Surface tension is an effect where the surface of a liquid is strong. The surface can hold up a weight, and the surface of a water droplet holds the droplet together, in a ball shape. Some small things can float on a surface because of surface tension, even though they normally could not float. Some insects (e.g. water striders) can run on the surface of water because of this. This property is caused by the molecules in the liquid being attracted to each other (cohesion), and is responsible for many of the behaviors of liquids.

Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.

In materials science, surface tension is used for either surface stress or surface free energy.

Causes

The cohesive forces among the liquid molecules cause surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some internal pressure and forces liquid surfaces to contract to the minimal area.

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be perfectly spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

Another way to view it is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules). So, the boundary molecules have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized quantity of boundary molecules results in a minimized surface area.

As a result of surface area minimization, a surface will assume the smoothest shape it can. Any curvature in the surface shape results in greater area and a higher energy. So, the surface will push back against any curvature in much the same way as a ball pushed uphill will push back to minimize its gravitational potential energy.

Effects in everyday life

Water
Studying water shows several effects of surface tension:

A. Rain water forms beads on the surface of a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.

B. Formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.

C. Objects denser than water still float when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect's feet cause indentations in the water's surface, increasing its surface area.

D. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called "interface tension", but its physics are the same.

E. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol. It is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

Surfactants
Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

 Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Notice that surfactants actually reduce the surface tension of water by a factor of three or more.
 Emulsions are a type of solution in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

Basic physics

Two definitions

Surface tension, represented by the symbol γ is defined as the force along a line of unit length, where the force is parallel to the surface but perpendicular to the line. One way to picture this is to imagine a flat soap film bounded on one side by a taut thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2L (the factor of 2 is because the soap film has two sides, hence two surfaces). Surface tension is therefore measured in forces per unit length. Its SI unit is newton per meter but the cgs unit of dyne per cm is also used. One dyn/cm corresponds to 0.001 N/m.

An equivalent definition, one that is useful in thermodynamics, is work done per unit area. As such, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, δA, is needed. This work is stored as potential energy. Consequently surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm2. Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume.

The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.

Surface curvature and pressure

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation:

where:
Δp is the pressure difference.
 is surface tension.
Rx and Ry are radii of curvature in each of the axes that are parallel to the surface.

The quantity in parentheses on the right hand side is in fact (twice) the mean curvature of the surface (depending on normalization).

Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension. (Another example is the shape of the impressions that a water strider's feet make on the surface of a pond).

The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)

Liquid surface

It is hard to find the shape of the minimal surface bounded by some arbitrary shaped frame using just mathematics. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles

The surface of any liquid is an interface between that liquid and some other medium. The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid's interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater than) its surface tension with the walls of a container. Where the two surfaces meet, the geometry will balance all forces.

Where the two surfaces meet, they form a contact angle, , which is the angle the tangent to the surface makes with the solid surface. The diagram to the right shows two examples. Tension forces are shown for the liquid-air interface, the liquid-solid interface, and the solid-air interface. The example on the left is where the difference between the liquid-solid and solid-air surface tension, , is less than the liquid-air surface tension, , but is still positive, that is

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium. The horizontal component of  is canceled by the adhesive force, .

The more important balance of forces, though, is in the vertical direction. The vertical component of  must exactly cancel the force, .

Since the forces are in direct proportion to their respective surface tensions, we also have:

where
 is the liquid-solid surface tension,
  is the liquid-air surface tension,
  is the solid-air surface tension,
  is the contact angle, where a concave meniscus has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.

This means that although the difference between the liquid-solid and solid-air surface tension, , is difficult to measure directly, it can be inferred from the liquid-air surface tension, , and the equilibrium contact angle, , which is a function of the easily measurable advancing and receding contact angles (see main article contact angle).

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid-solid/solid-air surface tension difference must be negative:

Special contact angles
Observe that in the special case of a water-silver interface where the contact angle is equal to 90°, the liquid-solid/solid-air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon approaches this. Contact angle of 180° occurs when the liquid-solid surface tension is exactly equal to the liquid-air surface tension.

Methods of measurement

Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimal depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed.

 Du Noüy Ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on this measuring technique. Maximum pull exerted on the ring by the surface is measured.
 Du Noüy-Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds. First commercial multichannel tensiometers [CMCeeker] were recently built based on this principle.
 Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.
 Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.
 Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For details, see Drop.
 Bubble pressure method (Jaeger's method): A measurement technique for determining surface tension at short surface ages. Maximum pressure of each bubble is measured.
 Drop volume method: A method for determining interfacial tension as a function of interface age. Liquid of one density is pumped into a second liquid of a different density and time between drops produced is measured.
 Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed below.
 Stalagmometric method: A method of weighting and reading a drop of liquid.
 Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).
 Vibrational frequency of levitated drops: The surface tension of superfluid 4He has been measured by studying the natural frequency of vibrational oscillations of drops held in the air by magnetics. This value is estimated to be 0.375 dyn/cm at T = 0° K.

Effects

Liquid in a vertical tube

An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Torricelli's vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

We consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height the column is lifted to is given by:

where

  is the height the liquid is lifted,
  is the liquid-air surface tension,
  is the density of the liquid,
  is the radius of the capillary,
  is the acceleration due to gravity,
  is the angle of contact described above. If  is greater than 90°, as with mercury in a glass container, the liquid will be depressed rather than lifted.

Puddles on a surface

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimeter thick, and no thinner. Again this is due to the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only if the liquid does not adhere to the flat surface material. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:

where

{|
|  is the depth of the puddle in centimeters or meters.
|-
|  is the surface tension of the liquid in dynes per centimeter or newtons per meter.
|-
|  is the acceleration due to gravity and is equal to 980 cm/s2 or 9.8 m/s2
|-
|  is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter
|}

In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:

For mercury on glass, γHg = 487 dyn/cm, ρHg = 13.5 g/cm3 and θ = 140°, which gives hHg = 0.36 cm. For water on paraffin at 25 °C, γ = 72 dyn/cm, ρ = 1.0 g/cm3, and θ = 107° which gives hH2O = 0.44 cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.

