patient is asleep) or with spinal anesthesia, which numbs the body from the waist down.

When performing an amputation, the surgeon removes all damaged tissue while leaving as much healthy tissue as possible.

A doctor may use several methods to determine where to cut and how much tissue to remove. These include:

* Checking for a pulse close to where the surgeon is planning to cut
* Comparing skin temperatures of the affected limb with those of a healthy limb
* Looking for areas of reddened skin
* Checking to see if the skin near the site where the surgeon is planning to cut is still sensitive to touch

During the procedure itself, the surgeon will:

* Remove the diseased tissue and any crushed bone
* Smooth uneven areas of bone
* Seal off blood vessels and nerves
* Cut and shape muscles so that the stump, or end of the limb, will be able to have an artificial limb (prosthesis) attached to it

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The surgeon may choose to close the wound right away by sewing the skin flaps (called a closed amputation). Or the surgeon may leave the site open for several days in case there's a need to remove additional tissue.

The surgical team then places a sterile dressing on the wound and may place a stocking over the stump to hold drainage tubes or bandages. The doctor may place the limb in traction, in which a device holds it in position, or may use a splint.

Recovery From Amputation

Recovery from amputation depends on the type of procedure and anesthesia used.

In the hospital, the staff changes the dressings on the wound or teaches the patient to change them. The doctor monitors wound healing and any conditions that might interfere with healing, such as diabetes or hardening of the arteries. The doctor prescribes medications to ease pain and help prevent infection.

If the patient has problems with phantom pain (a sense of pain in the amputated limb) or grief over the lost limb, the doctor will prescribe medication and/or counseling, as necessary.

Physical therapy, beginning with gentle, stretching exercises, often begins soon after surgery. Practice with the artificial limb may begin as soon as 10 to 14 days after surgery.

Ideally, the wound should fully heal in about four to eight weeks. But the physical and emotional adjustment to losing a limb can be a long process. Long-term recovery and rehabilitation will include:

* Exercises to improve muscle strength and control
* Activities to help restore the ability to carry out daily activities and promote independence
* Use of artificial limbs and assistive devices
* Emotional support, including counseling, to help with grief over the loss of the limb and adjustment to the new body image

Additional Information:

Prevention

Methods in preventing amputation, limb-sparing techniques, depend on the problems that might cause amputations to be necessary. Chronic infections, often caused by diabetes or decubitus ulcers in bedridden patients, are common causes of infections that lead to gangrene, which, when widespread, necessitates amputation.

There are two key challenges: first, many patients have impaired circulation in their extremities, and second, they have difficulty curing infections in limbs with poor blood circulation.

Crush injuries where there is extensive tissue damage and poor circulation also benefit from hyperbaric oxygen therapy (HBOT). The high level of oxygenation and revascularization speed up recovery times and prevent infections.

A study found that the patented method called Circulator Boot achieved significant results in prevention of amputation in patients with diabetes and arteriosclerosis. Another study found it also effective for healing limb ulcers caused by peripheral vascular disease. The boot checks the heart rhythm and compresses the limb between heartbeats; the compression helps cure the wounds in the walls of veins and arteries, and helps to push the blood back to the heart.

For victims of trauma, advances in microsurgery in the 1970s have made replantations of severed body parts possible.

The establishment of laws, rules, and guidelines, and employment of modern equipment help protect people from traumatic amputations.

Prognosis

The individual may experience psychological trauma and emotional discomfort. The stump will remain an area of reduced mechanical stability. Limb loss can present significant or even drastic practical limitations.

A large proportion of amputees (50–80%) experience the phenomenon of phantom limbs; they feel body parts that are no longer there. These limbs can itch, ache, burn, feel tense, dry or wet, locked in or trapped or they can feel as if they are moving. Some scientists believe it has to do with a kind of neural map that the brain has of the body, which sends information to the rest of the brain about limbs regardless of their existence. Phantom sensations and phantom pain may also occur after the removal of body parts other than the limbs, e.g. after amputation of the breast, extraction of a tooth (phantom tooth pain) or removal of an eye (phantom eye syndrome).