The breakup of streams into drops

In day-to-day life we all observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability, which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

Data table

Gallery of effects

Notes

References

Other websites

 On surface tension and interesting real-world cases
 MIT Lecture Notes on Surface Tension
 Surface Tensions of Various Liquids
 Calculation of temperature-dependent surface tensions for some common components
 Surface Tension Calculator For Aqueous Solutions Containing the Ions H+, NH4+, Na+, K+, Mg2+, Ca2+, SO42–, NO3–, Cl–, CO32–, Br– and OH–.
 The Bubble Wall (Audio slideshow from the National High Magnetic Field Laboratory explaining cohesion, surface tension and hydrogen bonds)

Basic physics ideas
Fluid mechanics

Surface tension


A pixel (short for picture element) is a single point in a picture. On the monitor of a computer, a pixel is usually a square. Every pixel has a color and all the pixels together are the picture. The color of a pixel can be stored by using a combination of red, green and blue (RGB) but other combinations are also possible, such as cyan, magenta, yellow and black (CMYK).

The word "pixel"
The word "pixel" was first used in a paper by Frederic C. Billingsley in 1965. He did not create the word himself. He got it from Keith E. McFarland but Keith does not know where he got it from. Keith said that the word was in use in those days.

The word "pixel" uses "pix" as a shorter word (an abbreviation) for "picture". The word pix was first used in 1932 in Variety, a magazine. It was an abbreviation for "pictures" or movies. By 1938 the word "pix" was also used for pictures that did not move (still pictures).

The word "picture element" is even older. For example, the German word Bildpunkt (which means "picture point") was used in a 1888 patent of Paul Gottlieb Nipkow.

Related pages
 Display resolution
 Raster graphics

Computer graphics

Pixel


The Arabian horse is a breed famous for beauty and stamina. It is one of the oldest horse breeds in the world. Arabian horses are bred with horses of other breeds to add speed, beauty, endurance, and strong bones. Today, Arabian ancestors are found in almost every breed of riding horse.

The Arabian horse developed in the deserts of Arabia by the Bedouin people. People sometimes brought their horses into family tent for shelter and protection. This close relationship with humans made the Arabian a horse with a kind temper and quick to learn. It also was used as a war horse. This meant that it needed speed and to be very alert. This blend of traits makes it necessary for people today to treat Arabian horses with kindness and respect.

Breed Traits
Arabian horses have triangle-shaped heads, a wide forehead, big eyes, large nostrils, and small muzzles (noses). Most have a concave or "dished" profile. They have a slim, arched neck, smooth hindquarters and a naturally high-carried tail. Arabians have strong bone and good feet. They are especially noted for their excellent endurance. Arabians' hair coat colors are bay, gray, chestnut, and black. Arabians can have robicono and/or sabino genes. All Arabians have black skin under their hair coat, except under white markings.

The Bedouin sold many Arabian horses to people from Europe. Other Arabian horses were captured in war and taken to other countries outside of the Middle East. Today, Arabian horses are found all over the world. Arabian horse families are now labeled by where their most recent ancestors were bred, such as "Polish," "Spanish," "Crabbet" (from England), "Russian," "Egyptian", and "Domestic" (in the United States), and "Weil-Marbach" in Germany. For example, a horse called a "Polish Arabian" is an Arabian horse who has recent ancestors that were bred at farms in Poland, from horses the Polish people bought from the Bedouin in Arabia many centuries ago.

Uses
Arabians compete in many places, including horse racing, horse shows, Endurance riding, show jumping, and more. They also make good pleasure, trail, and working ranch horses for people who do not like competitive events. Arabians also are seen in movies, parades, circuses and other places where horses are used.

History

There are many legends and myths about Arabian horses. One legend says that the prophet Muhammad selected his five finest mares (female horses), called Al Khamsa ("the five") to be the foundation of the Arabian breed. Another legend says the Queen of Sheba gave an Arabian mare to King Solomon, and that is how the breed began. Yet another story says Allah made the Arabian horse from the south wind, saying, "I create thee, Oh Arabian...I give thee flight without wings."

In real history, Arabians are one of the oldest human-developed horse breeds in the world. Pictures of "Proto-Arabian" horses that looked a lot like modern Arabian horses were painted on rocks in the Arabian Peninsula as far back as 2,500 B.C. The ancestors of the Bedouin probably tamed horses not long after they tamed the camel. A horse skeleton was unearthed in the Sinai peninsula, dated to 1700 B.C., and is considered the earliest proof of the horse in Ancient Egypt. It was probably brought by the Hyksos invaders. This horse had a wedge-shaped head, large eye and small muzzle, just like the Arabian horse today.

In the desert, humans were the only source of food and water for the Arabian horse. Where there was no pasture, the Bedouin fed their horses dates, a fruit of the date palm tree, and camel's milk. Arabians needed to live on very little food, and survive a dry climate that was very hot in the day but very cold at night. Weak horses did not live, and the horses who survived the desert also had to survive being ridden for war. Therefore, the Arabian horse became very tough and able to live in a harsh world.

Famous Arabian horses
Napoleon rode a gray Arabian stallion named Marengo. George Washington rode a half-Arabian named Blueskin during the American Revolution. A fictional horse, "The Black Stallion," was played by a real Arabian stallion named Cass Ole in the movie that was based on the book by Walter Farley.

Aziziye Stud
In 1864 the Sultan Abdulaziz, founded a new Horse stud with Arabian horses and sent a commission to purchase in Bialocerkiew, the stud of Count Branicki in Poland, whose breeding have a very good reputation. The Commission purchased 92 horses, including some descendants of the 1855 stallion Indjanin imported from England.

Other websites
 Arabian Horse Association (USA)
 Arabian Horse site (AR)

Horse breeds

Arabian horse


Mikoyan is a Russian company that designs fighter airplanes. The company was first formed in December 1939 as a design office called Mikoyan-Gurevich or MiG, this was because its designers were Artem Mikoyan and Mikhail Gurevich. Mikoyan will join other Russian airplane companies in a new company called United Aircraft Corporation.

History
In 1939 Russia was part of the Soviet Union and was communist. In the Soviet communist system there were two types of airplane companies, companies that designed aircraft known as design offices or OKB, and companies that made airplanes called zavods. Artom Mikoyan and Mikhail Gurevich had been designers in another design office helping a designer called Nikolai Polikarpov. One airplane design that Artem Mikoyan and Mikhail Gurevich worked on at Polikarpov was called the I-200. When Nikolai Polikarpov lost the trust of the Soviet leader Stalin, Artem Mikoyan and Mikhail Gurevich were given the I-200 design to finish. This airplane was given a new name and was called the Mikoyan-Gurevich MiG-1. As it was being made, ways to make the MiG-1 into a better airplane were found and airplanes with these changes became known as the MiG-3 and later the MiG-7. However even with changes the MiG fighter airplanes were not as good as the fighter airplanes designed by the design offices of Lavochkin or Yakovlev.