A similar phenomenon is unexplained sensation in a body part unrelated to the amputated limb. It has been hypothesized that the portion of the brain responsible for processing stimulation from amputated limbs, being deprived of input, expands into the surrounding brain, such that an individual who has had an arm amputated will experience unexplained pressure or movement on his face or head.

In many cases, the phantom limb aids in adaptation to a prosthesis, as it permits the person to experience proprioception of the prosthetic limb. To support improved resistance or usability, comfort or healing, some type of stump socks may be worn instead of or as part of wearing a prosthesis.

Another side effect can be heterotopic ossification, especially when a bone injury is combined with a head injury. The brain signals the bone to grow instead of scar tissue to form, and nodules and other growth can interfere with prosthetics and sometimes require further operations. This type of injury has been especially common among soldiers wounded by improvised explosive devices in the Iraq War.

Due to technological advances in prosthetics, many amputees live active lives with little restriction. Organizations such as the Challenged Athletes Foundation have been developed to give amputees the opportunity to be involved in athletics and adaptive sports such as amputee soccer.

Nearly half of the individuals who have an amputation due to vascular disease will die within 5 years, usually secondary to the extensive co-morbidities rather than due to direct consequences of amputation. This is higher than the five year mortality rates for breast cancer, colon cancer, and prostate cancer. Of persons with diabetes who have a lower extremity amputation, up to 55% will require amputation of the second leg within two to three years.

Amputation is surgery to remove all or part of a limb or extremity (outer limbs). Common types of amputation involve:

* Above-knee amputation, removing part of the thigh, knee, shin, foot and toes.
* Below-knee amputation, removing the lower leg, foot and toes.
* Arm amputation.
* Hand amputation.
* Finger amputation.
* Foot amputation, removing part of the foot.
* Toe amputation.

Why are amputations done?

Amputation can be necessary to keep an infection from spreading through your limbs and to manage pain. The most common reason for an amputation is a wound that does not heal. Often this can be from not having enough blood flow to that limb.

After a severe injury, such as a crushing injury, amputation may be necessary if the surgeon cannot repair your limb.

You also may need an amputation if you have:

* Cancerous tumors in the limb.
* Frostbite.
* Gangrene (tissue death).
* Neuroma, or thickening of nerve tissue.
* Peripheral arterial disease (PAD), or blockage of the arteries.
* Severe injury, such as from a car accident.
* Diabetes that leads to nonhealing or infected wounds or tissue death.

amputee-care-feature.jpg

#24 Re: Science HQ » Outer Space » 2024-04-23 22:49:23

Big Bang : The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed in 1927 by Roman Catholic priest and physicist Georges Lemaître. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The overall uniformity of the universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments. However, physics currently lacks a widely accepted theory of quantum gravity that can successfully model the earliest conditions of the Big Bang.

Crucially, these models are compatible with the Hubble–Lemaître law—the observation that the farther away a galaxy is, the faster it is moving away from Earth. Extrapolating this cosmic expansion backwards in time using the known laws of physics, the models describe an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity"). In 1964 the CMB was discovered, which convinced many cosmologists that the competing steady-state model of cosmic evolution was falsified, since the Big Bang models predict a uniform background radiation caused by high temperatures and densities in the distant past. A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted. Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated 13.787±0.020 billion years ago, which is considered the age of the universe.

There remain aspects of the observed universe that are not yet adequately explained by the Big Bang models. After its initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, and later atoms. The unequal abundances of matter and antimatter that allowed this to occur is an unexplained effect known as baryon asymmetry. These primordial elements—mostly hydrogen, with some helium and lithium—later coalesced through gravity, forming early stars and galaxies. Astronomers observe the gravitational effects of an unknown dark matter surrounding galaxies. Most of the gravitational potential in the universe seems to be in this form, and the Big Bang models and various observations indicate that this excess gravitational potential is not created by baryonic matter, such as normal atoms. Measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to an unexplained phenomenon known as dark energy.