After World War II Mikoyan-Gurevich designed jet aircraft. In the Soviet system the airplane designs of the design offices would compete to see which was the best.  When the best design had been found the design would be built by the airplane manufacturing company.  Even though Mikoyan-Gurevich airplanes in World War II had not been as good as airplanes by Lavochkin or Yakovlev. Mikoyan-Gurevich jet aircraft won more of the competitions to be sent to the zavods and in the time of the Cold War Mikoyan-Gurevich, together with another design office called Sukhoi, became one of the two most important design offices of fighter planes in the Soviet Union.

In the Soviet system decisions were made to protect the government from its own soldiers. In many countries there is only one airforce, the Soviet Union had five airforces. Two of these airforces were the main users of Soviet fighter airplanes. One airforce was called PVO Strany, this airforce was used to defend the cities and land of the Soviet Union. One airforce was called Frontal Aviation, this airforce was used to defend the Soviet Union's ground soldiers against enemy fighter airplanes, and to attack enemy ground forces. Mikoyan-Gurevich became the main designer of aircraft for Frontal Aviation.

Aircraft made

Mikoyan has designed the following airplanes:

 Mikoyan MiG-1
 Mikoyan MiG-3 (also called MiG-7)
 MiG DIS
 MiG-9 Fargo
 MiG-15 Fagot
 MiG-17 Fresco
 MiG-19 Farmer
 MiG-21 Fishbed
 MiG-23 Flogger
 MiG-25 Foxbat
 MiG-27 Flogger
 MiG-29 Fulcrum
 MiG-31 Foxhound

Companies of Russia
Aircraft companies
1939 establishments in Europe
Transport in Russia

Mikoyan


A powiat (pronounced ; Polish plural: powiaty) is the second-level unit of local government and administration in Poland, equivalent to a county, district or prefecture (LAU-1 [formerly NUTS-4]) in other countries. The term "powiat" is most often translated into English as "county" or "district" (sometimes "poviat"). In historical contexts, this may be confusing because the Polish term hrabstwo (an administrative unit administered/owned by a hrabia (count) is also literally translated as "county".

A powiat is part of a larger unit, the voivodeship (Polish województwo) or province.

A powiat is usually subdivided into gminas (in English, often referred to as "communes" or "municipalities").  Major towns and cities, however, function as separate counties in their own right, without subdivision into gminas. They are termed "city counties" (powiaty grodzkie or, more formally, miasta na prawach powiatu) and have roughly the same status as former county boroughs in the UK.  The other type of powiats are termed "land counties" (powiaty ziemskie).

As of 2018, there were 380 powiat-level entities: 314 land counties, and 66 city counties. For a complete alphabetical listing, see "List of Polish counties". For tables of counties by voivodeship, see the articles on the individual voivodeships (e.g., Greater Poland Voivodeship).

History
The history of Polish powiats goes back to the second half of the 14th century. They remained the basic unit of territorial organization in Poland, then in the Polish–Lithuanian Commonwealth, until the latter's partitioning in 1795.

In the 19th century, the powiats continued to function in the part of Poland that had been incorporated into the Russian Empire ("Congress Poland")—the equivalent of the Russian uyezd–and, in the German-governed Grand Duchy of Poznań, as the Polish equivalent of the German Kreis.

After Poland regained independence in 1918, the powiats were again the second-level territorial units.

Powiats were abolished in 1975 in favour of a larger number of voivodeships but were reintroduced on 1 January 1999. This reform also created 16 larger voivodeships.

Functioning
Legislative power within a powiat is vested in an elected council (rada powiatu), while local executive power is vested in an executive board (zarząd powiatu) headed by the starosta, elected by the council. The administrative offices headed by the starosta are called the starostwo. However, in city counties these institutions do not exist separatelytheir powers and functions are exercised by the city council (rada miasta), the directly elected mayor (burmistrz or prezydent), and the city office/town hall (urząd miasta).

Sometimes, a powiat has its seat outside its territory. For example, Poznań County (powiat poznański) has its offices in Poznań, although Poznań is itself a city county, and is therefore not part of Poznań County.

Powiats have relatively limited powers since many local and regional matters are dealt with either at gmina or voivodeship level. Some of the main areas in which the powiat authorities have decision-making powers and competences include:

 education at the high-school level (the gminas run primary and middle schools)
 healthcare (at the county level)
 public transport
 maintenance of certain designated roads
 land surveying
 issuing of work permits to foreigners
 vehicle registration (see Polish car number plates).

Names and English equivalents
The Polish the name of a county, in the administrative sense, consists of the word powiat followed by a masculine-gender adjective (because powiat is a masculine noun). In most cases, this is the adjective formed from the name of the town or city where the county has its seat. Thus the county with its seat at the town of Kutno is named powiat kutnowski (Kutno County). (In modern Polish both parts of the name are written in lower case; however, names of powiats in the Grand Duchy of Poznań were written in upper case.) Suppose the name of the seat comprises a noun followed by an adjective, as in Maków Mazowiecki ("Mazovian Maków"). In that case, the adjective will generally be formed from the noun only (powiat makowski). There are also a few counties whose names are derived from the names of two towns (such as powiat czarnkowsko-trzcianecki, Czarnków-Trzcianka County), from the name of a city and a geographical adjective (powiat łódzki wschodni, Łódź East County), or a mountain range (powiat tatrzański, Tatra County).

There is more than one way to render such names into English. A common method is to translate the names as "(something County)", as in the examples above. (This system is the standard used in Wikipedia.) Thus in most cases, the English name for a powiat consists of the name of the city or town which is its seat, followed by the word County.

Different counties sometimes have the same name in Polish, since the names of different towns may have the same derived adjective. For example, the counties with their seats at Grodzisk Wielkopolski and Grodzisk Mazowiecki are both called powiat grodziski, and those with seats at Brzeg and Brzesko are both called powiat brzeski. In English, this ambiguity either does not occur (Brzeg County and Brzesko County) or can be avoided by using the complete name of the seat (Grodzisk Wielkopolski County and Grodzisk Mazowiecki County).

References
 Bankauskaite, V. et al. (2007), Patterns of decentralization across European health systems, in R.B. Saltman, V. Bankauskaite and K. Vrangbæk (ed.), "Decentralization in health care", London: Open University Press/McGraw-Hill.

See also
 Povit, equivalent in Ukraine

Types of administrative division
Former subdivisions of Lithuania
Former administrative divisions of Ukraine
Former subdivisions of Belarus
Administrative divisions of Poland

Powiat


A gamete is a specialized sex cell that fuses with another gamete during fertilization (conception) in organisms that reproduce sexually. Gametes are haploid—they have only one copy of each chromosome. All other cells in an animal are diploid—they have two copies of each chromosome. Gametes are produced by germ cells.

In species which produce two morphologically distinct types of gametes, and in which each individual produces only one type, a female is any individual which produces the larger type of gamete—called an ovum (or egg)—and a male produces the smaller type—called a spermatozoon (or sperm cell).

The name gamete was introduced by the Austrian biologist Gregor Mendel.

Gametogenesis
Gametogenesis is the development of diploid germ cells into haploid eggs or sperm, (respectively oogenesis and spermatogenesis). It is different for each species but the general stages are similar. The development of eggs (oogenesis) and sperm (spermatogenesis) have many features in common. They both involve:
 Meiosis
 Extensive morphological cell differentiation
 Unable to survive for very long if fertilization does not occur

They also have major differences, especially
 Different timing of maturation: oogenic meiosis is interrupted at one or more stages (for a long time) while spermatogenic meiosis is rapid and uninterrupted.

References

Reproductive system

Gamete


Orbital inclination is a term for the angle between two orbital planes. It is often used to describe the movement of celestial bodies such as stars and planets. In that context, one of the planes is the standard, or reference. Many stars are in a galaxy that has a galactic plane which is used as reference. For a planet's orbit, the inclination is the angle to the ecliptic plane. For a moon, an inclination of 0 degrees means the orbiting body orbits the planet in its equatorial plane, in the same direction as the planet rotates.

Orbits

Orbital inclination


The New York Mercantile Exchange (NYMEX) is a commodity futures exchange owned and operated by CME Group of Chicago. NYMEX is located at One North End Avenue in Brookfield Place in the Battery Park City section of Manhattan, New York City.

The company's two principal divisions are the New York Mercantile Exchange and Commodity Exchange, Inc (COMEX), once separately owned exchanges. NYMEX traces its history to 1882 and for most of its history, as was common of exchanges, it was owned by the members who traded there.  Later, NYMEX Holdings, Inc., the former parent company of the New York Mercantile Exchange and COMEX, went public and became listed on the New York Stock Exchange on November 17, 2006, under the ticker symbol NMX.  On March 17, 2008, Chicago based CME Group signed a definitive agreement to acquire NYMEX Holdings, Inc. for $11.2 billion in cash and stock and the takeover was completed in August 2008.  Both NYMEX and COMEX now operate as designated contract markets (DCM) of the CME Group.  The other two designated contract markets in the CME Group are the Chicago Mercantile Exchange and the Chicago Board of Trade.

The New York Mercantile Exchange handles billions of dollars' worth of oil transactions, energy carriers, metals, and other commodities being bought and sold on the trading floor and the overnight electronic trading computer systems for future delivery.  The prices quoted for transactions on the exchange are the basis for prices that people pay for various commodities throughout the world.

The floor of the NYMEX is regulated by the Commodity Futures Trading Commission, an independent agency of the United States government.  Each individual company that trades on the exchange must send its own independent brokers.  Therefore, a few employees on the floor of the exchange represent a big corporation and the exchange employees only record the transactions and have nothing to do with the actual trade.

Although mostly electronic since 2006, the NYMEX maintained a small venue, or "pit", that still practiced the open outcry trading system, in which traders employed shouting and complex hand gestures on the physical trading floor. A project to preserve the hand signals used at NYMEX has been published.
NYMEX closed the pit permanently at the end of trading Friday, December 30, 2016, because of shrinking volume.

Early history

Commodity exchanges began in the middle of the 19th century, when businessmen began organizing market forums to make buying and selling of commodities easier. These marketplaces provided a place for buyers and sellers to set the quality, standards, and establish rules of business. By the late 19th century there were about 1,600 marketplaces at ports and railroad stations. In 1872, a group of Manhattan dairy merchants got together and created the Butter and Cheese Exchange of New York. They were trying to bring order and standardization to the chaotic conditions that existed in their industry. Soon, egg trade became part of the business conducted on the exchange and the name was modified to the Butter, Cheese, and Egg Exchange. In 1882, the name finally changed to the New York Mercantile Exchange when opening trade to dried fruits, canned goods, and poultry.

As centralized warehouses were built into principal market centers such as New York and Chicago in the early 20th century, exchanges in smaller cities began to disappear giving more business to the exchanges such as the NYMEX in bigger cities. In 1933, the COMEX was established through the merger of four smaller exchanges; the National Metal Exchange, the Rubber Exchange of New York, the National Raw Silk Exchange, and the New York Hide Exchange. Through the 1970s, 80's and 90's COMEX, NYMEX, and other exchanges shared a single trading floor in 4 World Trade Center.

Goods
For years, the NYMEX traders had done a large business trading futures of Maine's potato crop. According to Leah McGrath Goodman's 2011 book The Asylum, manipulation in this market was commonplace, performed by various parties including potato inspectors and NYMEX traders. The worst incident was the 1970s potato bust, when Idaho potato magnate J. R. Simplot allegedly went short in huge numbers, leaving a large amount of contracts unsettled at the expiration date, resulting in a large number of defaulted delivery contracts. A public outcry followed, and the newly created Commodity Futures Trading Commission held hearings. NYMEX was barred not only from continuing to trade in potatoes futures, but from entering any new area in which it hadn't traded before. NYMEX's reputation was severely damaged, because, as future chairman Michel Marks told Goodman in his book, "The essence of an exchange is the sanctity of its contract."