Second part:

Humans have been present in space either, in the common sense, through their direct presence and activity like human spaceflight, or through mediation of their presence and activity like with uncrewed spaceflight, making "telepresence" possible. Human presence in space, particularly through mediation, can take many physical forms from space debris, uncrewed spacecraft, artificial satellites, space observatories, crewed spacecraft, art in space, to human outposts in outer space such as space stations. While human presence in space, particularly its continuation and permanence can be a goal in itself, human presence can have a range of purposes and modes from space exploration, commercial use of space to space settlement or even colonization and militarisation of space. Human presence in space is realized and sustained through the advancement and application of space sciences, particularly astronautics in the form of spaceflight and space infrastructure.

Humans have achieved some mediated presence throughout the Solar System, but the most extensive presence has been in orbit around Earth. Humans have sustained direct presence in orbit around Earth since the year 2000 through continuously crewing the ISS, and with few interruptions through crewing the space station Mir since the later 1980s. The increasing and extensive human presence in orbital space around Earth, beside its benefits, has also produced a threat to it by carrying with it space debris, potentially cascading into the so-called Kessler syndrome. This has raised the need for regulation and mitigation of such to secure a sustainable access to outer space.

Securing the access to space and human presence in space has been pursued and allowed by the establishment of space law and space industry, creating a space infrastructure. But sustainability has remained a challenging goal, with the United Nations seeing the need to advance long-term sustainability of outer space activities in space science and application, and the United States having it as a crucial goal of its contemporary space policy and space program.

#25 Re: Help Me ! » LaTeX - A Crash Course » 2024-04-23 22:37:52

Annulus

Annulus

An annulus is an inner region between two concentric circles i.e. two or more circles sharing the same center point. The annulus is shaped like a ring and has many applications in mathematics that we will be learning in this article. Some of the real-life examples are a doughnut, finger rings. etc. Let us learn more about the shape of the annulus and solve a few examples to understand the concept better.

Annulus Definition

An annulus is a two-dimensional flat figure shaped in a circular form which is constructed by two concentric circles. The region or the area formed in between these two concentric circles is called the annulus. Since it is a flat figure in a circular form, the edges are two circles with the same center. It is considered a circular disk having a circular hole in the middle.

Annulus Meaning

The word annulus is derived from a Latin word, 'annuli', meaning little rings. The shape of the annulus is flat and circular with a hole in between, much like a throw ring or a circular disc. Look at the image below showing two circles i.e. one small circle also called an inner circle and a big circle also called the outer circle. The point which is marked as red is the center of both circles. The shaded colored area, between the boundary of these two circles, is known as an annulus.

Area of the Annulus

The annulus area is the area of the ring-shaped space i.e. the enclosed region between the two concentric circles. To calculate the area of the annulus, we need the area of both the inner circle and the outer circle. The dimensions of an annulus are defined by the two radii R, and r, which are the radii of the outer ring and the inner ring respectively. Once the measurements of both the radii are known, we can calculate the area by subtracting the area of the small circle from the big circle. Hence, the formula used for finding the area of the annulus is:

Area \ of \ Outer \ Circle = \pi{R^2}

gives

Area \ of \ Inner \ Circle = \pi{r^2}

gives

Area of Annulus = Area of Outer Circle – Area of Inner Circle

Therefore, Area of Annulus =

\pi(R^2-r^2)

gives

square units, or it can be written as

\pi(R + r)(R - r)

gives

(R square units, where R is the radius of the outer circle, r is the radius of the inner circle, and

\pi

gives

(pi) is approximately 3.142. The area of the outer (bigger) circle - the area of the inner (smaller) circle = the area of the annulus.

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