When the potato ban came into effect, NYMEX's platinum, palladium and heating oil markets were not significantly affected. However, NYMEX's reputation suffered in Washington, D.C., especially with the regulations in the Commodity Futures Trading Commission (CFTC), the president of the exchange, Richard Leone brought in John Elting Treat, White House energy adviser to Presidents Carter and Reagan to help restore the credibility of NYMEX and to help the exchange explore the possibility of entering the petroleum market recognizing the great potential for moving well beyond the limited size of the New York Heating Oil market.  When Leone left NYMEX in 1981 as a result of a strong disagreement with the NYMEX board, John Elting Treat was asked to replace him as president.  The launching of the WTI crude oil contract was championed by Treat, who, with difficulty, convinced the board and the two Marks family members, veteran and highly respected floor trader Francis Marks and his son, Michael, who had just become chairman of the board, to take a chance on trading crude oil. Arnold Safir was one of the members of an advisory committee formed by Treat to help design the new contract. Treat, with Board Chairman Marks and the support of the rest of the NYMEX board, eventually chose West Texas Intermediate (WTI) as the traded product and Cushing, Oklahoma, as the delivery point. Robin Woodhead, who later became the first chairman of the International Petroleum Exchange (IPE) in London started an active dialogue with Treat about whether they could start a Brent Crude oil contracts. Treat was very supportive and  gave  Woodhead strong support and a lot of advice. Shortly thereafter, after substantial conversations, The IPE was formally launched and started trading Brent.

Treat and his research staff then began looking for other oil products to trade. Gasoline was clearly next on the product list but there was a lot of debate about where the delivery point should be.  The Gulf Coast was the easiest, but the exchange also looked at California markets, but decided they wouldn't work. Treat then started looking simultaneously at launching crude and later products options contracts.  He found that the existing NYMEX floor traders didn't have the mathematical skills necessary to trade options, so the exchange offered financial inducements to get members of the American Stock Exchange's options traders to come over and trade options on petroleum futures. Under Treat's leadership, NYMEX also began to research the potential for trading natural gas and electricity, but focused first on natural gas.  Product quality of natural gas was not an issue in that market, but the delivery point was a more difficult choice.

After launching the original crude oil futures contract, Treat began an aggressive marketing campaign to first bring in the large US and British oil companies and then moved on to pull in the large Middle East producers. It took almost a year to get the first US "majors"
to start trading, but several "majors" did not start for almost 5 years.  The initial resistance from the OPEC producers was almost impossible to break through, although some finally gave in, among the first being Venezuela. The rumors on the floor at that time were the Arab producers would trade gold futures as a proxy for oil prices (since the Arabs were major purchasers of gold and  would buy more when their pockets were filled by rising oil prices, and conversely sell when oil revenues fell and reduced their ability to buy gold).

After the potato ban, NYMEX's existence was in doubt. Most of the trading volume had been in potatoes. Without a good commodity, the traders had trouble making money. Eventually, the new chairman, Michel Marks – the son of commodities icon Francis Q. Marks – along with economist Arnold Safer, figured out that NYMEX could revamp an old heating oil futures contract. When the government deregulated heating oil, the contract had a chance of becoming a good object of trade on the floor. A new futures contract was carefully drawn up and trading began on a tiny scale in 1978. Some of the first users of NYMEX heating oil deliveries were small scale suppliers of people in the Northern United States.

NYMEX's business threatened some entrenched interests like big oil and government groups like OPEC that had traditionally controlled oil prices. NYMEX provided an "open market" and thus transparent pricing for heating oil, and, eventually, crude oil, gasoline, and natural gas. NYMEX's oil futures contracts were standardized for the delivery of West Texas Intermediate light, sweet crude oil to Cushing.

Growth

The energy trading business took off, and NYMEX boomed. The open outcry floor became a cacophony of shouting traders and pit cards. The pits became a place where many people without much education or ability to fit into Wall Street could have a chance at being rich.   Goodman's book tells the stories of many of the personalities that built the exchange in this era.

COMEX (Commodity Exchange, Inc), one of the exchanges that shared 4 World Trade Center with NYMEX, had traditionally looked down on NYMEX for being smaller and for having the toxic reputation from the potato bust. With NYMEX's energy trading boom, it became much larger and wealtheir than COMEX. On August 3, 1994, the NYMEX and COMEX finally merged under the NYMEX name. By the late 1990s, there were more people working on the NYMEX floor than there was space for them. In 1997, the NYMEX moved to a new building on the Southwestern portion of Manhattan, part of a complex called the World Financial Center.

Later history

September 11, 2001 attacks

The NYBOT's original headquarters and trading floor were destroyed in the September 11, 2001 terrorist attacks on the World Trade Center. Several NYMEX people were lost in the tragedy, even though the new NYMEX building itself was mostly undamaged. Despite the area's devastation, the exchange's management and staff quickly had the exchange working.

The WTC/WFC art gallery, long located in the Nymex building, continued showing world and community art until 2012.  The last-ever exhibit there was a solo show by actualist painter Terry Ward.

On February 26, 2003, the New York Board of Trade (NYBOT) signed a lease agreement with the NYMEX to move into its World Financial Center headquarters and trading facility. NYMEX maintained a close relationship with many organizations and people at World Trade Center, and After the attacks, the NYMEX built a $12 million trading floor backup facility outside of New York City with 700 traders' booths, 2,000 telephones, and a backup computer system. This backup was in case of another terrorist attack or natural disaster in Lower Manhattan.

Electronic trading
NYMEX held a virtual monopoly on "open market" oil futures trading (as opposed to the "dark market" or over-the-counter market. However, in the early 2000s the electronically based exchanges started taking away the business of the open outcry markets like NYMEX. Enron's online energy trading system was part of this trend. Jeff Sprecher's Intercontinental Exchange, or ICE, was another example. ICE eventually began trading oil contracts that were extremely similar to NYMEX's, taking away market share almost immediately.

The open outcry NYMEX pit traders had always been against electronic trading because it threatened their income and their lifestyle. The executives at NYMEX felt that electronic trading was the only way to keep the exchange competitive. NYMEX teamed up with the Chicago Mercantile Exchange to use Globex in 2006. The trading pits emptied out as many traders quit. Banks, hedge funds, and huge oil companies stopped making telephone calls to the pits and started trading directly for themselves over screens.

In this period the NYMEX also worked on founding the Dubai Mercantile Exchange in the United Arab Emirates. This was chronicled by Ben Mezrich in his New York Times Best Selling book Rigged which has been optioned for film adaptation by Summit Entertainment.

Sell-off

The final executive management of NYMEX decided to sell it off in pieces, take golden parachute buyouts, and leave. In 2006 NYMEX underwent an initial public offering (IPO) and was listed on the New York Stock Exchange. The executives and exchange members owning seats on the exchange saw their net worth increase by millions of dollars in a few hours - many of the pit traders, who leased their seats instead of owning, did not. Other parts of NYMEX were sold to private equity investors and the Chicago Mercantile Exchange. The CME got ownership of the physical facilities and began scrubbing the NYMEX logo and name off of various artifacts and closed the NYMEX museum. NYMEX eventually became little more than a brand name used by CME. By 2011, NYMEX open outcry trading was relegated for the most part to a small number of people trading options.

In 2009 it was reported that holders of COMEX gold futures contracts experienced problems taking delivery of their metal. Along with chronic delivery delays, some investors received delivery of bars not matching their contract in serial number and weight. The delays could not be easily explained by slow warehouse movements, as the daily reports of these movements showed little activity. Because of these problems, there were concerns that COMEX did not have the gold inventory to back its existing warehouse receipts.

Trading platforms
Pit (open outcry)
Electronic trading (Globex)

Commodities traded

NYMEX Division

Coal
Crude oil
Electricity
Gasoline
Heating oil
Natural gas
Palladium
Platinum
Propane
Uranium

COMEX Division
Aluminum
Copper
Gold
Silver

See also

 Commodity Exchange Act
 Energy law
 New York Cotton Exchange
 List of futures exchanges
 List of traded commodities

References
Notes

Bibliography

External links

 (NYMEX)
 (COMEX)
TradingPitHistory.com, a website to preserve the hand signal language of open outcry trading

Commodity exchanges in the United States
Companies based in New York City
Financial services companies established in 1882
1882 establishments in New York (state)
Futures exchanges
Battery Park City
CME Group

New York Mercantile Exchange


Lanai (or Lānaʻi) is sixth largest of the Hawaiian Islands, in the United States. It is also known as the "Pineapple Island". The island is almost a circle in shape and is 18 miles wide in the longest direction. The land area is 140 sq. miles (367 km2). It is separated from the island of Moloka'i by the Kalohi Channel to the north.

History
Lana'i was first seen by Europeans on 25 February 1779 by Captain Clerke, with HMS Resolution on the James Cook Pacific Ocean trip. Clerke took command of the ship after Capt. Cook was killed at Kealakekua Bay on February 14, and was leaving the islands for the North Pacific.

In 1922, Jim Dole, the president of Dole Pineapple Company, bought the island of Lana'i. He made a large part of it into the world's largest pineapple plantation.

Tourism
Tourism on Lana'i started not long ago. That was when the growing of pineapple was slowly coming to an end in the Islands. On Lana'i, you can be with nature and feel the mood of the Hawaiian countryside. Not like nearby O'ahu, the only town (Lana'i City) is small. It has no traffic or shopping centers. Tourists come mainly to relax.

There are three hotels on Lana'i and several golf courses.

Islands of Hawaii

Lanai


A record chart (sometimes called a music chart) is a way of giving music a rank. The rank comes from the popularity of the music. The Billboard Hot 100 is a popular chart. The information on charts comes from some different sources, like the number of objects sold, the number of times a song was played on radio, the number of times a song or album was downloaded, and other criteria. Charts are sometimes made for a special genre, for example "Top 10 Rock Songs".

Record chart


Doctor of Medicine (MD, from the Latin Medicinæ Doctor meaning "Teacher of Medicine") is a doctoral degree for physicians (medical doctors). The degree is given by medical schools.

It is a professional doctorate / first professional degree (qualifying degree) in some countries, including the United States and Canada. Students need to have completed 90 to 120 credit hours of university level work  (see second entry degree) and in most cases should already have a Bachelors Degree.

In other countries, such as the United Kingdom and Germany, the Doctor of Medicine is an advanced academic research degree similar to a PhD or a higher doctorate.  In Britain, Ireland, and many Commonwealth nations, the qualifying medical degree is the Bachelor of Science in Medicine, Bachelor of Medicine, Bachelor of Surgery (MBBS, BMBS, BM BCh, BM, MB BCh BAO, or MB ChB) and is the same as the M.D. degree in the U.S. system.

In these countries it is illegal to prescribe scrips (prescriptions) and perform operations without the basic degree; also usual is the membership of appropriate medical and/or surgical societies. The societies (such as the British Medical Association) act as a kind of sophisticated trades union for doctors. In the British system, the General Medical Council has legal authority for the medical register of doctors licensed to practice medicine. They can and do hold tribunals to decide whether doctors accused of misdeeds should be struck off the medical register. Therefore, to practice it is necessary not only to hold the medical degree(s), but also to be on the register.

References

Academic degrees

Doctor of Medicine


Àgbájọ'je itosile awujo ti won unfe ohun kanna, sakoso ise ara won, ti won si ni ipaala to pin won niya kuro ni ayika won.

In the social sciences, organizations are the object of analysis for a number of disciplines, such as sociology, economics, political science, psychology, management, and organizational communication. In more specific contexts, particularly for sociologists, the term "institution" may be preferred. The broader analysis of organizations is commonly referred to as organizational studies, organizational behavior or organization analysis. A number of different theories and perspectives exist, some of which are compatible,
 Organization – process-related: an entity is being (re-)organized (organization as task or action).
 Organization – functional: organization as a function of how entities like businesses or state authorities are used (organization as a permanent structure).
 Organization – institutional: an entity is an organization (organization as an actual purposeful structure within a social context)

Itokasi

Àwọn àgbájọ

Àgbájọ


A symphony is a piece of music written for an orchestra to play. It may be quite a long piece. Usually it is divided into parts, usually 3 or 4 parts, which are called movements.

The first movement of a symphony can be a fast movement, often in sonata form. The second movement can be a slow movement. The third movement can be a minuet or scherzo and a trio. The fourth movement may be called "Finale"; it can be in Rondo form or sonata form or a combination of these. There are lots of different ways of writing a symphony, but this is the pattern that was used by Joseph Haydn who is known as the "Father of the Symphony", and many composers since have used his pattern of movements for their symphonies.

Connotations
The word "symphony" comes from the Greek words "sym" (together) and "phone" (sound).

"Symphonic" means "like a symphony". It is often used to describe music which is quite long and develops tunes over a long period.

A large orchestra is often called a "symphony orchestra". This is to distinguish it from a small orchestra called a "chamber orchestra".

Some of the most famous composers of symphonies are Joseph Haydn, Wolfgang Amadeus Mozart, Ludwig van Beethoven, Franz Schubert, Felix Mendelssohn, Robert Schumann, Anton Bruckner, Johannes Brahms, Pyotr Tchaikovsky, Gustav Mahler, Jean Sibelius and Dmitri Shostakovich.

Related pages
Symphonic poem

Musical forms

Symphony


Metastasis is what happens when cancer spreads from its original place to another part of the body.  Cancer cells spread from the original site to other places in the body by traveling through the bloodstream. When the cancer cells stick to a new place in the body, they grow and form another tumor there. Metastasis makes cures more difficult, or in many cases impossible.

Cancer

Metastasis


A witness is someone who sees something happen. They are often used in court to help find the truth. During a trial, the two lawyers will bring in witnesses to help back up their arguments.

In a criminal trial, the prosecution lawyer will often bring in the victim of the crime to say what happened, and anyone else who can prove the accused person did the crime. The defense lawyer will nearly always call up the accused person to explain why they are not guilty, and bring in other witnesses who can prove the accused person is not guilty. Each time a lawyer brings in a witness, the other lawyer will cross examine the witness - they will ask them questions to make sure they are telling the truth.

Witnesses have to swear to tell the truth during the trial. If a witness lies in court, it is known as perjury, which is a crime. A witness can be subpoenad, which means they are required to testify in court. If the witness does not testify when given a subpoena, they can be punished.

Related pages
Notary

Other websites
Witness statements (UK)

Trials
Legal terms

Witness


In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

The polar coordinate system is especially useful in situations where the relationship between two points is most easily expressed with angles and distance; in the more familiar Cartesian or rectangular coordinate system, such a relationship can only be found through trigonometric formulae.

As the coordinate system is two-dimensional, each point is determined by two polar coordinates: the radial coordinate and the angular coordinate. The radial coordinate (usually denoted as ) denotes the point's distance from a central point known as the pole (equivalent to the origin in the Cartesian system). The angular coordinate (also known as the polar angle or the azimuth angle, and usually denoted by θ or ) denotes the positive or anticlockwise (counterclockwise) angle required to reach the point from the 0° ray or polar axis (which is equivalent to the positive x-axis in the Cartesian coordinate plane).

History

The concepts of angle and radius were already used by ancient peoples of the 1st millennium BCE. Hipparchus (190-120 BCE) created a table of chord functions giving the length of the chord for each angle, and there are references to his using polar coordinates in establishing stellar positions.
In On Spirals, Archimedes describes the Archimedean spiral, a function whose radius depends on the angle. The Greek work, however, did not extend to a full coordinate system.

There are various accounts of the introduction of polar coordinates as part of a formal coordinate system. The full history of the subject is described in Harvard professor Julian Lowell Coolidge's Origin of Polar Coordinates. Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-seventeenth century. Saint-Vincent wrote about them privately in 1625 and published his work in 1647, while Cavalieri published his in 1635 with a corrected version appearing in 1653. Cavalieri first used polar coordinates to solve a problem relating to the area within an Archimedean spiral. Blaise Pascal subsequently used polar coordinates to calculate the length of parabolic arcs.

In Method of Fluxions (written 1671, published 1736), Sir Isaac Newton examined the transformations between polar coordinates, which he referred to as the "Seventh Manner; For Spirals", and nine other coordinate systems. In the journal Acta Eruditorum (1691), Jacob Bernoulli used a system with a point on a line, called the pole and polar axis respectively. Coordinates were specified by the distance from the pole and the angle from the polar axis. Bernoulli's work extended to finding the radius of curvature of curves expressed in these coordinates.

The actual term polar coordinates has been attributed to Gregorio Fontana and was used by 18th-century Italian writers. The term appeared in English in George Peacock's 1816 translation of Lacroix's Differential and Integral Calculus. Alexis Clairaut was the first to think of polar coordinates in three dimensions, and Leonhard Euler was the first to actually develop them.

Converting between polar and Cartesian coordinates

The polar coordinates r and φ can be converted to the Cartesian coordinates x and y by using the trigonometric functions sine and cosine:

The Cartesian coordinates x and y can be converted to polar coordinates r and φ with r ≥ 0 and φ in the interval (−, ] by:
 (as in the Pythagorean theorem.

Cylindrical coordinates

Cylindrical coordinates take the same idea that polar coordinates use, but they extend it further. To get a third dimension, each point also has a height above the original coordinate system. Each point is uniquely identified by a distance to the origin, called r here, an angle, called  (phi), and a height above the plane of the coordinate system, called Z in the picture.

Spherical coordinates

The same idea as is used by polar coordinates can also be extended in a different way. Instead of using two distances, and one angle only, it is possible to use one distance only, and two angles, called  and  (theta).

Related pages
 Geographic coordinate system
 Spherical coordinate system

References

Other websites
FooPlot (online function plotter in polar coordinates)
Online conversion tool between polar and Cartesian coordinates

Coordinate systems

Polar coordinate system


Leo J. Powers (April 5, 1909 – July 14, 1967) was a United States Army soldier and a recipient of the United States military's highest decoration—the Medal of Honor—for his actions in World War II during the Battle of Monte Cassino.

Biography
A farmer before the war, Powers joined the Army from Alder Gulch, Montana, on September 17, 1942. By February 3, 1944, was serving as a private first class in the 133rd Infantry Regiment, 34th Infantry Division. On that day, northwest of Cassino, Italy, Powers single-handedly destroyed three German machine gun emplacements. He was awarded the Medal of Honor a year later, on January 15, 1945.

Powers reached the rank of Sergeant before leaving the Army. He died at age 58 and was buried in Holy Cross Cemetery, Butte, Montana.

Medal of Honor citation
Powers' official Medal of Honor citation reads:
For conspicuous gallantry and intrepidity at risk of life above and beyond the call of duty. On 3 February 1944, this soldier's company was assigned the mission of capturing Hill 175, the key enemy strong point northwest of Cassino, Italy. The enemy, estimated to be at least 50 in strength, supported by machineguns emplaced in 3 pillboxes and mortar fire from behind the hill, was able to pin the attackers down and inflict 8 casualties. The company was unable to advance, but Pfc. Powers, a rifleman in 1 of the assault platoons, on his own initiative and in the face of the terrific fire, crawled forward to assault 1 of the enemy pillboxes which he had spotted. Armed with 2 handgrenades and well aware that if the enemy should see him it would mean almost certain death, Pfc. Powers crawled up the hill to within 15 yards of the enemy pillbox. Then standing upright in full view of the enemy gunners in order to throw his grenade into the small opening in the roof, he tossed a grenade into the pillbox. At this close, the grenade entered the pillbox, killed 2 of the occupants and 3 or 4 more fled the position, probably wounded. This enemy gun silenced, the center of the line was able to move forward again, but almost immediately came under machinegun fire from a second enemy pillbox on the left flank. Pfc. Powers, however, had located this pillbox, and crawled toward it with absolutely no cover if the enemy should see him. Raising himself in full view of the enemy gunners about 15 feet from the pillbox, Pfc. Powers threw his grenade into the pillbox, silencing this gun, killing another German and probably wounding 3 or 4 more who fled. Pfc. Powers, still acting on his own initiative, commenced crawling toward the third enemy pillbox in the face of heavy machine-pistol and machinegun fire. Skillfully availing himself of the meager cover and concealment, Pfc. Powers crawled up to within 10 yards of this pillbox fully exposed himself to the enemy gunners, stood upright and tossed the 2 grenades into the small opening in the roof of the pillbox. His grenades killed 2 of the enemy and 4 more, all wounded, came out and surrendered to Pfc. Powers, who was now unarmed. Pfc. Powers had worked his way over the entire company front, and against tremendous odds had single-handedly broken the backbone of this heavily defended and strategic enemy position, and enabled his regiment to advance into the city of Cassino. Pfc. Powers' fighting determination and intrepidity in battle exemplify the highest traditions of the U.S. Armed Forces.

See also

List of Medal of Honor recipients
List of Medal of Honor recipients for World War II

References

Sources

1909 births
1967 deaths
United States Army personnel of World War II
United States Army Medal of Honor recipients
People from Beaverhead County, Montana
United States Army soldiers
People from Custer County, Nebraska
World War II recipients of the Medal of Honor

Leo J. Powers


A movie director is a person who leads the making of a movie (or film). They take care of the artistic things in the movie. They give instructions to the actors and direct the people that work on the movie.

Directors give many of their responsibilities to other members of their movie-making team (called a movie crew).  For example, the person who is responsible for the lighting is told by the director what style of lighting he wants and he then creates the lighting for him. It is common for movie directors to work closely with a movie producer. Movie producers are people who control the non-artistic side of movie making. For example, they control all the money that is used for making the movie.

The amount of control a director has in creating their movie is different for each director. It is most common for directors to have some control, while the rest of the movie-making is controlled by the movie studio, and by the people who pay for making the movie. This was very common for American movies made in the 1930s to 1950s. There are a small number of directors who are given complete control over making their movies. For example, Stanley Kubrick, Jean-Luc Godard, Steven Spielberg and James Cameron all had a great amount of control in making their movie.

Famous directors

References

Movie occupations

Movie director


In Computer science, a Design pattern is an abstract solution to a certain problem. Design patterns are used in object oriented programming. They give a possible solution to a problem of designing software.

Design patterns became popular around the year 1995. They also simplify the language between computer scientists. Ideally, a design pattern should be reusable many times. It is like a brick of a house, it can be used for many different problems. One can also build bridges with bricks, not only houses.

Examples
These examples are actual examples of design patterns as they are in use. They have not been simplified. It is only the language used to describe them that has been made simpler.

Flyweight
The flyweight design pattern is used to minimize the use of many similar objects. In a text-processing system each letter can have some attributes like formatting, typeface, and size. While it would be possible to create a new object for each character in the document and give it these attributes, it is extremely expensive.

Instead it would be better to create one object for each type of formatting and link the letter to that information. That needs a lot fewer objects. The only extra information that would need to be stored is the word or letter's position in the document. All similar letters would use the same object to define font, size, and other properties.

Singleton
Another easy to understand pattern is called Singleton. It is used when there can only be one instance of a given class. That class usually has some static method (e.g. getInstance()) which returns a new instance. It also saves the instance internally. So if it already created the instance, it can simply return it.
 public class Singleton {
   static Object theInstance=null;
   public Object getInstance() {
     if (theInstance==null) {
      theInstance=new Object();}
     return theInstance; }
  }

Computer science

Design pattern


Middle-earth is a fictional fantasy world invented by J. R. R. Tolkien. Several of his books take place there, such as The Hobbit and The Lord of the Rings. It is supposed to be a long gone mythological time of our earth.

Although Middle-earth is only one continent in Tolkien's world, it is often used for the whole fictional world and all stories Tolkien invented for it. Tolkien created and worked on Middle-earth through most of his life, and it is this creation for which he is most famous.

Middle-earth has its own geography, several different species and peoples (elves, dwarves, humans, hobbits), their languages, and a history that spans thousands of years. The stories of Middle-earth are also a kind of 'artificial myth'.

"Middle-earth" is called Endor (or Endóre) and Ennor in the fictional Elvish languages Quenya and Sindarin.

Peoples
The oldest people of Middle-earth are the immortal Elves. Second were the Dwarves. After them came mortal Men. In the Third Age, there appeared another people, the Hobbits. There are also the tree-like Ents.

Chronology
The history of the Middle-earth world is thousands of years long. Sometimes, when big historical events happen, a new Age is begun, which starts counting again with the year 1.

 First Age: The First Age can be divided into the "First Age of the Trees" and the "First Age of the Sun". Saying a year and "First Age" often means a year in the "First Age of the Sun".
 First Age of the Trees: Begins at the creation of the Two Trees. During it are the Awakening of the Elves and the Dwarves. It ends with the destruction of the Two Trees.
 First Age of the Sun (590 years): Begins with the creation of the Sun and Moon, and ends with the War of Wrath, the final imprisonment of Morgoth and the destruction of Beleriand.
 Second Age (S.A., 3441 years): Begins after the end of the War of Wrath. During it is the destruction of Númenor (T.A. 3319). Ends with the defeat of Sauron in the War of the Last Alliance.
 Third Age (T.A., 3021 years): Begins after the Last Alliance defeated Sauron. During it are the events of The Hobbit (T.A. 2941) and the War of the Ring (T.A. 3018-3019). Ends with the destruction of the One Ring and the defeat of Sauron.
 Fourth Age: Follows the defeat of Sauron and the One Ring, but starts officially when the Bearers of the Rings left for the West. During this Age the Elves become less and leave, while the humans become the dominant people of Middle-earth.

Related pages
Middle-earth characters
Middle-earth languages
Middle-earth locations

References

Middle-earth